{"id":19259,"date":"2022-06-03T12:30:10","date_gmt":"2022-06-03T07:00:10","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=19259"},"modified":"2022-05-21T12:26:28","modified_gmt":"2022-05-21T06:56:28","slug":"mcq-questions-for-class-12-maths-chapter-6","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-6\/","title":{"rendered":"MCQ Questions for Class 12 Maths Chapter 6 Application of Derivatives with Answers"},"content":{"rendered":"

Students can access the NCERT MCQ Questions for Class 12 Maths Chapter 6 Application of Derivatives with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 12 Maths with Answers<\/a> during preparation and score maximum marks in the exam. Students can download the Application of Derivatives Class 12 MCQs Questions with Answers from here and test their problem-solving skills. Clear all the fundamentals and prepare thoroughly for the exam taking help from Class 12 Maths Chapter 6 Application of Derivatives Objective Questions.<\/p>\n

Application of Derivatives Class 12 MCQs Questions with Answers<\/h2>\n

Students are advised to solve the Application of Derivatives Multiple Choice Questions of Class 12 Maths to know different concepts. Practicing the MCQ Questions on Application of Derivatives Class 12 with answers will boost your confidence thereby helping you score well in the exam.<\/p>\n

Explore numerous MCQ Questions of Application of Derivatives Class 12 with answers provided with detailed solutions by looking below.<\/p>\n

Question 1.
\nThe rate of change of the area of a circle with respect to its radius r at r = 6 cm is:
\n(a) 10\u03c0
\n(b) 12\u03c0
\n(c) 8\u03c0
\n(d) 11\u03c0<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 12\u03c0<\/p>\n<\/details>\n

\n

Question 2.
\nThe total revenue received from the sale of x units of a product is given by R (x) = 3x\u00b2 + 36x + 5. The marginal revenue, when x = 15 is:
\n(a) 116
\n(b) 96
\n(c) 90
\n(d) 126.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) 126.<\/p>\n<\/details>\n

\n

Question 3.
\nThe interval in which y = x\u00b2 e-x<\/sup> is increasing with respect to x is:
\n(a) (-\u221e, \u221e)
\n(b) (-2,0)
\n(c) (2, \u221e)
\n(d) (0, 2).<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) (0, 2).<\/p>\n<\/details>\n

\n

Question 4.
\nThe slope of the normal to the curve y = 2x\u00b2 + 3 sin x at x = 0 is
\n(a) 3
\n(b) \\(\\frac { 1 }{3}\\)
\n(c) -3
\n(d) –\\(\\frac { 1 }{3}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) –\\(\\frac { 1 }{3}\\)<\/p>\n<\/details>\n

\n

Question 5.
\nThe line y = x + 1 is a tangent to the curve y\u00b2 = 4x at the point:
\n(a) (1, 2)
\n(b) (2, 1)
\n(c) (1, -2)
\n(d) (-1, 2).<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) (1, 2)<\/p>\n<\/details>\n

\n

Question 6.
\nIf f(x) = 3x\u00b2 + 15x + 5, then the approximate value of f(3.02) is:
\n(a) 47.66
\n(b) 57.66
\n(c) 67.66
\n(d) 77.66.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) 77.66.<\/p>\n<\/details>\n

\n

Question 7.
\nThe approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is:
\n(a) 0.06 x\u00b3 m\u00b3
\n(b) 0.6 x\u00b3 m\u00b3
\n(c) 0.09 x\u00b3m\u00b3
\n(d) 0.9 x\u00b3 m\u00b3<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) 0.09 x\u00b3m\u00b3<\/p>\n<\/details>\n

\n

Question 8.
\nThe point on the curve x\u00b2 = 2y, which is nearest to the point (0, 5), is:
\n(a) (2 \u221a2, 4)
\n(b) (2 \u221a2, 0)
\n(c) (0, 0)
\n(d) (2, 2).<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) (2 \u221a2, 4)<\/p>\n<\/details>\n

\n

Question 9.
\nFor all real values of x, the minimum value of \\(\\frac { 1-x+x^2 }{1+x+x^2}\\) is
\n(a) 0
\n(b) 1
\n(c) 3
\n(d) \\(\\frac { 1 }{3}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) \\(\\frac { 1 }{3}\\)<\/p>\n<\/details>\n

\n

Question 10.
\nThe maximum value of [x (x – 1) + 1]1\/3<\/sup>, 0 \u2264 x \u2264 1 is
\n(a) (\\(\\frac { 1 }{3}\\))\\(\\frac { 1 }{3}\\)<\/sup>
\n(b) \\(\\frac { 1 }{2}\\)
\n(c) 1
\n(d) 0<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) 1<\/p>\n<\/details>\n

\n

Question 11.
\nA cylindrical tank of radius 10 mis being filled with wheat at the rate of 314 cubic m per minute. Then the depth of the wheat is increasing at the rate of:
\n(a) 1 m\/minute
\n(b) 0 \u00d7 1 m\/minute
\n(c) 1 \u00d7 1 m\/minute
\n(d) 0 \u00d7 5 m\/minute.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 1 m\/minute<\/p>\n<\/details>\n

