Every question in QA, searchable by chapter and source.
If α & β are roots of the equations x 2 - 2x – 35 = 0, where ( α ≥ β ), then find the value of 2 2 ( ) ( ) α β α β − + (a) 18 (B) 24 (C) 32 (D) 36 2. The set of inequalities 2x + 3y < 9, 5x - y > 3 has _________ region.
The feasible region formed by linear inequalities is always a _________ region.
The system of equations 2x + y = 10 4x + 6y = 36 has solution with x = _____________
If the difference between the annually compounded interest and simple interest on a certain sum of money at 8% per annum for 3 years is ` 788. Then the principle amount is ______________.
What will be the approximate future value of an annuity of ` 1000 made annually for 5 years at interest rate of 7% per annum, compounded annually? (Given (1.07) 5 = 1.40255)
Rakesh requires ` 1,00,000 to buy a scooter after 4 years. What will be the approximate present value of ` 1,00,000 if the interest rate is 10% per annum?
If the first term of a geometric progression exceeds the second term by 4 and the sum of its terms till infinity is 100, then the common ratio is ___________.
The sum of the first n terms of an arithmetic progression (A.P.) is 4n 2 + 3n. The 10 th term of the A.P. is ____________.
If the sum of 4 th and 8 th term of an arithmetic progression (A.P.) is 120, then the 6 th term of the A.P. is ____________.
The sum of infinite terms of the geometric series ... 1 1 1 1- + - +. 5 25 125 will be ____________.
For a given Revenue function R(x) =100x - 2x 2 , the maximum revenue occurs at x = ____________.
Find the next term in the series 11, 12, 14, 17, 22, 30, _____________.
Sharma points to a girl and says, "She is the mother of my son's wife's daughter". What is the relation of the girl with Sharma?
If the mean 40, k, 6k, 4k 2 , 8k-4k 2 is 20, then the value of k is _____________.
The standard deviation is zero only if all the observations assumed by a variable are _____________.
The mean of five observations is 28. Among the five observations, three observations are 10, 23 and 62. The difference between the remaining two observations is 13. Then the remaining two observations are _______.
Which of the followings is a property of Arithmetic Mean?
The probability of getting pass in an examination is x 3 . If the probability of getting fail is 3 2 , then the value of x is ___________.
The mean of 10 observations is 15. If one observation 12 is replaced by 22, what will be the new mean?
If ƒ (x) = kx 2 , 0 ≤ x ≤ 1 is a probability density function of a random variable x, then the value of k is ___________.
In a binomial distribution, the probability of success is 0.7. The variance for n = 15 is ____________.
For a Binomial Distribution with mean = 4 and variance = 3, what are the values of n and p?
The covariance between two variables X and Y is 4. The standard deviation of X is 10 and the correlation coefficient between X and Y is 0.4. Find the standard deviation of Y.
The mean and mean deviation of a normal distribution are 13.5 and 4.8 respectively. Then the third quartile of the normal distribution is _________.
The mean of a binomial distribution is 4 and the variance is 3.2. If p < 0.5, find the value of p.
If 2x + 3y + 2 = 0 is the regression equation of x on y and the arithmetic mean of y is -2, then arithmetic mean of x is _________.
A price index with base 2000 shows: Index for 2010: 140 Index for 2020: 210. What is the index for 2010 when base is shifted to 2020?
Which formula correctly represents Fisher's Price Index?
If Σ p0q0 = 400 and Σ pnq0 = 720 and Paasche's index number is 125, then the Fisher's index number is __________.
The product of two numbers is 7644 and their ratio is 12:13. Then, the smaller of two numbers is __________.
The compound interest for· ` 15,000 at 20% per annum for 2 years compounded semi-annually is __________.
The simple interest at the rate of p% per annum for p years will be ` p. Then, the principal is ____________.
The future value of an annuity of ` 2000 made annually for 8 years at interest rate of 14% per annum, compound annually is _______. (Given that (1.14) 8 = 2.8526)
Ravi deposits some amount in bank for 5 1 2 years at the simple interest rate of 7% per annum. Ravi receives ` 66,480 at the end of term. Compute the amount of initial deposit by Ravi in the Bank.
In how many years will ` 50,000 become ` 75,000 at 8% per annum compound interest? (Given log (1.5) = 0.1761 and log (1.08) = 0.0334)
Relation on integers is defined by: aRb ⇔ a - b is divisible by 5. This relation is __________.
Let the function ƒ : R → R is defined by ƒ (x) = x 2 + 3, then ƒ 1 − (12) is
Find the next term of the series: 7, 8, 18, 57, 232, 1165, ____________.
Six persons A, B, C, D, E, and F are seated at a round table facing outside the centre but not necessarily in the same order. A sits at the immediate right of E. C sits after one person to the right of A. B sits beside A and F sits at the immediate right of D. How many persons are sitting between A & D?
Which of the following statement is true?
The given frequency distribution is: X 1 2 3 4 5 6 7 Y 5 9 12 17 14 10 6 The arithmetic mean of the Frequency distribution is ___________.
What will be the mean deviation for the numbers {2, 4, 7, 8, 9, 12} from the mean?
The arithmetic mean (A.M.) of two positive numbers exceeds their harmonic mean by 30. If their A.M. is 45, Then, their geometric mean will be ___________.
Two groups of students have harmonic means of 50 and 30 for their test scores, with 10 students in the first group and 15 students in the second group. What will be the combined harmonic mean of the two groups?
A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability that the card drawn is either a King or a Heart?
If the standard deviation of a Poisson distribution is 3, then P(X = 0) is _______________.
In a Shooting competition, A hit the target 6 out of 13 shots, and B hit 8 out of 11 shots. If they both try once, what is the probability that the target would be hit at least once?
