Practice Questions

Q84.The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b ? (1) a = 0, b = 7 (2) a = 5, b = 2 (3) a = 1, b = 6 (4) a = 3, b = 4 JEE Main 2008 JEE Main Previous Year Paper

Q85. AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is 60∘ . He moves away from the pole along the line BC to a point D such that CD = 7 m. From D the angle of elevation of the point A is 45∘ . Then the height of the pole is (1) 7√3 + 1)m 2 ⋅ √3−11 m (2) 7√32 ⋅(√3 (3) 7√3 2 ⋅(√3 −1)m (4) 7√32 ⋅ √3+11

Q86.Let R be the real line. Consider the following subsets of the plane R × R. S = {(x, y) : y = x + 1 and 0 < x < 2}, T = {(x, y) : x −y is an integer }. Which one of the following is true? (1) neither S nor T is an equivalence relation on R (2) both S and T are equivalence relations on R (3) S is an equivalence relation on R but T is not (4) T is an equivalence relation on R but S is not

Q87.Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity matrix. Denote by tr(A), the sum of diagonal entries of A . Assume that A2 = 1. Statement -1: If A ≠1 and A ≠−1, then det A = −1. Statement −2 : If A ≠1 and A ≠−1, then tr(A) ≠0. (1) Statement −1 is false, Statement −2 is true (2) Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1 (3) Statement −1 is true, Statement −2 is true; (4) Statement −1 is true, Statement −2 is false. Statement −2 is not a correct explanation for Statement −1

Q88.Let A be a square matrix all of whose entries are integers. Then which one of the following is true? (1) If det A = ±1, then A−1 exists but all its entries (2) If det A ≠±1, then A−1 exists and all its entries are not necessarily integers are non-integers (3) If det A = ±1, then A−1 exists and all its entries (4) If det A = ±1, then A−1 need not exist are integers

Q89.Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + bz, y = az + cx and z = bx + ay. Then a2 + b2 + c2 + 2abc is equal to (1) 2 (2) −1 (3) 0 (4) 1

Q90.The value of cot (cosec−1 53 + tan−1 23 ) is (1) 6 (2) 3 17 17 (3) 4 (4) 5 17 17

Q91.Let f : N →Y be a function defined as f(x) = 4x + 3, where Y = {y ∈N : y = 4x + 3 for some x ∈N}. Show that f is invertible and its inverse is (1) g(y) = 3y+43 (2) g(y) = 4 + y+34 (3) g(y) = y+34 (4) g(y) = y−34 1 ), if x ≠1 x−1 . Then which one of the following is true?

Q92.Let f(x) = −1) sin ( {(x0, if x = 1 JEE Main 2008 JEE Main Previous Year Paper (1) f is neither differentiable at x = 0 nor at x = 1 (2) f is differentiable at x = 0 and at x = 1 (3) f is differentiable at x = 0 but not at x = 1 (4) f is differentiable at x = 1 but not at x = 0

Q93.Suppose the cube x3 −px + q has three distinct real roots where p > 0 and q > 0. Then which one of the following holds? (1) The cubic has minima at √p3 and maxima at (2) The cubic has minima at −√p3 and maxima at −√p3 √p3 and The cubic has maxima at both and (3) The cubic has minima at both √p3 −√p3 (4) √p3 −√p3

Q94.How many real solutions does the equation x7 + 14x5 + 16x3 + 30x −560 = 0 have? (1) 7 (2) 1 (3) 3 (4) 5

Q95.The value of √2 ∫ sin xdx is sin(x−π4 ) (1) x + log cos (x −π4 ) + c (2) x −log sin (x −π4 ) + c (3) x + log sin (x −π4 ) + c (4) x −log cos (x −π4 ) + c dx. Then which one of the following is true?

