CBSE Guess paper class XII Mathematics 2008 5


EGuess Paper – 2008

Class – XII

Subject – Mathematics

DIFFERENTIATION

1.

x2 sin xy + y cos x = 2

2.

(x2 + 2y)2 + x3 + y2 = 2x

3.

tan-1 _3x – 4_

1 + 12x

4.

tan-1 √(1 + a2x2) – 1

ax

5.

cos-1 3 + 5cosx

5+3cos x

6.

cos-1 1 – x2p

1 + x2p

7.

x2 sin3 x cos4 x

8.

log sinm x

cosn x

9.

log tan x – cot x log (1+sin x)

2

10.

__sin2x__ + __cos2x__

1 + cot x 1 + tan x

11.

If y = √x + 1/x, show that

2x dy/dx + y = 2√x

12.

If y = 1 + x + x2 + x3 +…+ xn

2! 3! n!

show that, dy + xn = y

dx n!

13.

If y = log 1 + tan x 1/2

1 – tan x

prove that dy/dx = sec 2x

14.

If yx + xy = K, show that

dy = - yx log y + yxy – 1

dx xy log x + xyx – 1

15.

If x + y = sin (x + y), show that dy/dx = - 1

16.

If ex+ y = xy, show that

dy/dx = y (1 – x)/x ( y – 1)

17.

If √(1–x4) + √(1–y4) = k (x2– y2)

s.t. y√(1–x4) dy/dx = x √(1–y4)

18.

If y= tan-1xn+tannx – tan-1 a+xn

1-axn

s.t.dy/dx = n tann-1x sec2x

19.

If x = a(cos θ + θ sin θ) and

y = a(sin θ – θ cos θ), show that, a θ d2y/dx2 = sec3 θ

20.

If y = sin-1 x/ √(1–x2), show that,

(1–x2)d2y/dx2 –3x dy/dx–y =0

Wave: SAM

 

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