Practice Questions

Q72.The contrapositive of the statement ''if I am not feeling well, then I will go to the doctor" is (1) if I will go to the doctor, then I am not feeling (2) if I am feeling well, then I will not go to the well. doctor. (3) if I will not go to the doctor, then I am feeling (4) if I will go to the doctor, then I am feeling well. well. ¯

Q73.The statement ∼(p ↔~q) is (1) A tautology (2) A fallacy (3) Equivalent to p ↔q (4) Equivalent to ~p ↔q

Q74.The proposition ∼(p∨∼q)∨∼(p ∨q) is logically equivalent to: (1) p (2) q (3) ∼p (4) ∼q

Q74.Let ¯X and M.D. be the mean and the mean deviation about ¯X of n observations xi, i = 1, 2,n. If each of the observations is increased by 5 , then the new mean and the mean deviation about the new mean, respectively, are : – (1) ¯X , M.D. (2) X + 5, M.D. – (3) ¯X , M.D. +5 (4) X + 5, M.D. +5 JEE Main 2014 (12 Apr Online) JEE Main Previous Year Paper

Q75.The contrapositive of the statement "I go to school if it does not rain" is (1) If it rains, I go to school. (2) If it rains, I do not go to school. (3) If I go to school, it rains. (4) If I do not go to school, it rains.

Q75.A relation on the set A = {x : |x| < 3, x ∈Z}, where Z is the set of integers is defined by R = {(x, y) : y = |x|, x ≠−1}. Then the number of elements in the power set of R is: (1) 32 (2) 16 (3) 8 (4) 64

Q76.The principal value of tan−1(cot 43π4 ) is (1) π 4 (2) −π4 (3) 3π 4 (4) −3π4

Q77.The function f(x) = |sin 4x| + |cos 2x|, is a periodic function with a fundamental period (1) π (2) 2π (3) π (4) π 4 2 f is

Q79.If g is the inverse of a function f and f ′(x) = 1 , then g′(x) is equal to 1+x5 (1) 1 (2) 1 + {g(x)}5 1+{g(x)}5 (3) 1 + x5 (4) 5x4

Q80.If f(x) = x2 −x + 5, x > 21 , and g(x) is its inverse function, then g′(7) equals: (1) −13 (2) 131 (3) 3 1 (4) −113 x , ≠0 1 ) x and g(x) = xf(x) Statement I: f is x

Q81.If the volume of a spherical ball is increasing at the rate of 4π cc / sec then the rate of increase of its radius (in cm / sec), when the volume is 288π cc is (1) 1 (2) 1 9 6 (3) 1 (4) 1 24 36

Q89.If the distance between planes, 4x −2y −4z + 1 = 0 and 4x −2y −4z + d = 0 is 7 , then d is: (1) 41 or −42 (2) 42 or −43 (3) −41 or 43 (4) −42 or 44

Q90.If A and B are two events such that P(A ∪B) = P(A ∩B), then the incorrect statement amongst the following statements is : (1) P(A) + P(B) = 1 (2) P(A ∩B′) = 0 (3) A & B are equally likely (4) P(A′ ∩B) = 0 JEE Main 2014 (09 Apr Online) JEE Main Previous Year Paper

Q63.The sum of the series : (2)2 + 2(4)2 + 3(6)2 + … upto 10 terms is : (1) 11300 (2) 11200 (3) 12100 (4) 12300

Q64.If a1, a2, a3, … , an, … . are in A.P. such that a4 −a7 +a10 = m, then the sum of first 13 terms of this A.P., is : (1) 10 m (2) 12 m (3) 13 m (4) 15 m

Q66.If for positive integers r > 1, n > 2, the coefficients of the (3r)th and (r + 2)th powers of x in the expansion of (1 + x)2n are equal, then n is equal to: (1) 2r + 1 (2) 2r −1 (3) 3r (4) r + 1

Q68.The expression 1−cotA tanA + 1−tanAcotA can be written as : (1) tanA + cotA (2) secA + cosecA (3) sinAcosA + 1 (4) secAcosecA + 1

Q69.If the x-intercept of some line L is double as that of the line, 3x + 4y = 12 and the y-intercept of L is half as that of the same line, then the slope of L is : (1) −3 (2) −3/8 (3) −3/2 (4) −3/16

Q69.If the circle x2 + y2 −6x −8y + (25 −a2) = 0 touches the axis of x, then a equals. (1) 0 (2) ±4 (3) ±2 (4) ±3

Q74.Let p and q be any two logical statements and r : p →(∼p ∨q). If r has a truth value F , then the truth values of p and q are respectively: (1) F, F (2) T, T (3) T, F (4) F, T

Q74.The statement p →(q →p) is equivalent to : (1) p →q (2) p →(p ∨q) (3) p →(p →q) (4) p →(p ∧q)

Q76.All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given ? (1) mode (2) variance (3) mean (4) median

Q76.The mean of a data set consisting of 20 observations is 40 . If one observation 53 was wrongly recorded as 33 , then the correct mean will be: (1) 41 (2) 49 (3) 40.5 (4) 42.5

Q77.Let R = {(3, 3)(5, 5), (9, 9), (12, 12), (5, 12), (3, 9) , (3, 12), (3, 5)} be a relation on the set A = {3, 5, 9, 12} . Then, R is : (1) reflexive, symmetric but not transitive. (2) symmetric, transitive but not reflexive. (3) an equivalence relation. (4) reflexive, transitive but not symmetric. Q78. ⎡3 4 1 ⎤ If p, q, r are 3 real numbers satisfying the matrix equation, [pqr] 3 2 3 = [3 0 1 ] then 2p + q −r ⎣2 0 2 ⎦ equals : (1) −3 (2) −1 (3) 4 (4) 2

Q77.The matrix A2 + 4A −5I , where I is identity matrix and A = [14 −32 ], equals : (1) 2 1 (2) 0 −1 4 4 [2 0 ] [2 2 ] (3) 2 1 (4) 1 1 32 32 [2 0 ] [1 0 ]