Q96.Let I = ∫10 sin√xx dx and J = ∫10 cos√xx (1) I > 32 and J > 2 (2) I < 23 and J < 2 (3) I < 32 and J > 2 (4) I > 23 and J < 2

Q97.The area of the plane region bounded by the curves x + 2y2 = 0 and x + 3y2 = 1 is equal to (1) 5 (2) 1 3 3 (3) 2 (4) 4 3 3

Q98.The solution of the differential equation dx dy = x+yx satisfying the condition y(1) = 1 is (1) y = ln x + x (2) y = x ln x + x2 (3) y = xe(x−1) (4) y = x ln x + x

Q99.The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is (1) (x −2)y′2 = 25 −(y −2)2 (2) (y −2)y′2 = 25 −(y −2)2 (3) (y −2)2y′2 = 25 −(y −2)2 (4) (x −2)2y′2 = 25 −(y −2)2 Q100.The non-zero verctors →a,→b and →c are related by →a = 8→b and →c = −7→b. Then the angle between →a and→cis (1) 0 (2) π/4 (3) π/2 (4) π Q101.The vector →a = α^i + 2^j + β^k lies in the plane of the vectors →b = ^i + ^j and →c = ^j + ^k and bisects the angle between →b and →c. Then which one of the following gives possible values of α and β ? (1) α = 2, β = 2 (2) α = 1, β = 2 (3) α = 2, β = 1 (4) α = 1, β = 1 Q102.The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz− plane at the point (0, 172 , −132 ). Then JEE Main 2008 JEE Main Previous Year Paper (1) a = 2, b = 8 (2) a = 4, b = 6 (3) a = 6, b = 4 (4) a = 8, b = 2 Q103.If the straight lines x−1 k = y−22 = z−33 and x−23 = y−3k = z−12 intersect at a point, then the integer k is equal to (1) −5 (2) 5 (3) 2 (4) −2 Q104.It is given that the events A and B are such that P(A) = 41 , P ( BA ) = 12 and P ( BA ) = 32 . Then P(B) is (1) 1 (2) 1 6 3 (3) 2 (4) 1 3 2 Q105.A die is thrown. Let A be the event that the number obtained is greater than 3 . Let B be the event that the number obtained is less than 5 . Then P(A ∪B) is (1) 3 (2) 0 5 (3) 1 (4) 2 5 JEE Main 2008 JEE Main Previous Year Paper

Q1. The velocity of a particle is v = v0 + gt + ft2 . If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is (1) v0 + 2g + 3f (2) v0 + g/2 + f/3 (3) v0 + g + f (4) v0 + g/2 + f

Q2. A particle is projected at 60∘ to the horizontal with a kinetic energy K. The kinetic energy at the highest point is (1) K (2) Zero (3) K/2 (4) K/4

Q3. A particle just clears a wall of height b at distance a and strikes the ground at a distance c from the point of projection. The angle of projection is (1) tan−1 acb (2) 45∘ (3) tan−1 a(c−a)bc (4) tan−1 bca

Q4. A block of mass ' m ' is connected to another block of mass ' M ' by a spring (massless) of spring constant ' k '. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force ' F' starts acting on the block of mass ' M' to pull it. Find the force on the block of mass ' m' (1) mF (2) (M+m)F M m (3) mF (4) MF (m+M) (m+M)

Q5. A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10, 000. N/m. The spring compresses by (1) 5.5 cm (2) 2.5 cm (3) 11.0 cm (4) 8.5 cm

Q6. A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are (1) 12 kg and 13 kg (2) 5 kg and 5 kg (3) 5 kg and 12 kg (4) 5 kg and 13 kg

Q7. A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α/R from the centre of the bigger disc. The value of α is (1) 1/3 (2) 1/2 (3) 1/6 (4) 1/4 JEE Main 2007 JEE Main Previous Year Paper

Q8. For the given uniform square lamina ABCD, whose centre is O, (1) √2IAC = IEF (2) IAD = 3IEF (3) IAC = IEF (4) IAC = √2IEF

Q9. A round uniform body of radius R, mass M and moment of inertia ' I', rolls down (without slipping) an inclined plane making an angle θ with the horizontal. Then its acceleration is θ g sin g sin (1) θ (2) I MR2 1+ 1+ MR2 I (3) g sinI θ (4) g sin θ 1− MR2 1−MR2I