A bag contains 5 red, 4 blue, and 3 green balls. Two balls are drawn at random without replacement. What is the probability that both balls are of different colours?
For a set of observations on variables x and y, the following summary statistics are given: n = 5, 2 x = 10, y = 25, xy = 70, x = 30 ∑ ∑ ∑ ∑ . The regression equation of y on x is expressed as: y = a +bx. What is the value of the slope b?
The product of the price index and the quantity index are equal to the corresponding value index in __________.
The Spearman's Rank correlation coefficient between Economics and Accountancy marks for a class student 75 99 is and the sum of Square of differences in ranks for Economics and Accountancy marks is 40. What is the number of students in the class?
When the two regression coefficients are given as bxy = 0.6 and byx = 0.9, determine the value of the coefficient of correlation.
A ratio a:b is said to be in its simplest form when:
If a:b = c:d, then a, b, c, d are said to be in proportion; this relationship is generally expressed as which of the following being equal?
If a:b = b:c, then b is called the:
If a:b = c:d, then the relation obtained by adding 1 to both sides (a+b)/b = (c+d)/d is generally known as an application of which rule?
The rule of 'dividendo', applied to a proportion a/b = c/d, yields:
A ratio compounded of two equal ratios, i.e. the ratio a^2:b^2 derived from a:b, is called the:
The sub-duplicate ratio of a:b is defined as:
According to the law of indices, a^m x a^n is equal to:
According to the law of indices, (a^m)^n simplifies to:
By definition of indices, a^0 (for any non-zero base a) is equal to:
a^(-n), where n is a positive integer and a is non-zero, is defined as:
The logarithm of a number N to a given base b (where b > 0, b ≠ 1) is defined as the index x such that:
According to the fundamental laws of logarithms, log(mn), where m and n are positive numbers to the same base, equals:
According to the laws of logarithms, log(m/n), where m and n are positive numbers to the same base, equals:
According to the laws of logarithms, log(m^n), for a positive number m and any real n, equals:
The value of log_b(b), i.e. the logarithm of a positive number to itself as the base, is always equal to:
The value of log_b(1), i.e. the logarithm of 1 to any valid base b, is always equal to:
A logarithm calculated to the base 10 is generally called a:
A logarithm calculated to the base e (the mathematical constant approximately 2.71828) is called a:
If the ratio between two quantities remains constant however both are increased or decreased by the same non-zero factor, this property illustrates that a ratio is fundamentally a comparison of:
If three quantities a, b, c are said to be in 'continued proportion', this means:
The rule of 'alternendo', applied to a/b = c/d, yields which relation?
The 'invertendo' rule, applied to a/b = c/d, yields:
Which of the following best describes 'compound ratio'?
According to the change-of-base rule for logarithms, log_b(N) can be expressed in terms of logarithms to a different base 'a' as:
An equation involving only one variable raised to the first power (degree one) is called a:
An equation of the form ax^2 + bx + c = 0 (a ≠ 0) is generally called a:
The general (quadratic) formula for finding the roots of ax^2 + bx + c = 0 is:
In a quadratic equation ax^2 + bx + c = 0, the expression (b^2 - 4ac) is called the:
For a quadratic equation ax^2 + bx + c = 0, if the discriminant (b^2 - 4ac) is exactly zero, the roots are:
For a quadratic equation ax^2 + bx + c = 0, if the discriminant (b^2 - 4ac) is negative, the roots are:
For a quadratic equation ax^2 + bx + c = 0 (a ≠ 0), the sum of the two roots is given by:
For a quadratic equation ax^2 + bx + c = 0 (a ≠ 0), the product of the two roots is given by:
A system of two (or more) equations that must be satisfied by the same set of values of the unknowns simultaneously is called a system of:
Which of the following methods is commonly used to solve a pair of simultaneous linear equations by eliminating one variable through addition or subtraction?
Which method solves a pair of simultaneous linear equations by expressing one variable in terms of the other from one equation, and substituting that expression into the second equation?
An equation that remains true for every value of the variable(s) involved, rather than for only specific values, is called a(n):
A system of simultaneous linear equations that has no solution satisfying all the equations at once is described as:
A polynomial equation of the third degree, of the general form ax^3 + bx^2 + cx + d = 0 (a ≠ 0), is called a:
According to the Fundamental Theorem of Algebra, a polynomial equation of degree n (with real or complex coefficients) has exactly how many roots, counting multiplicity, in the complex number system?
An equation is said to be in 'standard form' when it is arranged such that:
If one root of a quadratic equation with real coefficients is a complex number (say p + iq), then, by a standard property, the other root must be:
Solving an equation by the method of 'factorisation' generally involves:
An equation containing the variable under a radical (square root) sign, such as √(x+1) = 3, is generally called a:
When solving a radical equation by squaring both sides, it is essential to check the resulting solutions against the original equation, primarily because:
A quadratic equation with real coefficients whose discriminant is a perfect square (and positive) will have roots that are:
An equation containing the variable in the denominator of one or more terms, such as 1/x + 2 = 5, is generally referred to as a:
In solving simultaneous equations by the 'cross-multiplication method' for two linear equations in two variables, the values of the variables are expressed as ratios derived from the coefficients using a specific determinant-like pattern; this method is essentially a shortcut form of:
When a quadratic equation ax^2 + bx + c = 0 has a = 0 (i.e. the coefficient of the squared term vanishes), the equation reduces to:
Which of the following is generally true about the graph of a quadratic equation y = ax^2 + bx + c (a ≠ 0) in two variables?
