#### First Mid Term Model Questions

11th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
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

(a)

A\B

(b)

A'

(c)

B'

(d)

B\A

3. Find a so that the sum and product of the roots of the equation 2x2+(a-3)x+3a-5 = 0 are equal is

(a)

1

(b)

2

(c)

0

(d)

4

4. In a $\triangle$ ABC, C = 90° then the value of sin A + sin B-2$\sqrt{2} cos{A\over2}cos {B\over 2}is$

(a)

-1

(b)

1

(c)

0

(d)

${1\over 2}$

5. If nPt = 720 nCr, then the value of r =

(a)

6

(b)

5

(c)

4

(d)

7

6. 5 x 2 = 10
7. Write the set {-1, 1} in set builder form.

8. It sec $\theta$ + tan $\theta$ = p, obtain the values of sec $\theta$, tan $\theta$ and sin $\theta$ in terms of p

9. Find the value of $\frac { 12! }{ 9!\times 3! }$

10. In how many ways can the letters of the word PENCIL be arranged so that N is always next to E.

11. A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected, if the team has atleast one boy and one girl

12. 5 x 3 = 15
13. A salesperson whose annual earnings can be represented by the function A(x)=30,000 + 0.04x, where x is the rupee value of the merchandise he sells.His son also in sales and his earnings are represented by the function S(x)=25,000 + 0.05x.Find (A+S) (x) and determine the total family income if they each sell Rs.1,50,00,000 worth of merchandise.

14. Find the range of the following functions given by  $f(x) = \frac { 1 }{ 2-sin\ 3x } .$

15. If $tan A=\frac{5}{6},tan B=\frac{1}{11}$show that A + B = 45°.

16. If the letter of the word 'RACHIT' are arranged in all possible ways as listed in dictionary, then what is the rank of the word 'RACHIT'?

17. If${1\over 7!}+{1\over9!}={x\over10!},$findx.

18. 4 x 5 = 20
19. A simple cipher takes a number and codes it, using the function f(x)=3x-4. Find the inverse of this function, determine whether the inverse is also a function and verify the symmetrical property about the line y=x(by drawing the lines)

20. 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

21. A committee of 7 peoples has to be formed from 8 men and 4 women. In how many ways can this be done when the committee consists of
(i) exactly 3 women?
(ii) at least 3 women?
(iii) at most 3 women?

22. For any natural number n, 7n - 2n is divisible by 5.