1	The value of lo g  10  1 + lo g 10  10 + lo g 10  10... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Special Functions Logarithms
2	A sequence 192, 360, 576……. is formed by multiplying the corresponding terms of two di... CAT Quantitative Ability Algebra Sequences and Series AP, GP
3	Find the value of C0 + C2 + C4 +... in the expansion of (1+x)8. Type in your answer ... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Polynomials Algebraic Identities Binomial Theorem
4	Consider a, b and c in a G.P. such that | a+b+ c |=15 . The median of these three terms is a , and b... CAT Quantitative Ability Algebra Sequences and Series AP, GP
5	Second term of a geometric progression is 1000 and the common ratio is = 1/n, where n is a natural n... CAT Quantitative Ability Algebra Sequences and Series AP, GP
6	The maximum value of ( 3−x ) 3 ( 2−x ) 4  when ( ( 2<x<3 ) ) ... CAT Quantitative Ability Algebra Equations and Polynomials Equations Inequations
7	A quadratic function f( x ) attains a max of 3 at x=1 , the value of the function at x=0 is ... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Graphs of Functions Maxima and Minima
8	How many positive integer values can x take that satisfy the inequality (x - 8) (x - 10) (x - 12)...... CAT Quantitative Ability Algebra Equations and Polynomials Equations Inequations
9	Let a+b+c=1 . Find the minimum value of ( 1 a −1)( 1 b −1)( 1 c −1). Type... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Graphs of Functions Maxima and Minima
10	If the first, third and thirteenth terms of an arithmetic progression are in geometric progression, ... CAT Quantitative Ability Algebra Sequences and Series AP, GP AP
11	The sum of all the real roots of the equation | x−2 | 2 + |  x−2 |&minu... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations
12	What is the minimum value of sum of the squares of  the roots of the equation  x 2 &min... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Graphs of Functions Maxima and Minima
13	x + y = 8 and P=5 x 2  + 11 y 2 , where x, y≥0 . W... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations
14	For graph of f(x)= 1 x−4 , what is the value of x for which f(x) reaches infinity? ... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Special Functions
15	Find the range of p such that one root of the equation x 2 −8x+p lies between 0 and 1. ... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations
16	What is the area enclosed by the curve | x+4 |+| y−2 |=4  (in sq. units)? Type in y... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Special Functions
17	If x is any integer from -6 to 2 inclusive, how many values of x satisfy the following inequation:... CAT Quantitative Ability Algebra Equations and Polynomials Equations Inequations
18	Which of the following inequalities has a solution set that when graphed on the number line, is a si... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations
19	If a and b are roots of equation 3 x 2 +5x+k=0 , a 2  − b 2  =25&nbsp... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations
20	Find the area bounded by the curves 3|-x| = 6 + 2|y| and |y| = 3 (in sq. units) Type in your answer... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Special Functions Modulus Graphs of Functions
21	If α, β be the roots of the quadratic equation x 2  − 5x +&nbsp... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations
22	Every Monday, Marina eats one croissant and every Tuesday she eats two croissants. On each subsequen... CAT Quantitative Ability Algebra Sequences and Series AP, GP
23	If x2– x – 6 < 0,  -x2+ 6x – 5 > 0 and x2– 10x + 16 < 0, then ... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Quadratic Equations Inequations
24	The roots of the equation x 2  −x( a+b )+ab− b 2 =0 (where a & b ar... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations
25	If a, b, and c are odd integers, then the roots of ax2+bx+c = 0 cannot be: A) Ration... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Polynomials Algebraic Identities
26	Find the values of parameter ‘a’ such that the roots α and  β of th... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Quadratic Equations
27	Find a and b such that (x + 1) and (x + 2) are factors of the polynomial x 3 +a ... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Polynomials Operations on Polynomials
28	If log 3 2 , log 3 ( 2 x −5) and log 3 ( 2 x −7/2) are in AP, then fi... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Special Functions Logarithms Sequences and Series AP, GP AP