\n

Question 12.
\nThe slope of the tangent to the curve x = t\u00b2 + 3t – 8, y = 2 t\u00b2 – 2t – 5 at the point (2, -1) is:
\n(a) \\(\\frac { 22 }{7}\\)
\n(b) \\(\\frac { 6 }{7}\\)
\n(c) \\(\\frac { 7 }{6}\\)
\n(d) \\(\\frac { -6 }{7}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) \\(\\frac { 6 }{7}\\)<\/p>\n<\/details>\n

\n

Question 13.
\nThe line y = mx + 1 is a tangent to the curve y\u00b2 = 4x if the value of m is:
\n(a) 1
\n(b) 2
\n(c) 3
\n(d) \\(\\frac { 1 }{2}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 1<\/p>\n<\/details>\n

\n

Question 14.
\nThe normal at the point (1, 1) on the curve 2y + x\u00b2 = 3 is
\n(a) x + y = 0
\n(b) x – y = 0
\n(c) x + y + 1 = 0
\n(d) x – y + 1 = 0.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) x – y = 0<\/p>\n<\/details>\n

\n

Question 15.
\nThe normal to the curve x\u00b2 = 4y passing through (2, 1) is:
\n(a) x + y = 3
\n(b) x – y = 3
\n(c) x + y = 1
\n(d) x – y = 1.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) x + y = 3<\/p>\n<\/details>\n

\n

Question 16.
\nThe points on the curve 9y\u00b2 = x\u00b3, where the normal to the curve makes equal intercepts with the axes are
\n(a) (4, \u00b1\\(\\frac { 8 }{3}\\))
\n(b) (4, –\\(\\frac { 8 }{3}\\))
\n(c) (4, \u00b1\\(\\frac { 3 }{8}\\))
\n(d) (\u00b14, \\(\\frac { 3 }{8}\\))<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) (4, \u00b1\\(\\frac { 8 }{3}\\))<\/p>\n<\/details>\n

\n

Question 17.
\nThe abscissa of the point on the curve 3y = 6x – 5x\u00b3, the normal at which passes through origin is:
\n(a) 1
\n(b) \\(\\frac { 1 }{3}\\)
\n(c) 2
\n(d) \\(\\frac { 1 }{2}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 1<\/p>\n<\/details>\n

\n

Question 18.
\nThe two curves x\u00b3 – 3xy\u00b2 + 2 = 0 and 3x\u00b2y – y\u00b3 = 2
\n(a) touch each other
\n(b) cut at right angle
\n(c) cut at an angle \\(\\frac { \u03c0 }{3}\\)
\n(d) cut at an angle \\(\\frac { \u03c0 }{4}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) cut at right angle<\/p>\n<\/details>\n

\n

Question 19.
\nThe tangent to the curve given by:
\nx = et<\/sup> cos t, y = et<\/sup> sm t at t = \\(\\frac { \u03c0 }{4}\\) makes with x-axis an angle:
\n(a) 0
\n(b) \\(\\frac { \u03c0 }{4}\\)
\n(c) \\(\\frac { \u03c0 }{3}\\)
\n(d) \\(\\frac { \u03c0 }{2}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) \\(\\frac { \u03c0 }{2}\\)<\/p>\n<\/details>\n

\n

Question 20.
\nThe equation of the normal to the curve y = sin x at (0, 0) is
\n(a) x = 0
\n(b) y = 0
\n(c) x + y = 0
\n(d) x – y = 0.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) x + y = 0<\/p>\n<\/details>\n

\n

Question 21.
\nThe point on the curve y\u00b2 = x, where the tangent makes an angle of \\(\\frac { \u03c0 }{4}\\) with x-axis is:
\n(a) (\\(\\frac { 1 }{2}\\), \\(\\frac { 1 }{4}\\))
\n(b) (\\(\\frac { 1 }{4}\\), \\(\\frac { 1 }{2}\\))
\n(c) (4, 2)
\n(d) (1, 1).<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) (\\(\\frac { 1 }{4}\\), \\(\\frac { 1 }{2}\\))<\/p>\n<\/details>\n

\n

Question 22.
\nLet f: R \u2192 R be a positive increasing function with:
\n\\( \\lim _{x \\rightarrow \\infty}\\) \\(\\frac { f(3x) }{f(x)}\\) = 1. Then \\( \\lim _{x \\rightarrow \\infty}\\) \\(\\frac { f(2x) }{f(x)}\\) =
\n(a) 1
\n(b) \\(\\frac { 2 }{3}\\)
\n(c) \\(\\frac { 3 }{2}\\)
\n(d) 3.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 1
\nHint:
\nSince f(x) is a positive increasing function
\n\u2234 0 < f(x) < f(2x) < f(3x)
\n\"MCQ<\/p>\n<\/details>\n