A statement involving a sign of inequality (such as <, >, ≤, or ≥) between two algebraic expressions is called a(n):
When both sides of a linear inequality are multiplied or divided by the same negative number, the inequality sign must:
When the same positive number is added to, or subtracted from, both sides of an inequality, the direction of the inequality:
The solution set of a linear inequality in one variable, such as x > 3, is generally represented graphically on a number line as:
For a strict inequality such as x > 3 (as opposed to x ≥ 3), the boundary point on a number line is generally represented by:
The solution region of a system of linear inequalities in two variables, when represented graphically, is generally:
In the context of linear programming, the region satisfying all the given constraints (inequalities) simultaneously is called the:
A linear inequality in two variables, such as 2x + 3y ≤ 12, when graphed, divides the coordinate plane into two regions; these regions are generally called:
An inequality of the form ax + b ≤ 0 (or with any of <, >, ≥), where the variable x appears only to the first power, is called a:
Which of the following correctly describes the transitive property applied to inequalities: if a > b and b > c, then:
The solution set of the inequality x^2 ≤ 0 (in real numbers) consists of:
In a system of linear inequalities used to model a linear programming problem, a constraint requiring a variable (such as quantity produced) to be non-negative is generally expressed as:
A 'corner point' (or vertex) of the feasible region in a linear programming problem is significant because, by the Fundamental (Extreme Point) Theorem of linear programming:
If the feasible region of a linear programming problem is unbounded, the objective function:
An inequality that holds true only for a restricted set of values of the variable is called a:
If a feasible region of a linear programming problem is empty (no point satisfies all constraints simultaneously), the problem is described as:
Reversing an inequality by swapping the two sides, e.g. converting 'a > b' to 'b < a', reflects which basic property of inequalities?
An inequality involving the modulus (absolute value) of an expression, such as |x| < 5, is generally solved by converting it into which equivalent form?
An absolute-value inequality of the form |x| > a (for a > 0) is equivalent to which compound statement?
In graphing the solution region for a linear inequality such as 3x + 2y ≤ 6, which of the following is the standard first step?
When the boundary line of an inequality is included in the solution set (as with ≤ or ≥), it is conventionally drawn as a:
If a > 0 and b > 0, and a > b, then it follows (for the reciprocals of a and b) that:
The intersection of the solution sets of two or more linear inequalities, when solved simultaneously, represents:
Which of the following is an example of a 'double' (compound) linear inequality?
In business applications, a linear inequality such as 'total cost ≤ available budget' is typically used to represent a:
Under 'simple interest', the interest for each period is calculated on:
Under 'compound interest', interest for a given period is calculated on:
The general compound-interest formula for the amount A after n periods, given principal P and periodic rate i (as a decimal), is:
The simple-interest formula for the amount A after n periods, given principal P and periodic rate i (as a decimal), is:
'Present value' of a future sum of money refers to:
An 'annuity' is generally defined as:
An annuity in which each payment is made at the END of each period is generally called an:
An annuity in which each payment is made at the BEGINNING of each period is called an:
An annuity that continues indefinitely, with payments never coming to an end, is generally called a:
An annuity in which the first payment is postponed for a certain number of periods after the annuity is set up is called a:
A 'sinking fund' is generally established for the specific purpose of:
'Effective rate of interest' (or effective annual rate) refers to:
The process of finding the present value of a future sum by discounting it back at a given rate is generally called:
'Amortisation' of a loan generally refers to:
The 'nominal rate of interest' generally refers to:
As the frequency of compounding within a year increases (e.g. from annual to monthly to daily), for a given nominal annual rate, the effective annual rate of interest:
The 'present value of an annuity' represents:
'Future value' of a sum of money, or of an annuity, refers to:
The concept that a given sum of money available today is worth more than the same nominal sum receivable at a future date is generally referred to as the:
In calculating equal periodic instalments (EMIs) to repay a loan of a given principal over a fixed number of periods at a given rate, the underlying mathematical concept applied is that the:
When interest is said to be 'compounded continuously', the compounding is assumed to occur:
Which of the following best distinguishes 'simple interest' from 'compound interest' over multiple periods (assuming the same principal and rate)?
'Depreciation' calculated by applying a fixed percentage rate to the reducing (written-down) balance of an asset each period follows the same underlying mathematical pattern as:
A 'valuation of a bond' using the present-value approach discounts:
If the number of compounding periods per year for a given nominal rate is doubled (e.g. from annual to semi-annual compounding), the periodic interest rate applied in each compounding period is generally:
A 'permutation' of a set of objects refers to:
A 'combination' of a set of objects refers to:
The formula for the number of permutations of n distinct objects taken r at a time (nPr) is:
The formula for the number of combinations of n distinct objects taken r at a time (nCr) is:
By definition, 0! (zero factorial) is equal to:
n! (n factorial), for a positive integer n, is defined as the product of:
The relationship between nPr and nCr, for the same n and r, is given by:
By a standard identity of combinations, nCr is always equal to:
According to the 'Fundamental Principle of Counting' (multiplication principle), if one task can be done in m ways and, independently, a second task can be done in n ways, the two tasks together can be done in:
According to the 'Addition Principle' of counting, if a first task can be done in m ways and an alternative, mutually exclusive second task can be done in n ways, then either task can be accomplished in:
The number of ways in which n distinct objects can be arranged in a straight line, taking all of them at a time, is:
