## Differential Calculus

Published in: AIEEE | IIT JEE Mains | Mathematics
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• ### Pulkit

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Differential Calculus, Quadratic Equations, Trigonometric Ratios, Equations Test for JEE Mains Pattern.

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1. DIFFERENTIAL CALCULUS, QUADRATIC EQUATIONS, TRIGONOMETRIC RATIOS & EQUATIONS TEST Duration — 1 hr JEE MAINS PATTERN No. of Questions 30 , Marking Scheme: 4 marks for correct answer, 1. Range of function f(x) = 16sin- x —rl + 18cos- x —71 is 2. x = e, then the range of f(x) is If e + e 3. If f(x) = x + tanx and f(x) is inverse of g(x), then g'(x) is equal to 1 1 Total Marks -120 -1 for wrong answer. 1 (0) 2 4. x The function y 1+1 xl A. One-One, Onto B. One-One, Into, Odd C. Many-One, Onto, Odd D. One-One,Onto, Odd 5. The sum of all the values of 'm' for which the roots Xl, xz of quadratic equation — 2mx + m - 0 satisfy x? + xe 3 2 is 6. For x, the solution of [x +21+ Ix is greatest integer function) 11, 3]
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7. If + 2f(1 given by (x-2)2 3 (3) (x-2)2 (4) 3 8. (3) 9. If f(x) —x) = xZ+2Vx= R then f(x) is If tan 10 = t, the value of cos 20 + t sin 20 is — min(lx12 — 51xl, 1) then f(x) is non differentiable at pointS% then Z + 13 equals (3) 12 (4) 16 10. The maximum value of —xa -3b is where b > 0. if b varies then the minimum value of g(b) is 2 2 9 (3) 4 9 (4) 2
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11. The range of the function f(x) = (1 + sec-I cos-l x) is {1(1 +7)2} 12. 3sinAcosA then tan (A + B) equals tana 1— 3cos2 A (1) —tanA 2 (2) 2 cot A (3) (4) 13. —tan A — 3cotA A function f from integers to integers is defined as f(x) n+3 n is odd . If k is n is even 2 an odd integer and = 27 then the sum of digits of k is 12 14.
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If rx) 3 then which of the following is FALSE (1) f(x) has a local maximum at x = 0 (2) •f(x) is strictly decreasing on 'the left of x = 0 (3) f'(x) is strictly increasing on the left of (4) f'(x) is strictly increasing on the right of 15. If the thrice repeated roots of equation x + ax +bx2+cx—1 = 0 is 1, then a+b+2c is equal to 16. 24 The minimum value of f(x) x (where x > 0) is (1) 12 (2) 16 (3) 20 17. 2 The value of dx is, -2 (where [.1 represent greatest integer function] 1 (1) 2 2
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18. The solution of the equation 2cos x + cosx— 2cosx sin2x— 3sin2x + 1 = 0 is 19. If a variable tangent to the curve x2y makes intercepts ab on x and y axes respectively, then the value of a2b is (1) 27c3 27 27 27 3 (5) 20. lim is equal to log4 —log4 (2) log2 log2 (4) —210g 4 (5) 21.
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One of the point on the curve 3y = 6x— 5xa normal at which passes through the origin, is 238) 4) 22. Let f : R is a function satisfying = f(2+X) and f(20 The graph of y =f(x) is not symmetrical about (a)x=2 23. The minimum value of sec x) f(x) Yx e R. For this function f, (b ) x -10 (d) None of these is then Z + is. 24. Let (x) 1 sin 2M x L2x2 + 4 1 2 | . If y = g(x) is 1 then absolute image of y — f(x) in value off(l) g(l) is (1)0 25. y-axis,
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Let g(x) be a polynomial of degree one and f(x) be defined by f(x) = goo, sin x continuous satisfying f'(l) = f(—l), then g(x) is (A) (1 + sin +1 (B) (I-sin I)X+I 26. (C) (I-sin . If f(x) is (D) (1 + sin l)x-l Let f: R + R be a continuous onto function satisfying f(x) + f(—x) = 0, Y x e R. If f(—3) = 2 and f(5) = 4 in [—5, 5], then the equation f(x) = 0 has (A) exactly three real roots (C) atleast five real roots 27. 28. 29. 30. lim x 22 (A) 3 (C) 3 2x 3 (B) (D) (B) (D) O and f(l) = 3 then 2 (B) 3 None of these (B) exactly two real roots (D) atleast three real roots 16 9 8 3 x]} then is equal to 28 does not exist Let f(x) = {x} + {x + + {x + [e (where { } F.P.F [.] G.I.F) ( A) 14 If f(x) is a quadratic expression such that f(— 1 9 2 (C) 9 x [I + s inx]+ 2 + Sin — Range of f(x) = 2 the greatest integer function, is (D) (C) 2 2 2 2 2 2 + 3 + sin (B) (D) 2 2 2 3 3 f(x) 2 lim cncosx Vx e [0,Tt], where [.] denotes 2

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