\n

Question 23.
\nThe real number k for which the equation 2x\u00b3 + 3x + k = 0 has two distinct real roots in [0,1]:
\n(a) lies between 2 and 3
\n(b) lies between -1 and 0
\n(c) does not exist
\n(d) lies between 1 and 2.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) does not exist
\nHint:
\nIf 2x\u00b3 + 3x + k = 0 has two distinct real roots in [0, 1], then f'(x) will change sign.
\nBut f'(x) = cx\u00b2 + 3 > 0
\nHence, no value of k exists.<\/p>\n<\/details>\n

\n

Question 24.
\nIf f and g are differentiable functions on [0, 1] satisfying f(0) = 2 = g(l), g(0) = 0 and f(1) = 6, then for some c \u2208 ] 0, 1 [:
\n(a) 2f'(c) = 3g'(c)
\n(b) f'(c) = g'(c)
\n(c) f'(c) = 2g'(c)
\n(d) 2f'(c) = g'(c).<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) f'(c) = 2g'(c)
\nHint:
\nLet h(x) = f(x) – 2g(x).
\n\u2234 h'(x) =f'(x) – 2g'(x).
\nHere h(0) = h(1) = 2.
\nBy Rolle\u2019s Theorem, h’ (c) = 0
\n\u21d2 f'(c) = 2g'(c).<\/p>\n<\/details>\n

\n

Question 25.
\nTwenty metres of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower bed is:
\n(a) 25
\n(b) 30
\n(c) 12.5
\n(d) 10.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 25
\nHint:
\nTotal length = r + r + r\u03b8 = 20
\n\"MCQ
\n\u2234 r = 5 gives max-area.
\nHence, from (2) maximum area,
\nA =10(5) – 25 = 25.<\/p>\n<\/details>\n

\n

Question 26.
\nLet f (x) = x\u00b2 – \\(\\frac { 1 }{x^2}\\) and g(x) = x – \\(\\frac { 1 }{x}\\), x \u2208 R – {-1, 0, 1}. If h(x) = \\(\\frac { f(x) }{g(x)}\\), then the local minimum value of h(x) is:
\n(a) 3
\n(b) -3
\n(c) -2\u221a2
\n(d) 2\u221a2.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) 2\u221a2.
\nHint:
\n\"MCQ<\/p>\n<\/details>\n

\n

Fill in the blanks<\/span><\/p>\n

Question 1.
\nRate of change of the area of a circle with respect to its radius when r = 4 cm is ……………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: 8\u03c0 cm\u00b2\/m.<\/p>\n<\/details>\n

\n

Question 2.
\nRate of change of the volume of a ball with respect to its radius is ………………<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: 4\u03c0r\u00b2<\/p>\n<\/details>\n

\n

Question 3.
\nThe function f(x) = |x| is strictly ……………… in (0, \u221e)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: Increasing.<\/p>\n<\/details>\n

\n

Question 4.
\nLogarithmic function is strictly ………………. in (0, \u221e).<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: Increasing.<\/p>\n<\/details>\n

\n

Question 5.
\nThe value of \u2018a\u2019 for which f(x) = sin x – ax + b is decreasing function on R is ……………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: \u2264 1.<\/p>\n<\/details>\n

\n

Question 6.
\nSlope of the tangent to the curve x = at\u00b2, y = 2t at t = 2 is ……………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: \\(\\frac { 1 }{2}\\)<\/p>\n<\/details>\n

\n

Question 7.
\nIf tangent to the curve y\u00b2 + 3x – 7 = 0 at the point (h, k) is parallel to like x – y – 4, then the value of k is ……………….<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: –\\(\\frac { 3 }{2}\\)<\/p>\n<\/details>\n

\n

Question 8.
\nFor the curve y = 5x – 2x\u00b3, if x increases at the tangents of 2 units\/sec; then at x = 3 the slope of the curve is changes at ……………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: decreasing at the rate of 72 units\/sec.<\/p>\n<\/details>\n

\n

Question 9.
\nIf x > 0, y > 0 and xy = 5, then the minimum value of x + y is ………………<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: 10.<\/p>\n<\/details>\n

\n

Question 10.
\nMaximum value of:
\nf(x) = – (x – 1)\u00b2 + 2 is ………………<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: 2.<\/p>\n<\/details>\n

\n

We believe the knowledge shared regarding NCERT MCQ Questions for Class 12 Maths Chapter 6 Application of Derivatives with Answers Pdf free download has been useful to the possible extent. If you have any other queries regarding CBSE Class 12 Maths Application of Derivatives MCQs Multiple Choice Questions with Answers, feel free to reach us via the comment section and we will guide you with the possible solution.<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can access the NCERT MCQ Questions for Class 12 Maths Chapter 6 Application of Derivatives with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 12 Maths with Answers during preparation and score maximum marks in the exam. Students …<\/p>\n

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