The number of ways to arrange n distinct objects in a circle (where only relative order matters, and rotations of the same arrangement are considered identical) is generally given by:
When arranging n objects, of which p are identical of one kind, q are identical of a second kind, and the rest are distinct, the number of distinct permutations of all n objects is given by:
The number of ways to select r objects out of n distinct objects, where repetition of an object is not allowed, is given by:
If repetition is allowed, the number of ways to arrange r positions where each position can independently be filled by any one of n distinct items is:
nC0 (the number of ways to choose 0 objects out of n) is always equal to:
nCn (the number of ways to choose all n objects out of a set of n) is always equal to:
Pascal's Triangle, in the context of combinations, is used to display the values of:
The standard recurrence relation connecting binomial coefficients, known from Pascal's rule, is:
A permutation problem in which certain specified objects must always occupy specified positions (or always appear together) is generally solved by:
The number of diagonals that can be drawn in a polygon of n sides can be derived using combinations, since it equals the number of ways to choose 2 vertices out of n, minus the number of sides; this reflects an application of:
When forming a committee of r members selected from a group of n people, where the members have no distinct roles (all are equivalent 'committee members'), the correct count to use is:
If, however, a committee of r members from a group of n is to be formed with each member assigned a distinct designated role (e.g. Chairperson, Secretary, Treasurer), the correct count to use is:
The total number of subsets (including the empty set and the full set itself) that can be formed from a set of n distinct elements is:
When some of the n objects being arranged are alike (not all distinct), the number of DISTINCT permutations taken all at a time will, compared to arranging n fully distinct objects, generally be:
A 'sequence' in mathematics refers to:
A 'series' is generally obtained from a sequence by:
An 'Arithmetic Progression' (AP) is a sequence in which:
The n-th term of an Arithmetic Progression with first term a and common difference d is given by:
The sum of the first n terms of an Arithmetic Progression, with first term a and common difference d, is given by:
A 'Geometric Progression' (GP) is a sequence in which:
The n-th term of a Geometric Progression with first term a and common ratio r is given by:
The sum of the first n terms of a Geometric Progression (with common ratio r ≠ 1) is given by:
The sum to infinity of a Geometric Progression exists (converges to a finite value) only when the common ratio r satisfies:
The formula for the sum to infinity of a Geometric Progression (when it exists) is:
If three quantities a, b, c are in Arithmetic Progression, then b (the middle term) is called the:
If three quantities a, b, c are in Geometric Progression, then b (the middle term) is called the:
A sequence in which the reciprocals of the terms form an Arithmetic Progression is called a:
In an Arithmetic Progression, if the common difference d is negative, the sequence is generally described as:
For a Geometric Progression, if the common ratio r is negative, the terms of the sequence will:
The sum of the first n natural numbers (1 + 2 + 3 + ... + n) is given by the standard formula:
The sum of the squares of the first n natural numbers (1^2 + 2^2 + ... + n^2) is given by the standard formula:
The sum of the cubes of the first n natural numbers (1^3 + 2^3 + ... + n^3) is given by the standard formula:
Adding a fixed constant k to every term of an existing Arithmetic Progression results in:
Multiplying every term of an existing Geometric Progression by a fixed non-zero constant k results in:
A sequence in which each term (after the first two) is the sum of the two preceding terms is a well-known example of which type of sequence, distinct from a standard AP or GP?
For an Arithmetic Progression, if the number of terms n is odd, the middle term of the AP can be found at position:
An 'Arithmetico-Geometric Series' is generally understood as a series formed by multiplying corresponding terms of:
Given an AP with first term a and common difference d, if all the terms are known to be positive and d > 0, then as n increases, the terms of the sequence:
In business applications, a quantity that grows by a fixed PERCENTAGE each period (such as an amount compounding at a constant periodic rate) is best modelled by which type of progression?
A 'set', in mathematics, is defined as:
A set containing no elements at all is called the:
The set of all elements under consideration in a particular context, of which every other set being discussed is a subset, is called the:
Set A is said to be a 'subset' of set B if:
The 'union' of two sets A and B (A ∪ B) consists of:
The 'intersection' of two sets A and B (A ∩ B) consists of:
The 'complement' of a set A (with respect to a universal set U), denoted A' (or Ac), consists of:
Two sets A and B are said to be 'disjoint' if:
The number of elements in a finite set A is generally denoted, and referred to, as the:
According to the general formula for the union of two finite sets, n(A ∪ B) equals:
The 'power set' of a set A refers to:
A 'relation' from a set A to a set B is generally defined as:
A 'function' from a set A (the domain) to a set B (the codomain) is a special type of relation in which:
The set of all possible input values for which a function is defined is called the function's:
The set of all actual output values that a function produces, as its input varies over the domain, is called the function's:
A function in which every element of the range corresponds to exactly one element of the domain (no two different inputs give the same output) is called:
A function in which every element of the codomain is the image of at least one element of the domain is called:
A function that is both one-to-one (injective) and onto (surjective) is called a:
The 'limit' of a function f(x) as x approaches a particular value a describes:
A function f(x) is said to be 'continuous' at a point x = a if, among other conditions, the limit of f(x) as x approaches a exists and:
If a function is 'discontinuous' at a particular point, this generally means:
A function f(x) = c, where c is a fixed constant for every value of x, is called a:
The Cartesian product A x B of two sets A and B consists of:
According to De Morgan's Laws for sets, the complement of the union of two sets A and B, i.e. (A ∪ B)', is equal to:
Which of the following best describes an 'identity function' on a set A?
