Category: Worksheets

Question. If DA a AB b = = , and CB a =k , wherek > 0and X Y, are the mid-points of DB and AC respectively such that |a|  =17 and | XY | =4, then k isequal to(a) 8/17(b) 9/17(c) 5/17(d) 4/17 Question. If a and b are two unit vectors inclined to x-axis at angles 30° […]

Question. If the line ax by c + + = 0 is a normal to the curve xy = 1, then(a) a >0,b< 0(b) a < 0,b > 0(c) Both (a) and (b)(d) None of these Question. If the line joining the points (0, 3) and 5,-2) ) is a tangent to the curve y=c/x+1′, then the value […]

Question. If tanh2 x = tan2θ , then cosh 2x is equal to:(a) − sin 2θ(b) sec 2θ(c) cos 3θ(d) cos 2θ Question. The value of sinh−1 (1) is:(a) 0(b) log(√2 + 1)(c) log(1 − √2)(d) None of these Question. If cos(u +iv) = x +iy, then x2 + y2 +1is equal to:(a) cos2 u + sinh2 v(b) […]

Question. If f (x) = x2 sin1/x, where x ≠ 0, then the value of the function f at x = 0, so that the function is continuous at x = 0, is(a) 0(b) – 1(c) 1(d) None of these Question. If sin y + e–x cos y = e , then dy/dx at (1, π) is equal […]

Question. The solution of the differential equation cos2x d2y/dx2 = 1 is:  (a) y = log cos x + cx(b) y = logsec x + c1x + c2(c) y = logsec x − c1x + c2(d) None of these Question. The differential equation of system of concentric circles with centre (1,2) is Question. The differential equation of all circles […]

Question. If centroid of tetrahedron OABC, where A, B, C are given by (a, 2, 3), (1, b, 2) and (2, 1, c) respectively be (1, 2, –1), then distance of P(a, b, c) from origin is equal to:(a) √107(b) √14(c) √(107 /14)(d) None of these Question. Distance of the point (x1, y1, z1) from the […]

Question. (a) θ = nΦ, n = 0, 1, 2, ……(b) θ + Φ = n π , n = 0, 1, 2, …..(c) θ = Φ + (2n + 1) π/2, n = 0, 1, 2, …(d) θ = Φ + nπ/2, n = 0, 1, 2, … Question.  Question.  (a) B(b) A(c) O(d) I Question. […]

Question. Which of the following is always true?                (a) ( p⇒q) ≡ ~ q⇒~ p(b) ~ ( p ∨ q) ≡ ∨ p ∨ ~ q(c) ~ ( p⇒q) ≡ p ∧ ~ q(d) ~ ( p ∨ q) ≡ ~ p ∧ ~ q Question. The logically equivalent […]

Question. The angle between the lines xy = 0 is equal to:        (a) 45°(b) 60°(c) 90°(d) 180° Question. If the line 2x + 3ay − 1 = 0 and 3x + 4y + 1 = 0 are mutually perpendicular, then the value of a will be:         (a) 1/2(b) 2(c) […]

Question. From a book containing 100 pages, one page is selected randomly. The probability that the sum of the digits of the page number of the selected page is 11, is:(a) 2/25(b) 9/100(c) 11/100(d) None of these      A Question. One card is drawn from each of two ordinary packs of 52 cards. The probability that […]