The derivative of eax cos(bx) with respect x is reax cos(bx) tan-

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

If A = 3211, then A2 + xA + yI = 0 for (x, y) is

  • (- 4, 1)

  • (- 1, 3)

  • (4, - 1)

  • (1, 3)


2.

The constant term of the polynomial x + 3xx + 2xx + 1x - 1x + 22x3x + 1 is

  • 0

  • 2

  • - 1

  • 1


3.

If a > b > 0, sec-1a + ba - b = 2sin-1x, then x is

  • - ba +b

  •  ba +b

  • -  aa +b

  • aa +b


4.

If x  , x  2n + 1π2, n  Z, then sin-1cosx + cos-1sinxtan-1cotx + cot-1tanx is

  • π2

  • π6

  • π4

  • π3


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5.

The function f(x) = [x], where [x] denotes the greatest integer not greater than x , is

  • continuous for all non-integral values of x

  • continuous only at positive integral values of x

  • continuous for all real values of x

  • continuous only at rational values of x


6.

If A is a 3 x 3 non-singular matrix and if A = 3, then 2A- 1 is

  • 24

  • 3

  • 13

  • 124


7.

The inverse of 2010 in the group Q* of all positive rational under the binary operation * defined by a * b = ab2010, a, b  Q+ is

  • 2009

  • 2011

  • 1

  • 2010


8.

If the three function f(x), g(x) and h(x) are such that h(x) = f(x) g(x) and f'(x) g'(x) = c where c is constant, then

f''xfx + g''xgx + 2cfx . gx is equal to

  • h'(x) . h''(x)

  • hxh''x

  • h''xhx

  • hxh'x


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9.

The derivative of eax cos(bx) with respect x is reax cos(bx) tan-1ba when a>0,b>0, then a value of r, is

  • a2 + b2

  • 1ab

  • ab

  • a + b


A.

a2 + b2

Given, ddxeaxcosbx = reaxcosbx +α, then r = ?Let y = eaxcosbx  dydx = aeaxcosbx - beaxsinbx  dydx = eaxacosbx - bsinbxLet a = rcosαb = rsinα      ...iThen, dydx = eax . rcosbx . cosα - sinbx . sinα          dydx = eax . rcosbx + α     ...iiwhere, tanα = ba  α = tan-1baand r2cos2α + sin2α = a2 +b2                                    r2 = a2 +b2                                     r = a2 +b2


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10.

In ABC, if a = 2, B = tan-112 and C = tan-113, then (A, b) equals

  • 3π4, 25

  • π4, 225

  • 3π4, 225

  • π4, 25


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