Manipur Class 10 Sample Paper Maths

Manipur

SAMPLE PAPER
Class 10

SAMPLE QUESTION PAPER
MATHEMATICS
CLASS - X
TIME : 3 HRS FULL MARK : 80

Attempt all questions.

For question nos. 1 to 5, write the letter corresponding to the correct answer. The figures in the
right margin indicate full marks for the questions.

1. The number of days within which the stock exchange is supposed to resolve dispute at their
end is
(A) 10 (B) 15 (C) 20 (D) 30 1
2. The remainder when 4x + 4 x + x - 4 is divided by 2x – 1
3 2

(A) 2 (B) -2 (C) 4 (D) - 4 1
3. The sum of the first n terms of the AP whose first term is 1 and common difference is 2 is :
(A) 3n (B) 2n - 1 (C) n2 (D) n(n + 1) 1
4. A point P is at a distance of 13 cm from the centre of a circle. If the radius of the circle is 5 cm,
the length of the tangent from P to the circle is 1
(A) 12 cm (B) 13 cm (C)15 cm (D) 18 cm
5. The volume of the hemisphere of radius r is 1
4 1 2
(A) πr3 (B) πr3 (C) πr3 (D) 4πr3
3 3 3
6. Write the statement of Euclid's Division Lemma. 1
7. What is the first term of the quotient when 2x3 + x2 – 3x + 5 is divided by 1-3x + x2 ? 1
8. Write down the quadratic equation whose roots are 2 and -3. 1
9. Write the full form of SCORES. 1
10. How many tangents can be drawn to a circle through a point lying outside the circle ? 1
11. Write down the formula to find the area of a triangle whose vertices are (x1,y1), (x2,y2) and
(x3,y3). 1
12. Find the area of a circle whose radius is 7 cm. 1
13. Define mode of a frequency distribution. 1
14. If x,y,z are real numbers, x ≠ 0, and xy = xz, prove that y= z. 2
15. Prove that xn – yn is divisible by x+y only when n is even. 2
16. The nth term of a sequence is given by an = 5n-3. Show that the sequence is an AP. 2
17. State Pythagoras theorem and also its converse. 2
3
18. If Cos A = , calculate Sin A and Tan A. 2

5
19. Show that the square of an odd integer is of the form 8k + 1. 3

20. Solve the quadratic equation ax2 + bx + c = 0, (a ≠ 0) by the method of completing square. 3
21. Solve graphically :
2x + 3y = 5
5x – 4y + 22 = 0 3
22. In a right triangle ABC, right angled at B, Prove that Sin A = Cos (900 – A) and
Cos A = Sin (900 – A). 3
𝜋𝑟 2 𝜃
23. Prove that the area of a sector of sectorial angle and radius r is . 3
360

24. Find the lower quartile of the following distribution of marks. 3
. Marks No. of students
0-4 10
4-8 12
8-12 18
12-14 7
14-18 5
18-20 8
20-25 4
25 and above 6
1
25. Show that 𝑎3 + 𝑏 3 + 𝑐 3 − 3𝑎𝑏𝑐 = 2 (𝑎 + 𝑏 + 𝑐){(𝑎 − 𝑏)2 + (𝑏 − 𝑐)2 + (𝑐 − 𝑎)2 } 4
26. The ratio of incomes of two persons is 9:7 and the ratio of their expenditures is 4:3.1f each of
them saves Rs. 5000 per month, find their monthly incomes. 4
27. Find the area of the quadrilateral whose vertices are (1,1), (3,4), (5,-2) and (4, -7) taken in order.
4
Or,
If three consecutive vertices of a parm are A(1, -2), B(3, 6) and C(5, 10), find its fourth vertex.
3
28. Construct a triangle similar to the triangle ABC with its side's equal to of the corresponding
5
sides of the ABC. Write the steps of construction also. 5.
Or,
Divide a line AB in the ratio 2:3. Write the steps of construction also.

29. A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h.
At a point on the plane, the angle of elevation of the bottom of the flagstaff is α and that of the
𝒉 𝐭𝐚𝐧∝
top of the flagstaff is β . Prove that the height of the tower is . 5
𝐭𝐚𝐧 𝜷−𝒕𝒂𝒏𝜶

30. A metallic sphere of radius 9 cm is melted and recast to form a cylinder of radius 3 cm. Find the

curved surface area of the cylinder. 5

31. State and prove Basic Proportionality Theorem. 6
Or,
Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their
corresponding sides.

32. Find the mean and median of the following distribution : 6
Class Frequency
30 - 40 12
40 - 50 18
50 - 60 20
60 - 70 15
70 - 80 12
80 - 90 11
90 -100 6
100 - 110 4
110 - 120 2
Total 100