CBSEGuess



GUESS PAPER - 2009

Class : XII

MATHEMATICS

Time: 3 hrs Marks: 100

General Instructions:

( i ) All questions are compulsory.

( ii ) The question paper consists of 29 questions divided into three sections –A, B, and C. Section A contains 10 questions of 1 mark each, Section B is of 12 questions of 4 marks each, Section C is of 7 questions of 6 marks each.

( iii ) All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.

( iv ) There is no overall choice. However, an internal choice has been provided in four question of four marks each, two questions of six marks each You have to attempt only one of the alternatives in all such questions.

( v ) Use of calculator is not permitted. You may ask for logarithmic tables, if required.

SECTION A

1. If ω is one of the imaginary cube root of unity , find the value of

1 ω ω2

ω ω2 1

ω2 1 ω

2. Evaluate the following integral;

∫xex/(1+x)2 dx

3. Show that the function f: R R such that f(x) = x2 is neither one –one nor onto.

4. Simplify

tan-1 (acosx – bsinx) / (bcosx + asinx) if a/b tanx > -1, -π/2 < x < π/2

5. Find the angle between the line

x + 1 = y - 1 = z – 2

3 2 4

And the plane 2x+y-3z+4=0

6. If a = 5i-j-3k and b = i + 3j – 5k then show that the vectors a + b and a – b are orthogonal.

7. Find x if

1 0 x

x - 1 = 0

-2 -3 3

8. Find the equation of the tangent and normal to the parabola y2 = 4 a x at ( at2, 2at).

9. Express the matrix

3 -4

A =

1 -1

as the sum of symmetric and a skew- symmetric matrix.

10. Write the position vector of a point dividing the line segment joining the points A and B with position vector a and b externally in the ratio 1: 4 where a = 2i + 3j + 4k and b = -i + j + k.

SECTION B

11. Find the value of constant k so that the function given by

f(x) = k cosx / (π – 2x) if x ≠ π/2

3 if x = π/2

is continuous at x = π/2.

12. If x √(1+y) + y√(1+x) = 0 prove that

dy/dx = - 1/(1+ x)2

OR

√(1+x2) - 1

Differentiate tan-1 , x ≠ 0 w.r.t. x

x

13. For the determinant

a2 (b+c)2 bc

b2 (c+a)2 ca

c2 (a+b)2 ab

Show that (a+b+c) and (a2+b2+c2) are the factors.

14. Evaluate ∫ √tanx / (sinx. cosx ) dx.

OR

Evaluate ∫ dx/ (x4+1).

4

15. Evaluate ∫ x-1 + x-2 + x-3 dx

1

π /2

16. Evaluate 0∫ log sin x dx

17. Let f: R [ -5, ∞) given by f(x) = 9x2 + 6x – 5. Show that function f is invertible and f-1 (y) = {√(y+6) -1}/3

18. Prove that

√(1+cosx) + √(1+cosx)

tan-1 = π/4 + x/2, 0 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download