The 'derivative' of a function f(x) at a point is generally understood as representing:
Differentiation is generally described as the mathematical process of finding a function's:
According to the power rule of differentiation, the derivative of x^n (with respect to x) is:
The derivative of a constant (a fixed number, unrelated to the variable) is always:
In economics, 'marginal cost' is generally defined, using calculus, as:
'Marginal revenue', in economics, is generally defined, using calculus, as:
To find the point(s) at which a function attains a local maximum or minimum value, the standard first step in calculus is to:
At a point where a function attains a local maximum, the second derivative of the function is generally:
At a point where a function attains a local minimum, the second derivative of the function is generally:
'Integration', as the reverse process of differentiation, is generally used in applications to find:
Given a marginal cost function, the corresponding TOTAL cost function can generally be recovered by:
According to the standard power rule of integration, the indefinite integral of x^n (for n ≠ -1) is:
The 'constant of integration' (usually denoted C) appears in an indefinite integral because:
A 'definite integral', as distinguished from an indefinite integral, is evaluated:
In economics, if the total revenue function is R(x), the point where marginal revenue equals zero generally corresponds to:
Profit is typically maximised, in a standard calculus-based economic model, at the output level where:
The chain rule of differentiation is applied when differentiating:
According to the product rule of differentiation, the derivative of the product of two functions u(x) and v(x) is given by:
According to the quotient rule of differentiation, the derivative of u(x)/v(x) (for v(x) ≠ 0) is given by:
'Elasticity' in economics, when derived using calculus, is generally expressed as a measure of:
When a function has a derivative that is positive throughout an interval, the function is said to be:
When a function has a derivative that is negative throughout an interval, the function is said to be:
The point on a total cost curve at which marginal cost equals average cost typically corresponds to:
Given a demand function expressing price as a function of quantity, 'consumer's surplus' at a given price is generally calculated, using integral calculus, as:
Which of the following best describes the relationship between differentiation and integration, as expressed by the Fundamental Theorem of Calculus?
In a 'number series' reasoning question, the primary task is generally to:
A number series in which each term increases by a constant amount (e.g. 3, 7, 11, 15, ...) follows a pattern most similar to which type of progression?
A number series in which each term is obtained by multiplying the previous term by a constant factor (e.g. 2, 6, 18, 54, ...) follows a pattern most similar to which type of progression?
In 'coding-decoding' reasoning problems, a 'code' generally refers to:
'Letter coding', a common type of coding-decoding problem, typically involves:
In an 'odd man out' (or 'odd one out') reasoning question, the task is to identify:
In an odd-man-out set such as {Apple, Banana, Carrot, Mango}, the item that does not belong is 'Carrot', because:
When solving a coding problem where 'CAT' is coded as 'DBU' (each letter shifted forward by one position in the alphabet), the same rule applied to 'DOG' would yield:
A number series such as 2, 4, 8, 16, 32, ... follows which underlying rule?
A number series such as 1, 4, 9, 16, 25, ... follows which underlying rule?
A common variant of number series problems involves alternating operations, such as 1, 2, 4, 7, 11, 16, ..., where the DIFFERENCE between consecutive terms itself follows a pattern; in this example, the differences (1, 2, 3, 4, 5, ...) form:
In coding-decoding problems, a code that assigns each letter of the alphabet its corresponding reverse-order position (A↔Z, B↔Y, C↔X, and so on) is generally called a:
An 'odd man out' question involving the set {Square, Triangle, Circle, Sphere} would typically identify 'Sphere' as the odd one, because:
In a coding scheme where numbers are substituted for letters based on their position in the alphabet (A=1, B=2, C=3, ...), the word 'BAD' would be coded as:
Which of the following number series follows a pattern of alternating addition and multiplication (e.g. +1, x2, +1, x2, ...)?
In odd-man-out questions based on numerical properties, in the set {9, 16, 25, 30, 49}, the odd one out would generally be identified as:
A key skill tested by coding-decoding questions is the ability to:
In a number series where terms are 3, 9, 27, 81, ..., the next term in the series would be found by:
A coding scheme in which each letter is replaced by the letter a fixed number of positions LATER in the alphabet (wrapping around from Z back to A if necessary) is known generically as a:
For the odd-man-out set {Doctor, Teacher, Engineer, Hospital}, the item that does not belong is 'Hospital', because:
In a number series puzzle, if the pattern involves the sum of the two preceding terms to generate the next (as in 2, 3, 5, 8, 13, ...), this reflects the same logic as the:
When decoding a message encrypted with a known consistent code, the general strategy is to:
In the odd-man-out set {2, 3, 5, 7, 9}, the item that does not belong is generally identified as:
A number series with a repeating cyclic pattern, such as 1, 2, 3, 1, 2, 3, 1, 2, 3, ..., is best described as:
Reasoning-based number series and coding-decoding questions, as a category, primarily assess a candidate's:
In 'direction sense' reasoning problems, the four main (cardinal) directions are generally taken as:
On a standard compass/map orientation used in direction reasoning, if North is at the top, East is generally shown to the:
If a person is facing North and turns 90 degrees clockwise, they will now be facing:
If a person is facing North and turns 90 degrees anticlockwise, they will now be facing:
If a person is facing East and turns 180 degrees, they will now be facing:
The direction exactly opposite to North-East is:
If a person walks 5 km North and then 5 km East, their shortest (straight-line) distance from the starting point can be found using:
In direction sense problems, if a person's final position is determined to be in the same direction and distance as where they started, this means they have effectively:
The direction midway between North and East, at a 45-degree angle from each, is called:
If a person is facing South and turns 90 degrees clockwise, they will now be facing:
When solving a multi-step direction problem, the generally recommended approach is to:
If a person walks 3 km East, then 4 km North, their straight-line displacement from the start is:
'Left' and 'Right' turns in a direction-sense problem are relative to:
If Point B is to the North of Point A, and Point C is to the East of Point B, then Point C is located, relative to Point A, generally in the:
A full 360-degree turn (a complete rotation) always results in a person facing:
In direction reasoning, three consecutive 90-degree clockwise turns are equivalent, in net effect, to a single:
If a person is facing West and turns 45 degrees clockwise, they will now be facing:
When two people start at the same point and walk in exactly opposite directions for the same distance, the straight-line distance between them at the end is:
A shadow-based direction question (e.g. 'in the morning, a person's shadow falls to their left') relies on the general premise that the sun rises in the:
If, in the evening, a person's shadow falls exactly behind them and they are told they are facing the setting sun, they must be facing which direction (since the sun sets in the West)?
