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ISC XII Mathematics Practice Paper

Quiz by Isha Jarande

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40 questions
Show answers
  • Q1

    1. Theside of an equilateral triangle is increasing at the rate of 2 cm/s. Therate at which area increases when the side is 10 is

    (a) 10 cm2/s

    (b) cm2/s

    (c) 10 cm2/s

    (d)  cm2/s

    (d)

    (a)

    (c)

    (b)

    30s
  • Q2

    2. Thepoint(s) on the curve y= x2,at which y-coordinate ischanging six times as fast as x-coordinateis/are

    (a) (2, 4)

    (b) (3, 9)

    (c) (3, 9), (9, 3)

    (d) (6, 2)

    (d)

    (a)

    (b)

    (c)

    30s
  • Q3

    3. The equation of the normal to the curve y = sin x at (0, 0) is

    (a) x = 0

    (b) y = 0

    (c) x + y = 0

    (d) x – y = 0

    (b)

    (c)

    (a)

    (d)

    30s
  • Q4
    30s
  • Q5

    5. The line y = x + 1 is a tangent to the curve y2 = 4x at the point

    (a) (–1, 2)

    (b) (1, 2)

    (c) (1, –2)

    (d) (2, 1)

    (a)

    (c)

    (d)

    (b)

    30s
  • Q6

    6. The curves y = ae–x and y = bex are orthogonal if

    (a) a = b

    (b) a = –b

    (c) ab = –1

    (d) ab = 1

    (d)

    (b)

    (a)

    (c)

    30s
  • Q7

    7. If the curves ay + x2 = 7 and x3 = y cut orthogonally at (1, 1), then the value of a is (a) 1

    (b) 0

    (c) –6

    (d) 6

    (c)

    (b)

    (d)

    (a)

    30s
  • Q8
    30s
  • Q9

    9.  The absolute maximum value of y= x3 –3x + 2 in 0 ≤x ≤ 2 is

    (a) 4

    (b) 6

    (c) 2

    (d) 0

    (c)

    (b)

    (a)

    (d)

    30s
  • Q10

    10. The maximum value of xy, subject to x + y = 8 is

    (a) 8

    (b) 16

    (c) 20

    (d) 24  

    (a)

    (b)

    (d)

    (c)

    30s
  • Q11
    30s
  • Q12

    12. If the curves 4x = y2 and 4xy = k cut at right angles, then

    (a) k2 = 64

    (b) k2 = 512

    (c) k2 = 4

    (d) k2 = 256

    (a)

    (d)

    (b)

    (c)

    30s
  • Q13
    30s
  • Q14

    14. For the function y = x3 + 21, the value of x, when y increases 75 times as fast as x, is

    (a) ± 3

    (b) ± 5

    (c) ± 5

    (d)none of these

    (b)

    (d)

    (c)

    (a)

    30s
  • Q15

    15. Equation of tangent to the curve y= 1 – ex/2at the point of intersection with the y-axis is

    (a) x + 2y = 1

    (b) 2x + y = 0

    (c) x – y = 2

    (d) none of these

    (c)

    (d)

    (b)

    (a)

    30s

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