Practice Questions

Q75.If both the mean and the standard deviation of 50 observations 𝑥1, 𝑥2, … , 𝑥50 are equal to 16, then the mean of 𝑥1 - 42, 𝑥2 - 42, … , 𝑥50 - 42 is (1) 525 (2) 480 (3) 400 (4) 380

Q75.The mean and the median of the following ten numbers in increasing order 10, 22, 26, 29, 34, x, 42, 67, 70, y are 42 and 35 respectively, then xy is equal to: (1) 9 (2) 7 4 3 (3) 7 (4) 8 2 3

Q76.If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is : (1) 30 (2) 51 (3) 50 (4) 31 Q77. ⎡ 1 0 0⎤ 5 q21+q31 Let P = 3 1 0 and Q = [qij] be two 3 × 3 matrices such that Q −P = I3 . Then q32 is equal to : ⎣ 9 3 1⎦ (1) 10 (2) 9 (3) 15 (4) 135

Q79.For 𝑥∈𝑅- 0, 1, let 𝑓1𝑥= 𝑥, 𝑓2𝑥= 1 - 𝑥 and 𝑓3𝑥= 1 - 𝑥 be three given functions. If a function, 𝐽𝑥 satisfies 𝑓2𝑜𝐽𝑜𝑓1𝑥= 𝑓3𝑥 then 𝐽𝑥 is equal to: (1) 𝑓3𝑥 (2) 1 𝑥𝑓3𝑥 (3) 𝑓1𝑥 (4) 𝑓2𝑥

Q84.The value of 𝜋cos𝑥3𝑑𝑥 is ∫0 2 (1) (2) 0 3 (3) 4 (4) -4 3 3

Q87.Let →a = 2ˆi + λ1ˆj + 3ˆk, b = 4ˆi + (3 −λ2)ˆj + 6ˆk and →c= 3ˆi + 6ˆj + (λ3 −1)ˆk be three vectors such that → b = 2→a and →a is perpendicular to →c. Then a possible value of (λ1, λ2, λ3) is (1) (−12 , 4, 0) (2) (1, 5, 1) (3) ( 12 , 4, −2) (4) (1, 3, 1)

Q87.If a unit vector →a makes angles θ ∈(0, π) with ˆk, then a value of θ is: 3 with ˆi, π4 with ˆj and (1) 5π (2) 5π 6 12 (3) π (4) 2π 4 3

Q87.Let α = (λ −2) →a+ b and β = (4λ −2) →a+ 3 b, be two given vectors where vectors →a and b are non-collinear. → → The value of λ for which vectors α and β are collinear, is: (1) −4 (2) −3 (3) 4 (4) 3

Q89.In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is : (1) 1 (2) 5 6 6 (3) 1 (4) 2 3 3

Q90.Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is: (1) 8 (2) 6 (3) 5 (4) 7 JEE Main 2019 (10 Apr Shift 2) JEE Main Previous Year Paper

Q90.Four persons can hit a target correctly with probabilities 1 2 , 13 , 14 and 18 respectively. If all hit at the target independently, then the probability that the target would be hit, is (1) 25 (2) 7 192 32 (3) 1 (4) 25 192 32 JEE Main 2019 (09 Apr Shift 1) JEE Main Previous Year Paper

Q90.Let 𝐴 and 𝐵 be two non-null events such that 𝐴⊂𝐵. Then, which of the following statements is always correct? (1) 𝑃𝐴| 𝐵≥𝑃( 𝐴) (2) 𝑃𝐴| 𝐵= 𝑃𝐵- 𝑃𝐴 (3) 𝑃𝐴| 𝐵≤ 𝑃( 𝐴) (4) 𝑃𝐴| 𝐵= 1 JEE Main 2019 (08 Apr Shift 1) JEE Main Previous Year Paper

Q63. n - digit numbers are formed using only three digits 2,5 and 7 . The smallest value of n for which 900 such distinct numbers can be formed, is (1) 6 (2) 8 (3) 9 (4) 7

Q64.If b is the first term of an infinite G. P whose sum is five, then b lies in the interval. (1) (−∞, −10) (2) (10, ∞) (3) (0, 10) (4) (−10, 0)

Q64. n-digit numbers are formed using only three digits 2, 5 and 7 . The smallest value of n for which 900 such distinct numbers can be formed is : (1) 9 (2) 7 (3) 8 (4) 6

Q73.If p →(~p ∨~q) is false, then the truth values of p and q are, respectively (1) F, F (2) T, T (3) F, T (4) T, F

Q73.The mean of a set of 30 observation is 75 . If each observations is multiplied by non-zero number λ and then each of them is decreased by 25 , their mean remains the same. Then, λ is equal to : (1) 4 (2) 1 3 3 (3) 10 (4) 2 3 3

Q74.The Boolean expression ~(p ∨q) ∨(~p ∧q) is equivalent to (1) ~q (2) ~p (3) p (4) q

Q74.The mean of a set of 30 observations is 75 . If each other observation is multiplied by a nonzero number λ and then each of them is decreased by 25 , their mean remains the same. The λ is equal to equal to {0} (1) 103 (2) 43 (3) 1 (4) 2 3 3

Q75.If ∑9i=1(xi −5) = 9 and ∑9i=1 (xi −5)2 = 45, then the standard deviation of the 9 items x1, x2, … . , x9 is (1) 3 (2) 9 (3) 4 (4) 2

Q79.Let S be the set of all real values of k for which the system of linear equations x + y + z = 2 2x + y −z = 3 3x + 2y + kz = 4 has a unique solution. Then S is (1) an empty set (2) equal to R −{0} (3) equal to {0} (4) equal to R

Q79.Let S be the set of all real values of k for which the system of linear equations x + y + z = 2 2x + y −z = 3 3x + 2y + kz = 4 has a unique solution. Then, S is : (1) equal to R –{0} (2) an empty set (3) equal to R (4) equal to {0}

Q66.If (27)999 is divided by 7, then the remainder is (1) 3 (2) 1 (3) 6 (4) 2

Q69.A line drawn through the point P(4, 7) cuts the circle x2 + y2 = 9 at the points A and B. Then PA ⋅PB is equal to. (1) 74 (2) 53 (3) 56 (4) 65

Q71.Consider an ellipse, whose center is at the origin and its major axis is along the x-axis. If its eccentricity is 3 5 and the distance between its foci is 6, then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is: (1) 32 (2) 80 (3) 40 (4) 8