In direction problems, 'net distance travelled' (straight-line displacement) as distinguished from 'total distance walked', refers to:
If a person turns 90 degrees clockwise twice in succession, the net effect is the same as a single turn of:
South-West lies exactly midway between which two main cardinal directions?
A well-drawn direction-sense diagram is generally most useful for avoiding which common type of error?
In 'seating arrangement' reasoning problems, participants are typically arranged around a table or in a row/line, and the task is generally to:
In a 'circular' seating arrangement where all participants face the centre of the table, if person A is sitting to the immediate right of person B, then, from B's perspective:
In a circular arrangement with all participants facing OUTWARD (away from the centre), the concepts of left and right, relative to a fixed external observer, are generally:
In a straight 'linear' row arrangement (as opposed to circular), if person P is sitting at one extreme end of the row, this means:
If a row has an odd number of seats and no seat is vacant, the single 'middle' seat of the row is located at position:
When a seating-arrangement clue states 'X sits second to the left of Y' (in a circular, centre-facing arrangement), this generally means there is/are:
A key first step recommended for solving a complex seating arrangement puzzle with multiple clues is to:
In seating arrangement problems, a clue such as 'exactly two people sit between A and B' establishes:
In a rectangular table arrangement where some people sit along the longer sides and others at the shorter ends, participants seated at the ends generally:
When a seating puzzle states that 'no two arrangements described so far are unique' (i.e. more than one valid arrangement satisfies all given clues so far), this indicates that:
In a circular arrangement, the total number of distinct positions relative to one another remains the same regardless of which participant is used as the reference starting point, because:
If it is given that 'D sits immediately between C and E', this means:
A seating arrangement clue phrased as 'A does not sit next to B' is an example of a:
In seating arrangement puzzles involving people facing a certain direction (e.g. some participants facing North, others facing South around a table), correctly tracking each person's 'left' and 'right' requires accounting for:
When solving a seating puzzle with several clues, a clue that directly contradicts a previously deduced fact indicates:
'Linear arrangement facing each other' (e.g. two rows of people seated opposite one another) problems require tracking, in addition to left-right position within a row, which additional relationship?
A seating arrangement clue stating 'exactly one person sits between P and Q, but they are not on the immediate left/right of each other' is an example of what kind of clue combination?
When an arrangement problem specifies that a certain number of seats remain VACANT, solvers must additionally account for:
Seating-arrangement reasoning questions, as a category within Quantitative Aptitude's Logical Reasoning section, primarily test a candidate's ability to:
In a circular seating arrangement, if the total number of people is even and they are evenly spaced, the person sitting diametrically opposite a given individual is located:
A clue stating 'A is third to the right of B' in a circular, centre-facing arrangement means:
When two people are described as sitting 'facing each other' across a rectangular or circular table, this generally implies:
In solving a seating puzzle, if a clue can be satisfied in exactly one way while all other clues remain open to multiple possibilities, the recommended strategy is to:
If a row-based arrangement states 'exactly three people sit to the left of M', and the row has a known total number of people, this clue helps determine:
A seating-arrangement puzzle is generally considered 'solvable' (uniquely determined) once:
In 'blood relations' reasoning problems, the primary task is generally to:
If A is the father of B, and B is the father of C, then, relative to A, C is A's:
If A is the sister of B, and B is the father of C, then, relative to C, A is C's:
If A is the brother of B, and B is the mother of C, then, relative to C, A is C's:
If A is the son of B, and B is the sister of C, then, relative to C, A is C's:
'Pointing to a photograph, a man said, He is the son of my father's son' -- assuming the speaker has no other sons, the person in the photograph is the speaker's:
If A's mother is the only daughter of B, then B is A's:
If P is Q's husband's sister, then, relative to Q, P is Q's:
If A is the daughter of B's brother, then, relative to B, A is B's:
'X introduced Y as the daughter of the only brother of his father' -- Y is related to X's father as X's father's:
Two people, A and B, are described as having the 'same mother, but different fathers' -- A and B are therefore best described as:
If A's father is B, and C's father is also B, and A is not the same person as C, then A and C are most directly related as:
If A is B's father's only son, and B is not male, then A is related to B as B's:
'M is the son of P. P and Q are the only children of R. Q has no children.' Based on this, R is related to M as M's:
If A is the wife of B's son, then, relative to B, A is B's:
'Introducing a man, a woman said, His wife is the only daughter of my father' -- the man is related to the woman as her:
If A is the mother of B, and B is the sister of C, then, relative to C, A is C's:
'Pointing to a woman in a photograph, a man says, She is the daughter of my grandfather's only son' -- assuming the man's father is an only child, the woman is the man's:
If A is B's spouse, and B is C's parent, then A is related to C as C's:
When solving a multi-generational blood relations puzzle, the generally recommended technique is to:
If A is C's maternal uncle, this means A is specifically related to C through C's:
If A is B's daughter, and B is C's husband, then A is related to C (assuming A is also C's biological or step-child) as C's:
'Q is R's brother. S is R's mother. T is S's father.' Based on this chain, T is related to Q as Q's:
Blood relations reasoning questions, as a category, primarily test a candidate's ability to:
If A and B are described as 'twins', this specific relationship additionally implies, beyond being ordinary siblings, that they:
'Statistics', in the sense relevant to data analysis, is generally understood as the branch of knowledge concerned with:
'Primary data' refers to data that is:
'Secondary data' refers to data that:
