Practice Questions

Q81.If a metallic circular plate of radius 50 cm is heated so that its radius increases at the rate of 1 mm per hour, then the rate at which, the area of the plate increases (in cm2/ hour) is (1) 5π (2) 10π (3) 100π (4) 50π

Q82.If a circular iron sheet of radius 30 cm is heated such that its area increases at the uniform rate of 6πcm2/hr, then the rate (in mm/hr ) at which the radius of the circular sheet increases is (1) 1.0 (2) 0.1 (3) 1.1 (4) 2.0

Q83.The value of the integral ∫0.90 [x −2[x]]dx, where [.] denotes the greatest integer function is (1) 0.9 (2) 1.8 (3) −0.9 (4) 0

Q84.The area of the region bounded by the curve y = x3 , and the lines, y = 8 , and x = 0 , is (1) 8 (2) 12 (3) 10 (4) 16

Q86.Let ^a and ^b be two unit vectors. If the vectors →c = ^a + 2^b and →d = 5^a −4^b are perpendicular to each other, then the angle between ^a and ^b is (1) π (2) π 6 2 (3) π (4) π 3 4 −−

Q88.An equation of a plane parallel to the plane x −2y + 2z −5 = 0 and at a unit distance from the origin is (1) x −2y + 2z −3 = 0 (2) x −2y + 2z + 1 = 0 (3) x −2y + 2z −1 = 0 (4) x −2y + 2z + 5 = 0

Q88.If →a = ^i −2^j + 3^k,→b = 2^i + 3^j −^k and →c = λ^i + ^j + (2λ −1^k) are coplanar vectors, then λ is equal to (1) 0 (2) −1 (3) 2 (4) 1

Q88.Consider the following planes P : x + y −2z + 7 = 0 Q : x + y + 2z + 2 = 0 R : 3x + 3y −6z −11 = 0 (1) P and R are perpendicular (2) Q and R are perpendicular (3) P and Q are parallel (4) P and R are parallel

Q62.If ω(≠1) is a cube root of unity, and (1 + ω)7 = A + Bω. Then (A, B) equals (1) (1, 1) (2) (1, 0) (3) (−1, 1) (4) (0, 1)

Q72.If the mean deviation about the median of the numbers a, 2a, … , 50a is 50 , then |a| equals (1) 3 (2) 4 (3) 5 (4) 2

Q76.The domain of the function f(x) = 1 is √|x|−x (1) (0, ∞) (2) (−∞, 0) (3) (−∞, ∞) −{0} (4) (−∞, ∞)

Q83.If dy = y + 3 > 0 and y(0) = 2, then y(ln 2) is equal to dx (1) 5 (2) 13 (3) -2 (4) 7

Q84.Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equation dV(t)dt = −k(T −t), where k > 0 is a constant and T is the total life in years of the equipment. Then the scrap value V(T) of the equipment is (1) I −kT2 (2) 1 −k(T−t)22 (3) e−kT (4) T2 −1k → → → → 1 1 is

Q90.If C and D are two events such that C ⊂D and P(D) ≠0 , then the correct statement among the following is JEE Main 2011 JEE Main Previous Year Paper (1) P(C ∣D) ≥P(C) (2) P(C ∣D) < P(C) (3) P(C ∣D) = P(D)P(C) (4) P(C ∣D) = P(C) JEE Main 2011 JEE Main Previous Year Paper

Q63.There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is (1) 36 (2) 66 (3) 108 (4) 3

Q69.If two tangents drawn from a point P to the parabola y2 = 4x are at right angles, then the locus of P is (1) 2x + 1 = 0 (2) x = −1 (3) 2x −1 = 0 (4) x = 1 =

Q73.Let S be a non-empty subset of R. Consider the following statement: P : There is a rational number x ∈S such that x > 0. Which of the following statements is the negation of the statement P ? JEE Main 2010 JEE Main Previous Year Paper (1) There is no rational number x ∈S such that (2) Every rational number x ∈S satisfies x ≤0 x ≤0 (3) x ∈S and x ≤0 ⇒x is not rational (4) There is a rational number x ∈S such that x ≤0

Q80.The equation of the tangent to the curve y = x + 4 , that is parallel to the x-axis, is x2 (1) y = 1 (2) y = 2 (3) y = 3 (4) y = 0 . If f has a local minimum at x = −1, then a

Q86.If the vectors →a = ^i −^j + 2^k, b = 2^i + 4^j + ^k and→c= λ^i +^j + μ^k are mutually orthogonal, then (λ, μ) = (1) (2, −3) (2) (−2, 3) (3) (3, −2) (4) (−3, 2)

Q88.A line AB in three-dimensional space makes angles 45∘ and 120∘ with the positive x-axis and the positive y- axis respectively. If AB makes an acute angle θ with the positive z-axis, then θ equals (1) 45∘ (2) 60∘ (3) 75∘ (4) 30∘

Q65.The remainder left out when 82n −(62)2n+1 is divided by 9 is (1) 0 (2) 2 (3) 7 (4) 8

Q73.If A, B and C are three sets such that A ∩B = A ∩C and A ∪B = A ∪C , then (1) A = B (2) A = C (3) B = C (4) A ∩B = ϕ

Q74.Let A be a 2 × 2 matrix Statement-1 : adj(adj A) = A Statement-2 : |adj A| = |A| (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-2 is not a correct explanation for Statement-1 Statement-1 (3) Statement-1 is true, Statement-2 is false (4) Statement-1 is false, Statement-2 is true

Q77.For real x, let f(x) = x3 + 5x + 1, then (1) f is one-one but not onto R (2) f is onto R but not one-one (3) f is one-one and onto R (4) f is neither one-one nor onto R

Q89.In a binomial distribution B (n, p = 41 ), if the probability of at least one success is greater than or equal to 109 , then n is greater than 1 1 (1) 3 (2) 3 log10 4+log10 log10 4−log10 (3) 9 (4) 4 log10 4−log10 3 log10 4−log10 3