#### First Mid Term Model Questions

10th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
10 x 1 = 10
1. If n(A x B) =6 and A={1,3} then n(B) is

(a)

1

(b)

2

(c)

3

(d)

6

2. If g={(1,1), (2,3), (3,5), (4,7)} is a function givrn by g(x)=αx+β then the values of α and β are

(a)

(-1,2)

(b)

(2,-1)

(c)

(-1,-2)

(d)

(1,2)

3. 74k $\equiv$ ________ (mod 100)

(a)

1

(b)

2

(c)

3

(d)

4

4. An A.P. consists of 31 terms. If its 16th term is m, then the sum of all the terms of this A.P. is

(a)

16 m

(b)

62 m

(c)

31 m

(d)

$\frac { 31 }{ 2 }$

5. The value of (13+23+33+...153) - (1+2+3+...+15)is

(a)

14400

(b)

14200

(c)

14280

(d)

14520

6. The solution of (2x - 1)2 = 9 is equal to

(a)

-1

(b)

2

(c)

-1, 2

(d)

None of these

7. Graph of a linear polynomial is a

(a)

straight line

(b)

circle

(c)

parabola

(d)

hyperbola

8. 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

9. A tangent is perpendicular to the radius at the

(a)

centre

(b)

point of contact

(c)

infinity

(d)

chord

10. The two tangents from an external points P to a circle with centre at O are PA and PB.If $\angle APB$=70o then the value of $\angle AOB$ is

(a)

100°

(b)

110°

(c)

120°

(d)

130°

11. 5 x 2 = 10
12. Find the 8th term of the G.P 9,3,1,....

13. Find the geometric progression whose first term and common ratios are given by
a = 256 , r = 0.5

14. Use Euclid's algorithm to find the HCF of 4052 and 12756.

15. Solve the following system of linear equations in three variables.
x + y + Z = 6; 2x + 3y + 4z = 20;
3x + 2y + Sz = 22

16. Construct a triangle similar to a given triangle PQR with its sides equal to$\cfrac { 7 }{ 4 }$ of the corresponding sides of the triangle PQR (scale factor $\cfrac { 7 }{ 4 }$>1)

17. 5 x 3 = 15
18. Let f = {(2, 7); (3, 4), (7, 9), (-1, 6), (0, 2), (5,3)} be a function from A = {-1,0, 2, 3, 5, 7} to B = {2, 3, 4, 6, 7, 9}. Is this (i) an one-one function (ii) an onto function, (iii) both oneone and onto function?

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

20. Multiply $\frac { { x }^{ 4 }{ b }^{ 2 } }{ x-1 }$ by $\frac { { x }^{ 2 }-1 }{ { a }^{ 4 }{ b }^{ 3 } }$

21. PQ is a chord of length 8 cm to a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length of the tangent TP.

22. Draw a circle of diameter 6 cm from a point P, which is 8 cm away from its centre. Draw the two tangents PA and PB to the circle and measure their lengths.

23. 3 x 5 = 15
24. Graph the following quadratic equations and state their nature of solutions.
x2 + x + 7 = 0

25. The perpendicular from A on side BC at a $\triangle$ABC intersects BC at D such that DB = 3 CD. Prove that 2AB2 = 2AC2 + BC2.

26. In $\triangle$ABC, D and E are points on the sides AB and AC respectively such that DE||BC If AD=8x-7, DB=5x-3, AE=4x-3, and EC =3x, find the value of x.