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SHREE GURU GYAN TUTORIALS, Std 12: MATHS, Chapters:5, Total Marks: 50, Date:17/02/22, PAPER 1 TEXT BOOK BASED MCQ, Time:1Hour, Section A, Choose correct answer from the given options. [Each carries 1 Mark], [50], 2, If y = log| x + Vx + a, dy, then, dx, 1., 1, 1, (A), (В), Vx? + a?, (C) x? + a?, (D), ² + a?, .2, dy, If y = log1o sin x then, dx, 2., (A) cot x, (B) cot x · log, 10, (C) cot x · log10 e, (D) log1o cot x, Vsinx +, Vsinx, dy, then, dx, 3., y =, sinx +..... 00, cosx, Coox, (A), 2у-1, (B) cos x(2y + 1), (C), 2у +1, (D) give not, 4., flx), = x2e2(x-1), 0 < x < 1, = a sgn(x + 1) cos(2x - 2) + bx2, 1 < x s 2., If a function f(x) is differentiable at x = 1 then., (A) a = -1, b = 2, (B) a = 1, b = -2, (C) a = -3, b = 4, (D) a = 3, b = -4, Va?., Va + x - Ja - x, - ax + x - va + ax + x, 5., The value of f(0), so that f(x) =, becomes continuous for all x,, is given by, (A) ava, fix + y) = flx) fy), For Vx and y. If f(3) = 3 and f'(0) = 11 then f'(3), (B) va, (C) - Va, (D) - ava, 6., %3D, (A) 22, (B) 44, (C) 28, (D) None of these, 7., fix) = [x] + Jx - [x]. where [ .] is a greatest integer function then, .........., (A) f(x) is continuous in Rt, (C) flx) is continuous in R I, (B) f(x) is continuous in R, (D) None of these, tan 3x, The function f(x) = (sin 3.x), is continuous at x =, then f, 6., 8., (A) e, 1, (B), (C) eld), (D) e2, ,3, 9., y? = ax? + bx + c then, is a ..... ., function., %3D, dx2, (A) constant, (B) only for x, (C) only for y, (D) for x and y, 10., flx) = x + tan x and f is an inverse function of g then g'(x) = . ., 1, 1, 1, 1, (A), 1+ (g(x) – x)2, (B), 1- (g(x) – x)2, (C), 2 + (g(x) – x)2, (D), 2 - (g(x) – x)?, d, 11. If y = p(x) the is polynomial of order 3, then 2, dx, y, %3!, dx2, (A) p"'(x) + p'(x), (В) р" (х) - р" (х), (С) р(x) р" (х), (D) p(x) + p'" (х), Wish You - All The Best, 1

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dy, If + y? = t - and x + y*, 12 +, then xy, dx, 12., %3D, (A) -1, (В) 0, (C) 1, (D) None of these, dy, 1 + x - 2x cosa, A, If sin y = x sin(a + y) and, then the value of A is, %3D, 13., dx, (A) 2, (B) cos a, (C) sin a, (D), 14., flx + y) = flx) + fy), for Vx and y and flx) = (2x2 + 3x) g(x). For V x. If g(x) is a continuous function, %3D, and g(0) = 3 then f'(x), = .........., (A) 9, (B) 3, (C) 6, (D) None of these, dx17 then f, 4, 15., y = sin x - cos x and f(x) =, 1, (A) V2, (B) J2, (C) (V2)", (D) 0, dy, then, ax - b, y = tan, 16., bx + a, dx, x = -1, 1, (A), 2, (B) а, (C) ab, (D), du, u = f(tan x), v = g(sec x), f'(1) 2 and g'(V2) = 4 then, 17., dv, (A) 2, 1, (C), (B) 2, (D), 18., f(x), = sin?x + sin2² | x +, + cos x cos x +, then f'(x), (A) 1, (B) cos?x, (C) 0, (D) sin 2x, e 3x + 7, then yn, (0) =, 19., y =, (A) 1, (B) 3", (C) 3"e?, (D) 3" . (e? . 7), x = fit), y = o(t) then, dx, d²y, 2, 20., 0;(t)f,(t) – f;(t)»2(t), (A), (B), (C), (D) None of these, In the function flx) = 2x3 + bx2 + qx satisfies conditions of Rolle's theorem in [-1, 1] andc =, 1, then, 2, 21., the value of 2b + g is, ........, (A) 0, (B) 1, (C), (D) –1, a + bx, 22., If y =, where a, b, c, d are cons, ants and Ay,y3 = uy, then the value of u is, C + dx, where y, y2, y3 are respectively. first, second and third derivatives of y., (A) 42, (B) 81, (C) 64, (D) 27, 2- Vx + 16, 4,2, 23., The function f(x) =, is continuous at x = 0 then f(0) =, cos 2x - 1, 1, 1, 1, (A), 8, (B), 64, (C), 32, 2, 24., Let flx) = x3 - x2 + x + 1, = maxi {ft), 0sts x}, 0 s x s1, = 3 - x, 1 < x < 2, g(x), Wish You - All The Best, 2, 1/2, 一a

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Then in [0, 2] the points where g(x) is not differentiable is, (A) 0, (B) 1, (C) 2, (D) None of these, |sin x cosx|, 25., f(x), then f', tan x cotx, (A) 0, (B) - V2, (C) - 2/7, (D) 2, dy, x = P + 3t - 8, y 2t - 2t - 4. If at point (2, -1), =, dx, 26., then the value of A =. . ., (A) 2, 6, (B), (C) -6, (D) 7, d²y, 27. x = 2 + P, y = 2. If, (dy, is constant then n =, %3D, dx, (A) 4, (В) 1, (C) 0, (D) 3, If F(x) = (412 - 2F'() dt then F'(4) equals to, 28., 32, 64, 64, 32, (B), 3, (C), 9., (D), 3, -1, tan, 29., If, 2, = a · e, , a > 0 then the value of y'"(0) is, (A) e, -2, e, a, (B) ae, (C), (D) Does not exist, If fix - y), flx) fy) and flx + y) are in arithmatic progression and f0) # 0 then (for Vx and y), (D) f '(2) – f'(-2) = 0, 30., (A) f(2) + f'(2), = 0, (B) f'(2) + f'(-2) = 0, (C) f(2) - f'(-2) = 0, (secx =, d, 31., x=-3, 1, (C) E, 1, (D), 6/2, (A), (B), 1, 32. ir (r) =, dx, (x > 0), (A) x*-1, (B) x*, (C) 0, (D) x*(1 + logx), d, dr (sin lx + cos-x), (x| < 1), 33., (A) 0, (B), (C), (D) does not exist, d, (a"), dx, 34., (а > 0), %3D, ......, (A) a"(1 + loga), (B) 0, (C) a, (D) does not exist, d, dx, 35., (A) మ, (B) 5e5x, (C) 5x e5x - 1, (D) 0, d, 36., ...... (x t 0), dx (log Jx), 1, (A), 1, (B) -, (C) does not exist, (D) et, Wish You - All The Best, 3

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dy, If x = at,, y = 2at then, dx, where t + 0, 48., %3D, (A), (B) t, (C) -t, (D) a, d, - (log; x²) =, 49., dx, 1, 1, 1, (B), (A), (log 5)x, (C), (log 5)x, (D), (log 5)x2, 50., Derivative of tan-lx w.r. to cotx is, where, xe R, 1, (C), 1+ x?, 1, (A) -1, (B) 1, (D), 1+ x², Wish You- All The Best