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#### Important 1mark

11th Standard

Reg.No. :
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Maths

Time : 00:20:00 Hrs
Total Marks : 20
19 x 1 = 19
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. The function f:[0,2π]➝[-1,1] defined by f(x)=sin x is

(a)

one-to-one

(b)

on to

(c)

bijection

(d)

cannot be defined

3. Let X={1,2,3,4}, Y={a,b,c,d} and f={f(1,a),(4,b),(2,c),(3,d),(2,d)}. Then f is

(a)

an one-to-one function

(b)

an onto function

(c)

a function which is not one-to-one

(d)

not a function

4. For real numbers x and y, define xRy if x-y+√2 is an irrational number. Then the relation R is

(a)

reflexive

(b)

symmetric

(c)

transitive

(d)

none of these

5. Let R be the relation over the set of all straight lines in a plane such that l1Rl2 ⇔ l1丄l2 . Then  R is

(a)

symmetric

(b)

reflexive

(c)

transitive

(d)

an equivalent relation

6. The number of relations on a set containing 3 elements is

(a)

9

(b)

81

(c)

512

(d)

1024

7. If $f:R\rightarrow R$ is defined by $f(x)=2x-3:$

(a)

${1\over 2x-3}$

(b)

${1\over 2x+3}$

(c)

${x+3\over 2}$

(d)

${x-3\over 2}$

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

(a)

44

(b)

256

(c)

64

(d)

128

9. Let f and g be two odd functions then the function of f o g is

(a)

an even function

(b)

an odd function

(c)

neither even nor odd

(d)

a periodic function

10. For any four sets A, B, C and D, which of the following is not true?

(a)

A x C   B x D

(b)

(A x B) ∩ (C x D) = (A ∩ C) x (B ∩ D)

(c)

A x (B U,C) = (A x B) U (A x C)

(d)

A x (B ∩ C) = (A x B) ∩ (A x C)

11. 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

12. The domain and range of the function $f(x)={|x-4|\over x-4}$

(a)

R, [-1, 1]

(b)

R \ {4};{-1,1}

(c)

R \ {4};{-1,l}

(d)

R, (-1,1)

13. The unit vector parallel to the resultant of the vectors $\hat{i}+\hat{j}-\hat{k}$ and $\hat{i}-2\hat{j}+\hat{k}$ is

(a)

${\hat{i}-\hat{j}+\hat{k}\over\sqrt{5}}$

(b)

${2\hat{i}+\hat{j}\over\sqrt{5}}$

(c)

${2\hat{i}-\hat{j}+\hat{k}\over\sqrt{5}}$

(d)

${2\hat{i}-\hat{j}\over\sqrt{5}}$

14. A vector $\overrightarrow{OP}$ makes 60° and 45° with the positive direction of the x and y axes respectively.  Then the angle between $\overrightarrow{OP}$and the z-axis is

(a)

45°

(b)

60°

(c)

90°

(d)

30°

15. Two vertices of a triangle have position vectors $3\hat{i}+4\hat{j}-4\hat{k}$ and$2\hat{i}+3\hat{j}+4\hat{k}$If the position vector of the centroid is $\hat{i}+2\hat{j}+3\hat{k}$ ,then the position vector of the third vertex is

(a)

$-2\hat{i}-\hat{j}+9\hat{k}$

(b)

$-2\hat{i}-\hat{j}-6\hat{k}$

(c)

$2\hat{i}-\hat{j}+6\hat{k}$

(d)

$-2\hat{i}+\hat{j}+6\hat{k}$

16. If $|\overrightarrow{a}+\overrightarrow{b}|=60,$ $|\overrightarrow{a} - \overrightarrow{b}|=40$  and $|\overrightarrow{b}|=46$then $|\overrightarrow{a}|$ is

(a)

42

(b)

12

(c)

22

(d)

32

17. If $\overrightarrow{a}=\hat{i}+2\hat{j}+2\hat{k},|\overrightarrow{b}|=5$ and the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is ${\pi\over 6},$ then the area of the triangle formed by these two vectors as two sides, is

(a)

$7\over4$

(b)

$15\over4$

(c)

$3\over4$

(d)

$17\over4$

18. $\int tan^{-1}\sqrt{1-cos \ 2x\over 1+cos \ 2x}dx$ is

(a)

x2+c

(b)

2x2+c

(c)

${x^2\over2}+c$

(d)

$-{x^2\over2}+c$

19. $\int sin \sqrt{x}$ dx is

(a)

$2(-\sqrt{x}cos\sqrt{x}+sin\sqrt{x})+c$

(b)

$2(-\sqrt{x}cos\sqrt{x}-sin\sqrt{x})+c$

(c)

$2(-\sqrt{x}sin\sqrt{x}-cos\sqrt{x})+c$

(d)

$2(-\sqrt{x}sin\sqrt{x}+cos\sqrt{x})+c$

20. The condition that the equation ax2 + bx + c = 0 may have one root is the double the other is:

(a)

2b2 = 9ac

(b)

b2= ac

(c)

b2 = 4ac

(d)

9b2 = 2ac