If x = x = secθ, y = tan&thet

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

If x2y5 = (x + y)7, then d2ydx2 is equal to

  • y/x2

  • x/y

  • 1

  • 0


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2.

If x = x = secθ, y = tanθ, then the value of d2ydx2 at θ = π4 is

  • 0

  • 1

  • - 1

  • 2


C.

- 1

Given, x = secθ, y = tanθdx = secθtanθ, dy = cscθNow, d2ydx2 = ddxdydx                = ddxcscθdx                = - cscθcotθ × 1secθtanθ                = - 1tan3θAt θ = π4, d2ydx2θ = π4 = - 1tanπ43 = - 1


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3.

 If x = f(t) and y =g(t), then the value of d2ydx2 is

  • f'tg''t - g'tf''tf't3

  • f'tg''t - g'tf''tf't2

  • 'tf''t - g''tf'tf't2

  • g'tf''t - g''tf'tf't3


4.

The value of a and b such that the function

fx = - 2sinx,      - π  x  - π2asinx + b,     - π2 < x < π2cosx,                   π2  x  π

is continuous in - π, π, are

  • - 1, 0

  • 1, 0

  • 1, 1

  • - 1, 1


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5.

The equation of tangent to the curve y2 = ax2 + b at point (2, 3) is y = 4x - 5, then the values of a and b are

  • 3, - 5

  • 6, - 5

  • 6, 15

  • 6, - 15


6.

Let A = cosθ- sinθsinθ- cosθ, then the inverse of A is

  • cosθ- sinθsinθ- cosθ

  • - cosθsinθsinθcosθ

  • sinθ- cosθcosθ- sinθ

  • - sinθ- cosθ- cosθsinθ


7.

The value of f(4) - f(3) is

  • f2 + 2f1 + 3f1

  • f3 + 2f2 + 3f1

  • f2 + 2f1 + 3f0

  • None of these


8.

1 + nfa is equal to

  • f(a + h)

  • f(a + 2h)

  • f(a + nh)

  • f(a + (n - 1)h)


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9.

Simplify the Boolean function (x · y) + [(x + y') - y]'.

  • 0

  • 1

  • x + y

  • xy


10.

If matrix A = abcd, then A- 1 is equal to

  • ab - bc

  • 1ab - bc

  • 1ab - bcd- b- ca

  • None of these


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