The slope of the tangent to the curve x = 3t2 + 1, y = t3 - 1 at

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

In Z, the set of all integers, the inverse of - 7 w.r.t. * defined by ab = a + b + 7 for all a,b  Z is

  • - 14

  • 7

  • 14

  • - 7


2.

In ABC if 1ab1ca1bc = 0, if then sin2(A) + sin2(B) + sin2(C) is equal to

  • 49

  • 94

  • 33

  • 1


3.

Assuming that the sums and products given below are defined which ofthe following is not true for matrices?

  • AB = AC does not imply B = C

  • A + B = B + A

  • (AB)' = B'A'

  • AB = 0 implies A = 0 or B = 0


4.

Inverse of the matrix 1- 234 is

  • 1101- 234

  • 11042- 31

  • 42- 31

  • 1104- 2- 31


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5.

b2c2bcb +cc2a2cac + aa2b2a ba + b is equal to

  • 1abcab +bc + ca

  • ab  + bc + ca

  • 0

  • a + b + c


6.

sin12cos-145

  • - 110

  • 110

  • - 110

  • 110


7.

The derivative of cos-11 - x21 + x2 w. r. t. cot-11 - 3x23x - x3 is

  • 32

  • 1

  • 12

  • 23


8.

If y = 1 - x + x22! - x33! + x44! ..., then d2ydx2 is equal to

  • - x

  • x

  • y

  • - y


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9.

The slope of the tangent to the curve x = 3t2 + 1, y = t3 - 1 at x = 1 is

  • 12

  • 0

  • - 2


B.

0

Here, x = 3t2 +1        ...i  dxdt = 6t         y = t3 - 1         ...ii     dydt = 3t2 dydx = dydt × dtdx           = 3t2 × 16t = t2But from Eq. (i) when x = 1, then       1 = 3t2 +1     3t2 = 0    t = 0 When x = 1, then t = 0 dydx = 0


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10.

The rate ofchange of the surface area ofthe sphere of radius r when the radius is increasing at the rate of 2 cm/sec is proportional to

  • 1r2

  • 1r

  • r2

  • r


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