Practice Questions

Q74. lim ex2−cos x→0 sin2 x (1) 2 (2) 32 (3) 5 (4) 3 4

Q74.If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is: (1) 1 (2) √2 −1 2 (3) √2−1 (4) 2√2−1 2 2

Q74.The negation of ∽s ∨(∽r ∧s) is equivalent to JEE Main 2015 (04 Apr) JEE Main Previous Year Paper (1) s ∧ r (2) s ∧~r (3) s ∧(r ∧~s) (4) s ∨(r ∨~s)

Q75.Consider the following statements: P: Suman is brilliant Q: Suman is rich R: Suman is honest The negation of the statement, "Suman is brilliant and dishonest if and only if Suman is rich" can be equivalently expressed as (1) ~Q ↔~P ∨R (2) ~Q ↔P ∨~R (3) ~Q ↔P ∧~R (4) ~Q ↔~P ∧R

Q75.The mean of a data set comprising of 16 observations is 16 . If one of the observation value 16 is deleted and three new observations valued 3 , 4 and 5 are added to the data, then the mean of the resultant data is (1) 14 .0 (2) 16 .8 (3) 16 .0 (4) 15 .8

Q76.A factory is operating in two shifts, day and night, with 70 and 30 workers, respectively.If per day mean wage of the day shift workers is, ₹ 54 and per day mean wage of all the workers is ₹ 60, then per day mean wage of the night shift workers (in ₹ ) is : (1) 75 (2) 74 (3) 69 (4) 66

Q76.If the angles of elevation of the top of a tower from three collinear points A, B and C on a line leading to the foot of the tower are 30°, 45° and 60° respectively, then the ratio AB : BC , is (1) 2 : 3 (2) √3 : 1 (3) √3 : √2 (4) 1 : √3 Q77. ⎡ 1 2 2 ⎤ If A = 2 1 −2 is a matrix satisfying the equation AAT = 9I , where I is 3 × 3 identity matrix, then the ⎣ a 2 b ⎦ ordered pair (a, b) is equal to (1) (−2, −1) (2) (2, −1) (3) (−2, 1) (4) (2, 1)

Q76.Let 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation α at a point O on this line and all the poles are on the same side of O. If the height of the longest pole is h and the distance of the foot of the smallest pole from O is a; then the distance between two consecutive poles, is (1) h sin α+a cos α (2) h cos α−a sinα 9 cos α 9 sin α (3) h sin α+a cos α (4) h cos α−a sin α 9 sin α 9 cos α

Q77.If A is a 3 × 3 matrix such that |5 adjA| = 5, then |A| is equal to (1) ± 251 (2) ±5 (3) ± 51 (4) ±1

Q77.In a certain town, 25% of the families own a phone and 15% own a car; 65% families own neither a phone nor a car and 2000 families own both a car and a phone. Consider the following three statements: (i) 5% families own both a car and a phone. (ii) 35% families own either a car or a phone. (iii) 40000 families live in the town. Then, (1) Only (ii) and (iii) are correct (2) Only (i) and (ii) are correct (3) All (i), (ii) and (iii) are correct (4) Only (i) and (iii) are correct

Q78.If A = [ 01 −10 ] , then which one of the following statements is not correct? (1) A3 + I = A(A3 − I) (2) A4 −I = A2 + I (3) A2 + I = A(A2 −I) (4) A3 −I = A(A −I) JEE Main 2015 (10 Apr Online) JEE Main Previous Year Paper

Q78.The set of all values of λ for which the system of linear equations: 2x1 −2x2 + x3 = λx1 2x1 −3x2 + 2x3 = λx2 −x1 + 2x2 = λx3 has a non-trivial solution, (1) Contains more than two elements. (2) Is an empty set. (3) Is a singleton. (4) Contains two elements.

Q78. x2 + x x + 1 x −2 If 2x2 + 3x −1 3x 3x −3 = ax −12 , then a is equal to: x2 + 2x + 3 2x −1 2x −1 (1) −24 (2) 24 (3) −12 (4) 12

Q79.Let tan−1 y = tan−1 x + tan−1( 1−x22x ), where |x| < √31 ,Then a value of y is (1) 3x+x3 (2) 3x−x3 1+3x2 1−3x2 (3) 3x+x3 (4) 3x−x3 1−3x2 1+3x2 is differentiable, then the value of k + m is

Q79. (ex−1)2 , x ≠0 x ⎧ sin ( k ) log (1+ x4 ) Let k be a non - zero real number. If f(x) = is a continuous function at x = 0 ⎨ ⎩12 , x = 0 , then the value of k is (1) 2 (2) 4 (3) 3 (4) 1

Q79.The least value of the product xyz (such that x, y and z are positive real numbers) for which the determinant x 1 1 1 y 1 is non-negative is 1 1 z (1) −1 (2) −16√2 (3) −8 (4) −2√2

Q80.If f(x) = 2 tan−1 x + sin−1( 1+x22x ), x > 1, then f(5) is equal to (1) π 2 (2) tan−1( 15665 ) (3) π (4) 4 tan−1(5)

Q80.The equation of a normal to the curve, sin y = x sin( π3 + y) at x = 0, is: (1) 2x −√3 y = 0 (2) 2y −√3 x = 0 (3) 2y + √3 x = 0 (4) 2x + √3 y = 0

Q80.If the function g (x) = {k√xmx ++21 ,, 30 <≤xx ≤3≤5 (1) 4 (2) 2 (3) 16 (4) 10 5 3

Q81.Let k and K be the minimum and the maximum values of the function f(x) = (1+x)0.6 in [0, 1], respectively, 1+x0.6 then the ordered pair (k, K) is equal to: (1) (2−0.4, 1) (2) (2−0.6, 1) (3) (2−0.4, 20.6) (4) (1,20.6) JEE Main 2015 (11 Apr Online) JEE Main Previous Year Paper 1

Q81.If Rolle's theorem holds for the function f(x) = 2x3 + bx2 + cx, x ∈[−1, 1] at the point x = 12 , then 2b + c is equal to (1) 2 (2) 1 (3) −1 (4) −3

Q81.The normal to the curve x2 + 2xy −3y2 = 0 , at (1, 1) (1) Meets the curve again in the fourth quadrant (2) Does not meet the curve again (3) Meets the curve again in the second quadrant (4) Meets the curve again in the third quadrant

Q82.The distance from the origin, of the normal to the curve, x = 2 cos t + 2t sin t, y = 2 sin t −2t cos t at t = π4 , is : (1) √2 (2) 2√2 (3) 4 (4) 2

Q82.If ∫ log(t+√1+t2) dt = 2 (g(t))2 + c, where c is a constant, then g(2), is equal to √1+t2 (1) 2 + + √5) (2) log(2 √5) 1 log(2 √5 + log + (3) log(2 √5) (4) 12 (2 √5)

Q83.The integral ∫ 3dx 5 , is equal to (x+1) 4 (x−2) 4 (1) 1 1 4 + c 4( x+1x−2 ) 4 + c (2) −43 ( x+1x−2 ) (3) 1 1 4 + c 4( x−2x+1 ) 4 + c (4) −43 ( x−2x+1 )