29	If x and y are positive real numbers such that 12xy +21x+20y=46 , find the minimum value of ... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Graphs of Functions Maxima and Minima
30	Find the value of a for which 4 t −(a−4) 2 t +(9/4)a<0 where ‘t’ be... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Quadratic Equations
31	The real values of 'a' for which the quadratic equation 2x2 – (a3 + 8a -1)x +a2 &ndash... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Applications of Linear and Quadratic Equations
32	Given the value of a1, b1, c1, a2, b2, c2 ≠ 0 and the following 2 linear equations,  can the... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Linear Equations
33	The ratio of the sum to n terms of two APs is (7n+1): (4n+27), then the ratio of their 9th term... CAT Quantitative Ability Algebra Sequences and Series AP, GP
34	Let Sk be the sum of the first k terms of the arithmetic progression t1, t2, ..., tk. If Sm/Sn = m2/... CAT Quantitative Ability Algebra Sequences and Series AP, GP AP
35	If c is positive and 2a x 2 +3bx+5c=0 doesn’t have any real root, then ... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Quadratic Equations
36	If ( 2 + 4 + 6 +... 50 terms ) (1 + 3 +&nbsp... CAT Quantitative Ability Algebra Sequences and Series AP, GP
37	If | y |≥5 and x = −( y 5 )| k | , then which one of the following is n... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Linear Equations Inequations
38	On a fence, there are sparrows and pigeons. When five sparrows leave, there remain two pigeons for e... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations
39	If the difference between roots of the equation x 2 +ax+1=0 is less than 5,then find the set... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Quadratic Equations
40	Find the number of solutions when the following two in-equations are satisfied: y = 6x2 - 13x + 6&nb... CAT Quantitative Ability Algebra Equations and Polynomials Equations Inequations
41	Which of the following graphs represents the quadratic function f(x) = - x2 + 4x -4 ... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Graphs of Functions Identification of Graphs
42	Solve the following set of linear equations in two variables 10/(x  + y) + 2/(x - y) = 4 15/(... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Linear Equations
43	Find the number of non-negative integral solutions of 3x + 10y = 200. Type in your answer as an int... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Linear Equations
44	Find the value of x and y when the solution of the following equations is given by ( 3x-y+1)/3... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Linear Equations
45	A two-digit number is such that it is the product of two distinct perfect squares. The tens digit, u... CAT Quantitative Ability Algebra Sequences and Series AP, GP AP Theory of Numbers Numbers, Properties & Operations
46	Let f(x)=a x 2 +bx+c , where a, b and c are Real numbers, where ‘a’ is not equal to ... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Quadratic Equations
47	Simplify ( 8.73*8.73*8.73 )+( 4.27*4.27*4.27 ) ( 8.73*8.73 )−( 8.73*4.27 )+( 4.27*... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Polynomials Algebraic Identities
48	2x = 4y = 8z and xyz = 288, then the value of 1/2x + 1/4y + 1/8z is ... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Linear Equations
49	The sum of a number x and its reciprocal is 8/15 less than thrice the sum of another number y and th... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Linear Equations
50	How many consistent independent equations are needed to solve for n unknown variables? CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Linear Equations
51	F(x) is a fourth order polynomial with integer coefficients and with no common factor. The root... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Special Functions
52	If α and β  are the roots of the  equation, 2x2 –3x –6 =0... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Quadratic Equations
53	What should be the value of k, for the following equations to be consistent?  5x – 2y = ... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Linear Equations
54	If (x-1)3 is a factor of x4+ax3-bx2+cx-1 = 0, then find the other factor. ... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Polynomials Operations on Polynomials
