#### Quarterly Model Question Paper

11th Standard

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Maths

Time : 02:45:00 Hrs
Total Marks : 90
20 x 1 = 20
1. The number of constant functions from a set containing m elements to a set containing n elements is

(a)

mn

(b)

m

(c)

n

(d)

m+n

2. If A={1,2,3}, B={1,4,6,9} and R is a relation from A to B defined by "x is greater than y". The range of R is

(a)

{1,4,6,9}

(b)

{4,6,9}

(c)

{1}

(d)

None of these

3. $n(A\cap B)=4$ and $(A\cup B)=11$ then $n(p(A\triangle B))$ is:

(a)

44

(b)

256

(c)

64

(d)

128

4. If A and B are any two finite sets having m and n elements respectively then the cardinality of the power set of A x B is

(a)

2m

(b)

2n

(c)

mn

(d)

2mn

5. If 3 is the logarithm of 343 then the base is

(a)

5

(b)

7

(c)

6

(d)

9

6. If 8 and 2 are the roots of x2+ax+c=0 and 3,3 are the roots of x2+dx+b=0;then the roots of the equation x2+ax+b = 0 are

(a)

1,2

(b)

-1,1

(c)

9,1

(d)

-1,2

7. If $\frac{x}{x^2-5x+6}=\frac{A}{x-2}+\frac{B}{x-3}$ then value of A is:

(a)

2

(b)

0

(c)

3

(d)

-2

8. If the angles of a triangle are in A.P., then the measure of one of the angles in radians is

(a)

$\frac { \pi }{ 6 }$

(b)

$\frac { \pi }{ 3 }$

(c)

$\frac { \pi }{ 2 }$

(d)

$\frac { 2\pi }{ 3 }$

9. 2tan-1$\left( \frac { 1 }{ 5 } \right)$ is equal to

(a)

tan$\left( \frac { 5 }{ 12 } \right)$

(b)

$\frac { 5 }{ 12 }$

(c)

$\tan^{-1}\left({5 \over 12}\right)$

(d)

tan-1$\frac { 2 }{ 5 }$

10. If sin(45 ° + 10°) - sin(45° -10°) =$\sqrt{2}$sin x then x is

(a)

0o

(b)

(c)

10°

(d)

15°

11. If tanθ=$\frac{-4}{3}$, then sinθ is

(a)

$\frac{-4}{5}$

(b)

$\frac{4}{5}$

(c)

$\frac{-4}{5}\quad or\quad \frac{4}{5}$

(d)

None

12. The maximum value of 3 sinθ+4 cosθ is

(a)

1

(b)

3

(c)

4

(d)

5

13. The numerical value of tan-11+tan-12+tan-13=

(a)

$\pi$

(b)

$\frac{\pi}{2}$

(c)

0

(d)

$\frac{\pi}{4}$

14. A candidate is required to answer 7 question out of 12 questions, which are divided into two groups each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing questions.

(a)

779

(b)

781

(c)

780

(d)

782

15. The number of positive integral solution of $x\times y\times z=30$ is

(a)

3

(b)

1

(c)

9

(d)

27

16. The value of the series$\quad \frac { 1 }{ 2 } +\frac { 7 }{ 4 } +\frac { 13 }{ 8 } +\frac { 19 }{ 6 } +$.....is

(a)

14

(b)

7

(c)

4

(d)

6

17. 1 - 2x + 3x2 - 4x3 + ..., Ixl< 1 is:

(a)

(1-x)-2

(b)

(1+x)-2

(c)

(1-x)2

(d)

(1+x)2

18. The value of nC0 - nC1 + nC2 - nC3 ... + (-1)nnCis

(a)

2n+1

(b)

n

(c)

2n

(d)

0

19. $\theta$ is acute angle between the lines x2-xy- 6y2 = 0, then $\frac{2\cos\theta+3\sin\theta}{4\sin\theta+5\cos\theta}$ is

(a)

1

(b)

$-\frac{1}{9}$

(c)

$\frac{5}{9}$

(d)

$\frac{1}{9}$

20. The co-ordinates of a point on x+y+3=0 whose distance from x+2y+2=0 is $\sqrt 5$, is

(a)

(9,6)

(b)

(-9,6)

(c)

(6,-9)

(d)

(-9,-6)

21. 7 x 2 = 14
22. Write the set {-1, 1} in set builder form.

23. Let A={1,2,3,4} and B = {a,b,c,d}. Give a function from A$\rightarrow$B for each of the following:
neither one- to -one and nor onto.

24. Find the domain and range of the function f(x) = $\frac { { x }^{ 2 }-9 }{ x-3 }$.

25. Evaluate sin$\left( \frac { -11\pi }{ 3 } \right)$.

26. In a ABC, if a = 12 cm, b = 8 cm and 30° then show that its area is 24 sq. cm

27. Find the middle term in ${ \left( x-\frac { 1 }{ 2y } \right) }^{ 10 }$

28. Find the equation of the line perpendicular to x-axis and having intercept -2 on x-axis.

29. 7 x 3 = 21
30. Find the domain of $\frac { 1 }{ 1-2sinx }$

31. If one root of the equation 3x2+kx-81=0 is the square of the other then find k

32. Show that $\sin ^{ 2 }{ \frac { \pi }{ 18 } } +\sin ^{ 2 }{ \frac { \pi }{ 9 } } +\sin ^{ 2 }{ \frac { 7\pi }{ 18 } } +\sin ^{ 2 }{ \frac { 4\pi }{ 9 } } =2$

33. If $\theta$ is an acute angle, then find $\sin { \left( \frac { \pi }{ 4 } +\frac { \theta }{ 2 } \right) }$ when $\sin { \theta } =\frac { 8 }{ 9 }$

34. Prove that cos 20° cos 40° cos 60° cos 80°

35. Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the points.

36. Write the first six terms of the sequences given by a1=4,an+1=2nan.

37. 7 x 5 = 35
38. Show that the relation R on the set A = {x ∈ Z : 0 < x < 12} given by R = {(a, b) : la - b| is a multiple of 4} is an equivalence relation

39. Solve $(x+1)^{ \frac { 1 }{ 3 } }=\sqrt { x-3 }$

40. Using the mathematical induction show that for any natural number n, x2n - y2n is divisible by (x +y).

41. Prove that for any natural number n, an - bn is divisible by a-b, where a > b.

42. Find the sum to n terms of the series 1 - 5 + 9 - 13+ ......

43. Area of the triangle formed by a line with the coordinate axes, is 36 square units. Find the equation of the line if the perpendicular drawn from the origin to the line makes an angle of 45° with positive the x-axis.

44. If the equation 12x2-10xy+2y2+14x-5y+c=0 represents a pair of straight lines, find the value of c. Find the separate equations of the straight lines and also the angle between them.