#### August Monthly Model Test Paper

10th Standard EM

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Maths

Time : 02:30:00 Hrs
Total Marks : 100
14 x 1 = 14
1. A system of three linear equations in three variables is inconsistent if their planes

(a)

intersect only at a point

(b)

intersect in a line

(c)

coincides with each other

(d)

do not intersect

2. y2 + $\frac {1}{y^{2}}$ is not equal to

(a)

$\frac {y^{2} + 1}{y^{2}}$

(b)

${ \left( y+\frac { 1 }{ y } \right) }^{ 2 }$

(c)

${ \left( y-\frac { 1 }{ y } \right) }^{ 2 }+2$

(d)

${ \left( y+\frac { 1 }{ y } \right) }^{ 2 }-2$

3. The square root of $\frac { 256{ x }^{ 8 }{ y }^{ 4 }{ z }^{ 10 } }{ 25{ x }^{ 6 }{ y }^{ 6 }{ z }^{ 6 } }$ is equal to

(a)

$\frac { 16 }{ 5 } \left| \frac { { x }^{ 2 }{ z }^{ 4 } }{ { y }^{ 2 } } \right|$

(b)

$16\left| \frac { { y }^{ 2 } }{ { x }^{ 2 }{ z }^{ 2 } } \right|$

(c)

$\frac { 16 }{ 5 } \left| \frac { y }{ x{ z }^{ 2 } } \right|$

(d)

$\frac { 16 }{ 5 } \left| \frac { x{ z }^{ 2 } }{ y } \right|$

4. Transpose of a column matrix is

(a)

unit matrix

(b)

diagonal matrix

(c)

column matrix

(d)

row matrix

5. In $\angle$LMN, $\angle$L=60o,$\angle$M=50o, If $\triangle$LMN~$\triangle$PQR then the value of $\angle$R is

(a)

40o

(b)

70°

(c)

30°

(d)

110°

6. 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

7. In the adjacent figure $\angle BAC$=90o nd AD$\bot$BC then

(a)

BD-CD=BC2

(b)

AB.AC=BC2

(c)

(d)

8. Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?

(a)

13 m

(b)

14 m

(c)

15 m

(d)

12.8 m

9. A tangent is perpendicular to the radius at the

(a)

centre

(b)

point of contact

(c)

infinity

(d)

chord

10. The point of intersection of 3x − y = 4 and x + y = 8 is

(a)

(5, 3)

(b)

(2, 4)

(c)

(3, 5)

(d)

(4, 4)

11. The slope of the line joining (12, 3) , (4, a) is $\frac 18$The value of ‘a’ is

(a)

1

(b)

4

(c)

-5

(d)

2

12. 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

13. When proving that a quadrilateral is a trapezium, it is necessary to show

(a)

Two sides are parallel.

(b)

Two parallel and two non-parallel sides.

(c)

Opposite sides are parallel.

(d)

All sides are of equal length.

14. When proving that a quadrilateral is a parallelogram by using slopes you must find

(a)

The slopes of two sides

(b)

The slopes of two pair of opposite sides

(c)

The lengths of all sides

(d)

Both the lengths and slopes of two sides

15. 10 x 2 = 20
16. Solve x + 2y - z = 5; x - y + z = -2; -5x - 4y + z = -11

17. Solve x4 - 13x2 + 42 = 0

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

19. Using quadratic formula solve the following equations.
9x2-9(a+b)x+(2a2+5ab+2b2)=0

20. $\angle A=\angle CED$ prove that $\Delta\ CAB \sim \Delta CED$ Also find the value of x.

21. P and Q are the mid-points of the sides CA and CB respectively of a $\triangle$ABC, right angled at C.4(AQ2+BP2)=5AB2

22. In figure if PQ || RS Prove that $\Delta POQ\sim \Delta SOQ$

23. Two buildings of different heights are located at opposite sides of each other. If a heavy rod is attached joining the terrace of the buildings from (6,10) to (14,12), find the equation of the rod joining the buildings ?

24. A circular garden is bounded by East Avenue and Cross Road. Cross Road intersects North Street at D and East Avenue at E. AD is tangential to the circular garden at A(3, 10). Using the figure.

Where does the Cross Road intersect the
(i) East Avenue ?
(ii) North Street ?

25. If A (-5, 7), B (-4, -5), C (-1, -6) and D (4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

26. 10 x 5 = 50
27. Multiply $\frac { { x }^{ 3 } }{ 9{ y }^{ 2 } }$ by $\frac {27y} {x^{5}}$

28. Solve 2x2 - x - 1 = 0

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

30. Discuss the nature of solutions of the following quadratic equations.
x2 - 8x + 16 = 0

31. The sum of two numbers is 15. If the sum of their reciprocals is $\frac{3}{10}$, find the numbers.

32. In Fig,$\triangle$ABC is circumscribing a circle. Find the length of BC.

33. In Fig, ABC is a triangle with $\angle$B=90o, BC=3cm and AB=4 cm. D is point on AC such that AD=1 cm and E is the midpoint of AB. Join D and E and extend DE to meet CB at F. Find BF.

34. In $AD\bot BC$ prove that AB2+CD2 = BD2+AC2

35. BL and CM are medians of a triangle ABC right angled at A.
Prove that 4(BL+ CM2) = 5BC2.

36. If the points A(6, 1), B(8, 2), C(9, 4) and D(P, 3) are the vertices of a parallelogram, taken in order. Find the value of P.

37. 2 x 8 = 16
38. The number of seats in a row is equal to the total number of rows in a hall. The total number of seats in the hall will increase by 375 if the number of rows is doubled and the number of seats in each row is reduced by 5. Find the number of rows in the hall at the beginning.

39. There are 12 pieces of five, ten and twenty rupee currencies whose total value is Rs.105. When first 2 sorts are interchanged in their numbers its value will be increased by Rs.20. Find the number of currencies in each sort.