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#### Quarterly Model Questions Paper

10th Standard EM

Reg.No. :
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Maths

Time : 02:45:00 Hrs
Total Marks : 100
14 x 1 = 14
1. If n(A x B) =6 and A={1,3} then n(B) is

(a)

1

(b)

2

(c)

3

(d)

6

2. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

(a)

2025

(b)

5220

(c)

5025

(d)

2520

3. If $\triangle$ABC is an isosceles triangle with $\angle$C=90o and AC = 5 cm, then AB is

(a)

2.5 cm

(b)

5 cm

(c)

10 cm

(d)

$5\sqrt { 2 }$cm

4. if $\triangle$ABC, DE||BC, AB=3.6cm, AC=24 cm and AD=2.1 cm then the length of AE is

(a)

1.4 cm

(b)

1.8 cm

(c)

1.2 cm

(d)

1.05 cm

5. The slope of the line which is perpendicular to line joining the points (0, 0) and (–8, 8) is

(a)

–1

(b)

1

(c)

$\frac13$

(d)

-8

6. A straight line has equation 8y = 4x + 21. Which of the following is true

(a)

The slope is 0.5 and the y intercept is 2.6

(b)

The slope is 5 and the y intercept is 1.6

(c)

The slope is 0.5 and the y intercept is 1.6

(d)

The slope is 5 and the y intercept is 2.6

7. (1+tan$\theta$+sec$\theta$) (1+cot$\theta$-cosec$\theta$) is equal to

(a)

0

(b)

1

(c)

2

(d)

-1

8. If sin A=$\frac{1}{2}$, then the value of cot A is

(a)

$\sqrt{3}$

(b)

$\frac{1}{\sqrt{3}}$

(c)

$\frac{\sqrt{3}}{2}$

(d)

1

9. If ∆ABC is right angled at C, then the value of cos (A+B) is

(a)

0

(b)

1

(c)

$\frac{1}{2}$

(d)

$\frac{\sqrt{3}}{2}$

10. The value of sin2θ +$\frac { 1 }{ 1+{ tan }^{ 2 }\theta }$ of

(a)

sin2θ

(b)

cos2θ

(c)

secθ

(d)

1

11. The sum of all deviations of the data from its mean is

(a)

Always positive

(b)

always negative

(c)

zero

(d)

non-zero integer

12. If a letter is chosen at random from the English alphabets {a,b,...,z}, then the probability that the letter chosen precedes x

(a)

$\frac{12}{13}$

(b)

$\frac{1}{13}$

(c)

$\frac{23}{26}$

(d)

$\frac{3}{26}$

13. IF the probability of the non-happening of a event is q, then the probability of happening of that event is

(a)

1-q

(b)

q

(c)

q/2

(d)

∝q

14. The variance of 5 values is 16. If each value is doubled. them the standard deviation of new values is_______

(a)

4

(b)

8

(c)

32

(d)

16

15. 10 x 2 = 20
16. If A x B = {(3,2), (3,4), (5,2), (5,4)} then find A and B.

17. Find x if gff(x) = fgg(x), given f(x) = 3x+1 and g(x)=x+3.

18. LetA= {1,2, 3, 4} and B = {-1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} Let R = {(1, 3), (2, 6), (3, 10), (4, 9)} $\subseteq$ A x B bea relation. Show that R is a function and find its domain, co-domain and the range of R.

19. Solve 8x $\equiv$ 1 (mod 11)

20. If A = $\left[ \begin{matrix} 1 & 2 & 1 \\ 2 & -1 & 1 \end{matrix} \right]$ and B = $\left[ \begin{matrix} 2 & -1 \\ -1 & 4 \\ 0 & 2 \end{matrix} \right]$ show that (AB)T = BTAT

21. Find the equation of a straight line passing through (5, - 3) and (7, - 4).

22. $1+\frac { { cot }^{ 2 }\alpha }{ 1+cosex\alpha } =cosec\alpha$

23. The range of a set of data is 13.67 and the largest value is 70.08. Find the smallest value.

24. Find the mean and variance of the first n natural numbers.

25. The marks scored by 5 students in a test for 50 marks are 20, 25, 30, 35, 40. Find the S.D for the marks. If the marks are converted for 100 marks, find the S.D. for newly obtained
marks.

26. 10 x 5 = 50
27. The arrow diagram shows a relationship between the sets P and Q. Write the relation in (i) Set builder form (ii) Roster form (iii) What is the domain and range of R.

28. A functionf: [-7,6) $\rightarrow$ R is defined as follows.

f(-7) -f(-3)

29. The 13th term of an A.P is 3 and the sum of the first 13 terms is 234.Find the common difference and the sum of first 21 terms.

30. Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
4,10,16,22, ...

31. Draw the graph of y = x2 - 4x + 3 and use it to solve x2 - 6x + 9 = 0

32. Construct a triangle $\triangle$PQR such that QR = 5 cm, $\angle$P=30 and the altitude from P to QR is of length 4.2 cm.

33. Find the coordinates of the point of contact of line AB with the circle.

34. Find the area of a triangle whose vertices are (1, -1), (-4, 6) and (-3, -5).

35. If ATB=90o then prove that
$\sqrt { \frac { tanA\quad tanB+tanA\quad cotB }{ sinA\quad secB } } -\frac { { Sin }^{ 2 }A }{ { Cos }^{ 2 }A } =tanA$

36. Find the co-efficient of variation for the following data: 16, 13, 17,21, 18.

37. 2 x 8 = 16
38. A graph representing the function f (x) is given in Fig.1.16 it is clear that f (9) = 2.
(i) Find the following values of the function
(a) f(0)
(b) f(7)
(c) f(2)
(d) f(10)
(ii) For what value of x is f (x) = 1?
(iii) Describe the following (i) Domain (ii) Range.
(iv) What is the image of 6 under f ?

39. Using the functions f and g given below, find f o g and g o f. Check whether f o g = g o f.
f(x) = x-6, g(x)=x2