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

  2. The shaded region in the adjoining diagram represents.

    (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.

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