55	Solve for x: 3 ( x 2 −x) + 4 ( x 2 −x) =25 Type your answer as the sum of roo... CAT Quantitative Ability Algebra
56	If  2x+3y=10 , then the maximum value of x 2 y 3 is ( x, y>0 ) ... CAT Quantitative Ability Algebra Equations and Polynomials Equations Inequations
57	If the roots of 10 x 3 −c x 2 −54x−27=0 are in H.P, then find the value of c :... CAT Quantitative Ability Algebra Sequences and Series AP, GP AP
58	If the sum of four natural numbers in AP is 60 and the sum of their squares is 920, find the smalles... CAT Quantitative Ability Algebra Sequences and Series AP, GP AP
59	For how many values of b is the following set of equations inconsistent 4x + 6y = 14 2x + by = 7 ... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Linear Equations
60	a2n - b2n , for any positive integral values of n, is always divisible by ... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Polynomials Algebraic Identities
61	Solve x4 + 4x3 -12x2 <= 0 CAT Quantitative Ability Algebra Equations and Polynomials Equations Inequations
62	How many pairs of integer (p, q) are possible such that p2 – q2 = 288? ... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Polynomials Operations on Polynomials
63	x4 – px3 + qx2 – rx + 8 = 0 divided by x + 1 leaves a remainder of 3... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Polynomials Operations on Polynomials
64	What is the remainder when the given polynomial p(x) is divided by x? Type in your answer as an i... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Graphs of Functions
65	Aditya has a collection of cube-shaped toys where each of his cubes is of a different size. Before h... CAT Quantitative Ability Algebra Sequences and Series HP and Other Sequences and Series
66	Find the value of x if x= 1 3+ 1 3+ 1 3+ 1 3+....... ... CAT Quantitative Ability Algebra
67	Find the sum to n terms of the series 1 √1+√3 + 1 √3+√5 + 1 &radic... CAT Quantitative Ability Algebra Sequences and Series HP and Other Sequences and Series
68	Find the area bounded by the curves 30 = |10x| - |y| and 20 = |4y| - 5|x| (in sq. units) Type in yo... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Special Functions Modulus Graphs of Functions
69	If three positive real numbers a, b, c are in A.P. such that  abc = 4, then minimum value of b ... CAT Quantitative Ability Algebra Sequences and Series AP, GP AP
70	A quadratic function attains minimum value of –25 at x=1 . If f( 0 )=–24 , what is ... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Graphs of Functions Maxima and Minima
71	An equilateral triangle T2 is formed by joining the mid points of the sides of another equilateral t... CAT Quantitative Ability Algebra Sequences and Series
72	If S = 1 + x + x2+ x3+ --- to infinity, then x = CAT Quantitative Ability Algebra Sequences and Series
73	Find the combined area of the 2 quadrilaterals formed by the intersection of |x| + |5y| = 15 and 7 =... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Special Functions Modulus Graphs of Functions
74	If 1/(b+c), 1/(c+a), 1/(a+b) are in A.P., then what is true about a2,b2,c2? ... CAT Quantitative Ability Algebra Sequences and Series
75	If  a, b and c are in A.P. then a 3 + c 3 −8 b 3 is equal to: ... CAT Quantitative Ability Algebra Sequences and Series AP, GP AP
76	If [x] is the greatest integer function less than or equal to x then ,  [  500 1 5 ... CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Special Functions
77	If x, 2y, and 3z are in A.P.  where, the distinct numbers x, y, z are in G.P., then the common ... CAT Quantitative Ability Algebra Sequences and Series AP, GP AP
78	Find the sum of all the coefficients in the expansion of (x2+2x)20 CAT Quantitative Ability Algebra Equations and Polynomials Polynomials, Functions and Graphs Polynomials Algebraic Identities Binomial Theorem
79	( 1− 1 3 )⋅( 1− 1 4 )⋅...⋅( 1− 1 n ) equals ... CAT Quantitative Ability Algebra Sequences and Series
80	A child tore off one leaf from a book having page number from 1 to N. Summation of the remaining num... CAT Quantitative Ability Algebra Sequences and Series AP, GP Applications of AP and GP
81	A test has twenty questions worth 100 points.  The test consists of True/False questions worth ... CAT Quantitative Ability Algebra Equations and Polynomials Equations Linear and Quadratic Equations Linear Equations
82	If the roots of the equation a x 3 +b x 2 +cx+d=0  are in geometric progression, then whic... CAT Quantitative Ability Algebra Equations and Polynomials Equations