A 'variable' in statistics refers to a characteristic that:
A variable that can take only specific, distinct (countable) values, such as the number of children in a family, is called a:
A variable that can take any value within a given range (including fractional/decimal values), such as height or weight, is called a:
When raw statistical data is organised into a table showing the frequency (count) of observations falling into each of several classes or categories, this is called a:
The difference between the upper and lower boundaries of a class in a frequency distribution is called the:
The mid-point of a class in a frequency distribution, obtained by averaging its lower and upper boundaries, is called the:
'Cumulative frequency' of a class refers to:
A graphical representation of a frequency distribution using adjacent, connected vertical bars (with no gaps between them, for continuous data) is called a:
A graph obtained by plotting cumulative frequencies against the corresponding class boundaries, and joining the points with a smooth curve, is called an:
A circular graph divided into sectors, where each sector's area (angle) is proportional to the value/frequency it represents, is called a:
A 'frequency polygon' is generally constructed by:
'Classification' of data refers to the process of:
'Tabulation' of data refers to:
An 'inclusive' class interval, such as 10-19, 20-29, is one where:
An 'exclusive' class interval, such as 10-20, 20-30, is one where:
'Qualitative' data (as opposed to quantitative data) refers to data describing a characteristic that:
A 'sample', in statistical terminology, refers to:
The entire group of individuals or items about which statistical information is sought is called the:
The 'range' of a frequency distribution's classes, in terms of how the classes are constructed, is generally determined by:
A 'bivariate' frequency distribution, as distinguished from a univariate one, involves:
'Editing' of collected raw data, as a stage of statistical investigation, primarily involves:
Presenting statistical data in a well-organised, visually accessible manner (through tables, charts, or diagrams) primarily serves the purpose of:
A 'measure of central tendency' is a single value intended to:
The 'Arithmetic Mean' of a set of n observations is calculated as:
The 'Median' of a data set refers to:
The 'Mode' of a data set refers to:
When a data set has an even number of observations, the Median is generally calculated as:
A data set is described as 'bimodal' when it has:
'Dispersion' (or variability), as a statistical concept, refers to:
'Range', as a simple measure of dispersion, is calculated as:
'Quartile Deviation' (semi-interquartile range) is calculated using which two specific values of a data set?
'Mean Deviation' of a data set is calculated as the average of the:
'Standard Deviation' is generally regarded as the most widely used and reliable measure of dispersion because it is based on:
'Variance' of a data set is defined as:
The 'Coefficient of Variation' (CV) is generally used to:
A measure of dispersion is generally considered 'absolute' (as opposed to 'relative') when it is:
For a symmetric (non-skewed) distribution, the Mean, Median, and Mode are generally expected to:
A well-known empirical relationship for moderately skewed distributions relates the Mean, Median, and Mode approximately as:
Which of the following is a key drawback of using 'Range' as a measure of dispersion?
Which measure of central tendency is generally considered LEAST affected by extreme values (outliers) in a data set?
The 'Weighted Arithmetic Mean' differs from a simple Arithmetic Mean in that it:
For grouped (classified) data presented as a frequency distribution, the Arithmetic Mean is generally calculated using:
A key property of the Arithmetic Mean is that the sum of the deviations of all observations from the mean, taken with their proper algebraic sign (positive/negative), is always equal to:
Standard Deviation is always a:
If every observation in a data set is increased by the same fixed constant, the Standard Deviation of the data set:
If every observation in a data set is multiplied by the same constant k (k > 0), the Standard Deviation of the resulting data set is:
Which of the following best explains why 'Standard Deviation' is generally preferred over 'Mean Deviation' for advanced statistical analysis?
'Probability' is generally defined as a numerical measure of:
The probability of an event that is certain to occur is:
The probability of an impossible event (one that can never occur) is:
The probability of any event E always lies within which range?
According to the 'classical' (a priori) definition of probability, if an experiment has n equally likely outcomes, and an event E is favoured by m of those outcomes, the probability of E is defined as:
Two events are said to be 'mutually exclusive' if:
For two mutually exclusive events A and B, the Addition Theorem of probability states that P(A or B) equals:
For two events A and B that are NOT necessarily mutually exclusive, the general Addition Theorem of probability states that P(A or B) equals:
Two events are said to be 'independent' if:
For two independent events A and B, the Multiplication Theorem of probability states that P(A and B) equals:
'Conditional probability', denoted P(A|B), refers to:
For two dependent events A and B, the general Multiplication Theorem states that P(A and B) equals:
The 'complement' of an event A, denoted A' (or 'not A'), consists of all outcomes:
The probability of the complement of event A, P(A'), is related to P(A) by the formula:
The complete set of all possible outcomes of a random experiment is called the:
Bayes' Theorem is primarily used to:
When two events A and B are mutually exclusive, they are generally:
In probability theory, an 'event' refers to:
'Exhaustive events' in a sample space refer to a set of events such that:
When rolling a single fair six-sided die, the probability of obtaining an even number (2, 4, or 6) is:
'Odds in favour' of an event, as a way of expressing likelihood distinct from probability, is generally expressed as the ratio of:
If the probability of an event A is P(A) = 0.3, then, by the complement rule, the probability that A does NOT occur is:
An 'experiment' whose outcome cannot be predicted with certainty in advance, though all its possible outcomes are known, is called a:
The 'empirical' (relative frequency) approach to probability estimates the probability of an event based on:
Which of the following areas is a well-recognised practical application of probability theory in business and finance?
