IIT JEE & NEET Question Bank with Solution: 09/12/21

NCERT Application Of Derivatives
This MCQs are based on the Mathematics Part I Textbook of Maharashtra (click here for reference).
Answers are in Bold, Italic and underline form of option name.

Q.1. The equation of tangent to the curve $y equals x squared plus 4 x plus 1 space a t space left parenthesis negative 1 comma negative 2 right parenthesis$ is

(A) 2x-y=0

(B) 2x+y-5=0

(D) x+y-1=0

Q.2. Equation of the tangent to the curve $2 x squared plus 3 y squared minus 5 equals 0 space a t space left parenthesis 1 comma space 1 right parenthesis$ is

(A) 2x - 3y - 5 = 0

(B) 2x + 3y - 5 = 0

(D) 3x + 2y + 5 = 0

Q.3. The function $f left parenthesis x right parenthesis equals x cubed minus 3 x squared plus 3 x minus 100 comma space x element of space R$ is _______.

(A) increasing

(B) decreasing

(D) neither increasing nor decreasing

Q.4. If x = -1 and x = 2 are the extreme points of $y equals alpha space log space x space plus space beta x squared space plus space x comma$ then

(A) $alpha equals negative 6 comma space beta equals 1 half$

(B) $alpha equals negative 6 comma space beta equals negative 1 half$

(C) $alpha equals 2 comma space beta equals negative 1 half$

(D) $alpha equals 2 comma space beta equals 1 half$

Q.5. The normal to the curve $x squared plus 2 x y minus 3 y squared equals 0 space a t space left parenthesis 1 comma space 1 right parenthesis$

(A) meets the curve again in second quadrant.

(B) does not meet the curve again.

(D) meets the curve again in fourth quadrant.

Q.6. The equation of the tangent to the curve $y equals 1 minus e to the power of x over 2 end exponent$ at the point of intersection with Y-axis is

(A) x+2y=0

(B) 2x+y=0

(D) x+y=2

Q.7. A particle moves according to the law $s equals t cubed minus 6 t squared plus 9 t plus 25.$ The displacement of the particle at the time when its acceleration is zero, is

(A) -27 units

(B) 27 units

(D) 0 units

Q.8. Let $f space colon space left parenthesis negative 1 comma infinity right parenthesis rightwards arrow R space b e space d e f i n e d space b y space f left parenthesis 0 right parenthesis equals 1 space a n d space f left parenthesis x right parenthesis equals 1 over x log subscript e left parenthesis 1 plus x right parenthesis comma space x not equal to 0.$ Then the function f :

(A) decreases in $left parenthesis negative 1 comma space 0 right parenthesis$ and increases in $left parenthesis 0 comma infinity right parenthesis$

(B) increases in $left parenthesis negative 1 comma space 0 right parenthesis$ and decreases in $left parenthesis 0 comma infinity right parenthesis$

(D) decreases in $left parenthesis negative 1 comma infinity right parenthesis$

Q.9. If the tangent at (1, 1) on $y squared equals x left parenthesis 2 minus x right parenthesis squared$ meets the curve again at P, then P is

(A) (4, 4)

(B) (-1, 2)

(D) $open parentheses 9 over 4 comma 3 over 8 close parentheses$

Q.10. The approximate value of tan $left parenthesis 44 to the power of ring operator 30 apostrophe right parenthesis$ given that $1 to the power of ring operator$ = 0.0175, is

(A) 0.08952

(B) 0.9528

(D) 0.9825

Q.11. If Rolle's theorem holds for the function $f left parenthesis x right parenthesis equals x cubed plus b x squared plus a x minus 6 space f o r space x space element of space open square brackets 1 comma space 3 close square brackets comma space t h e n space a plus 4 b equals$

(A) 13

(B) -26

(C) -13

(D) 26

Q.12. Let f(x) and g(x) be differentiable for 0

(A) 1

(B) 3

(D) -1

Q.13. The equation of tangent to the curve $y equals 3 x squared minus x plus 1 space a t space P left parenthesis 1 comma space 3 right parenthesis$ is______.

(A) 5x-y=2

(B) x+5y=16

(D) 5x=y

Q.14. If the function $f left parenthesis x right parenthesis equals a x cubed plus b x squared plus 11 x minus 6$ satisfies conditions of Rolle's theorem in $open square brackets 1 comma space 3 close square brackets space a n d space f apostrophe open parentheses 2 plus fraction numerator 1 over denominator square root of 3 end fraction close parentheses equals 0 comma$ then values of a and b are respectively

(A) 1, -6

(B) -2, 1

(D) -1, 6

Q.15. If $f left parenthesis x right parenthesis space equals space fraction numerator x squared minus 1 over denominator x squared plus 1 end fraction comma$ for every real x, then the minimum value of f is

(A) 1

(B) 0

(C) -1

(D) 2

Q.16. A ladder 5 m in length is resting against vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of 1.5 m/sec. The length of the higher point of ladder when the foot of the ladder is 4.0 m away from the wall decreases at the rate of

(A) 1

(B) 2

(D) 3

Q.17. Let $f left parenthesis x right parenthesis equals x cubed minus 6 x squared plus 9 x plus 18 comma$ then f(x) is strictly decreasing in

(A) $open parentheses negative infinity comma space 1 close parentheses$

(B) $left square bracket 3 comma space infinity right parenthesis$

(C) $left parenthesis negative infinity comma space 1 right square bracket space union space left square bracket 3 comma space infinity right parenthesis$

(D) (1, 3)

Q.18. If $f left parenthesis x right parenthesis equals x cubed minus 3 x$ has minimum value of at x = a, then a =

(A) -1

(B) -3

(C) 1

(D) 3

Q.19. A spherical iron ball of 10cm radius is coated with a layer of ice of uniform thickness that melts at a rate of $50 c m cubed divided by m i n.$ When the thickness of ice is 5cm. then the rate (in cm/min.) at which of the thickness of ice decreases, is

(A) $fraction numerator 1 over denominator 18 straight pi end fraction$

(B) $fraction numerator 1 over denominator 54 straight pi end fraction$

(D) $fraction numerator 5 over denominator 6 straight pi end fraction$

IIT JEE & NEET Question Bank with Solution

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Sunday, September 12, 2021

HSC Application Of Derivatives All solved MCQs: Maharashtra Board