CBSE Guess Paper

Subject – Mathematics

Class - 10th

1. A number consists of two digits whose sum is 9. If 27 is added to the number, the digits are interchanged. Find the number.

2. Show that 2 + √3 is irrational number.

3. Prove that: cosA/(1+sinA) + (1+sinA)/cosA = 2secA.

4. The sum of the digits of a two digit no. is 12. The no. obtained by interchanging the digits exceeds the given no. by 18. Find the no.

5. Prove that the area of the equilateral Δ described on the side of a square is half the area of equilateral Δ described on its diagonals.

6. PQR is a right-angled triangle, having DQ = 90°, If QS = SR, Show that PR² = 4 PS² — 3 PQ² .

7. There are two poles, one each on either bank of a river. just opposite to each other. One pole is 60m high. From the top of this pole, the angles of depression of the top and the foot of the other pole are30⁰ and60⁰ respectively. Find the width of the river and the height of the other pole.

8. The co-ordinates of the vertices of ΔABC are A (4,1),B (-3,2) and C ( 0 , k).Given that the area of ABC is 12unit² find the value of k.

9. Find the 20^th term of the AP whose 7^th term is 24 less than the 11^th term, first term being 12.

10. A (6, 1), B (8, 2) and C (9, 4) are three vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of DADE.

11. Find the roots of the equation 63/x + 72/(x+6)=3.

12. From an external point B of a circle with centre O two tangents BC and BD are drawn such that ∠DBC=1200 .Prove that BC +BD = BO.

13. Find the area of Δ formed by vertices ( a, b+c) ( b,c+a) and (c , a+b).

14. Solve   cosA/(1 + sinA) + (1 + sinA)/cosA = 2 secA.

15. α, β are the zeros of the quadratic polynomial x² – (k-1)x + 2(2k-1). Find the value of k if α + β = ½ αβ.

16. Evaluate:

[{sec²θ – cot²(90 - θ)}/{5(sin² 52⁰ + sin² 38⁰)}] – [(3 cot² 60⁰. cosec² 72⁰. cos² 18⁰)/(cosec² 54⁰ – tan² 36⁰)]

17. Prove that: Sin⁶A + Sin⁴Acos²A – sin²Acos⁴A – Cos⁶A = 1 – 2 Cos²A.

18. On dividing x³- 3x²+ x +2 by a polynomial g(x), the quotient and remainder were x-2 and -2x + 4 respectively. Find g (x).

19. The following distribution gives the daily income of 50 workers of a factory.

Daily Income (In Rs)	100-120	120-140	140-160	160-180	180-200
No. of Workers	12	14	8	6	10

Convert the distribution above to a more than type cumulative frequency distribution, and draw its Ogive.

20. Find the value of ‘p’ if mean of following data is 53.

Class	0‐20	20‐40	40‐60	60‐80	80‐100
Frequency	12	15	32	p	13