A 'theoretical probability distribution' refers to:
A 'random variable' is generally defined as:
A random variable that can take only specific, countable values (such as 0, 1, 2, 3, ...) is called a:
The 'Binomial Distribution' is a discrete probability distribution that applies to a fixed number of independent trials, each having:
For a Binomial Distribution with n trials and probability of success p, the probability of exactly r successes is given by:
The mean (expected value) of a Binomial Distribution with n trials and probability of success p is given by:
The variance of a Binomial Distribution with n trials and probability of success p is given by:
The 'Poisson Distribution' is generally used to model the number of occurrences of a rare event over:
A distinguishing property of the Poisson Distribution is that its mean and variance are:
The 'Normal Distribution' is a continuous probability distribution characterised by a symmetric, bell-shaped curve, generally described by two parameters:
In a Normal Distribution, the Mean, Median, and Mode are:
Under the empirical rule for a Normal Distribution, approximately what percentage of observations fall within one standard deviation of the mean (μ ± 1σ)?
The 'Standard Normal Distribution' is a special case of the Normal Distribution with:
Converting a value X from any Normal Distribution to the Standard Normal Distribution is done using the transformation Z = :
The graph of a Normal Distribution curve is:
Which of the following is an essential condition (assumption) for a Binomial experiment, in addition to having a fixed number of trials?
As the number of trials (n) in a Binomial Distribution becomes very large, with the probability of success (p) small, the Binomial Distribution can generally be approximated by:
A 'discrete' probability distribution, such as the Binomial or Poisson, differs from a 'continuous' distribution, such as the Normal, primarily in that:
The 'Expected Value' (mean) of a discrete random variable X, taking values x1, x2, ..., xn with respective probabilities p1, p2, ..., pn, is calculated as:
In a Normal Distribution, the total area under the entire curve (representing total probability) always equals:
For a Poisson Distribution with parameter λ, the probability of exactly r occurrences is given by the formula:
'Skewness' of a probability distribution refers to:
Which of the following real-world scenarios is most appropriately modelled using the Binomial Distribution?
Which of the following real-world scenarios is most appropriately modelled using the Poisson Distribution?
Theoretical probability distributions such as the Binomial, Poisson, and Normal are widely used in business primarily because they allow:
'Correlation' between two variables refers to:
When two variables move in the SAME direction (as one increases, the other also tends to increase), the correlation between them is described as:
When two variables move in OPPOSITE directions (as one increases, the other tends to decrease), the correlation between them is described as:
The 'Karl Pearson Coefficient of Correlation' (r) always takes a value within which range?
A Karl Pearson correlation coefficient of exactly +1 indicates:
A correlation coefficient of exactly 0 (zero) generally indicates:
An important caution in interpreting correlation is that a high correlation coefficient between two variables:
'Spurious correlation' refers to a situation where:
'Regression analysis', as distinguished from correlation, is generally used to:
In a simple linear regression equation of the form Y = a + bX, the coefficient 'b' is generally called the:
There are generally two regression lines that can be fitted between two variables X and Y; these are known as:
The two regression lines (Y on X, and X on Y) intersect at a point corresponding to:
The relationship between the Karl Pearson correlation coefficient (r) and the two regression coefficients (byx and bxy) is given by:
If the two regression coefficients (byx and bxy) both have the same sign, that shared sign will also be the sign of:
The 'Method of Least Squares' used to fit a regression line is based on the principle of minimising the:
'Rank correlation' (such as Spearman's method) is generally used instead of Karl Pearson's method when:
Spearman's Rank Correlation Coefficient also lies within which standard range, just like Karl Pearson's coefficient?
'Scatter diagram' (or scatter plot), used as a preliminary tool in correlation analysis, is a graph that:
If a scatter diagram shows points clustering tightly around an upward-sloping straight line, this visually suggests:
'Coefficient of Determination' (r²) is generally interpreted as:
'Multiple regression', as distinguished from 'simple regression', involves:
In business forecasting, regression analysis is commonly applied to relationships such as:
A correlation coefficient close to zero, but a scatter diagram showing a clear U-shaped (curved, non-linear) pattern between two variables, illustrates that:
An 'Index Number' is generally defined as a statistical measure designed to show:
The 'base period' (or base year) in the construction of an index number refers to:
A 'Price Index Number' is specifically designed to measure the relative change in:
A 'Quantity Index Number' is specifically designed to measure the relative change in:
'Laspeyres' Price Index' uses the quantities of which period as weights in its calculation?
'Paasche's Price Index' uses the quantities of which period as weights in its calculation?
'Fisher's Ideal Index' is generally calculated as:
A 'Simple Aggregative' price index is calculated by:
A key limitation of the Simple Aggregative price index method is that it:
A 'weighted' index number, as distinguished from a simple (unweighted) index, assigns to each item:
A 'Consumer Price Index' (CPI) is primarily designed to measure changes in:
Index numbers are frequently described as an 'economic barometer' because they:
'Time Reversal Test', one of the recognised tests of adequacy for an index number formula, requires that:
'Factor Reversal Test', another recognised test of adequacy for an index number formula, requires that the product of a Price Index and the corresponding Quantity Index (with the roles of price and quantity data interchanged appropriately) should equal:
'Chain-based' index numbers, as distinguished from 'fixed-base' index numbers, calculate each period's index relative to:
'Deflating' a nominal economic value (such as nominal income or nominal GDP) using a price index is done in order to:
'Wholesale Price Index' (WPI), as distinguished from the Consumer Price Index (CPI), primarily measures price changes at the level of:
An index number can, in principle, be constructed to measure the relative change over time in a wide variety of variables beyond just prices, such as:
A 'price relative' for a single item is calculated as:
In constructing a weighted index number, the 'weights' assigned to different items are commonly based on:
Which of the following is a recognised practical difficulty (limitation) in the construction of index numbers?
An index number showing a value of 120 for a given period (with base period = 100) indicates that the measured variable has:
A 'Cost of Living Index' (or Consumer Price Index) is commonly used by employers and governments for purposes such as:
Index numbers, as a statistical tool, are best described as measuring: