#### CBSE Half Yearly Sample Paper 2020-21 Mathematics for class 10

Class-10

Time allowed-3:00 hours

Maximum Marks-80

All questions are compulsory.

(Question No. 1 to 15 are of 1 mark each)

1- Find HCF of 12 and 15.

2- Find the Simplest form of 148/185.

3- Find Zeros x^{2} – 2x – 3.

4- Verify that 2 is a zero of the polynomial x^{3} + 4 x^{2} – 3x – 18.

5- Solve 10x – 1/x = 3.

6- For what values of K, the roots of the equation x^{2} – kx + 1 = 0 are imaginary.

7- If (x + 2). 2x, (2x + 3) are these consecutive terms of an AP then x = ?

8- The 11^{th} term of the AP -3, -1/2, 2, ——–is.

9- Find the length of tangent drow to a circle with radius 8 cm from a point 17 cm away from the center of the circle.

10- Write general from of quadratic equation.

11- Sin^{2}θ + cos^{2}θ =?

12- Evaluate Sin60^{0} Cos30^{0} + Cos60^{0} Sin30^{0 }

13- If Sin θ = √3/2. Find Cos θ.

14- Find Sin^{2}60^{0 }– 1.

15- For what values of K does the pair of educations x – 2y = 3 and 3x + ky= 1 have unique solution ?

(Question No. 16 to 24 are of 2 marks each)

16- Prove that (1 – Sin^{2}60^{0}). Secθ = 1.

17- Given that HCF (306, 657) = 9, Find LCM (306, 657).

18- Find a quadratic polynomial as the sum and product of its zeroes are ¼ and -1.

19- Solve: x + y = 14 and x – y = 4.

20- Find the roots of x^{2} – 3x – 10.

21- Which term of AP: 3, 8, 13, 18, ———– is 78?

22- Determine if the points (1, 5), (2, 3), and (-2, 3) are Collinear.

23- Prove that Cos A/1+Sin A + 1+Sin A/Cos A = 2 Sec A.

24- Prove that 3 +2is irrational.

(Question No. 25 to 33 are of 3 marks each)

25- Obtain all other Zeroes of 3x^{4} + 6x^{3} – 2x^{2} -10x – 5.

26- For which values of a and b does the following pair of liner equations have an infinite Number of solutions?

2x + 3y = 7

(a – b) x + (a + b) y = 3a + b – 2

27- Find two numbers whose sum is 27 and product is 182.

28- The diagonals of a quadrilateral ABCD interest each other at the point O such that AO/BO = CO/DO.

29- Find the sum of the 40 positive integers divisible by 6.

30- If A and B are (-2, -2)and (2, -4) respectively.Find the coordinates of P such that AP = 3/7 AB and P lies on the on the line segment AB.

31- If tan (A + B) =√3 and tan (A – B) = 1/√3 ; θ^{0}< A + B ≤ 90^{0}. A > B, Find A and B.

32- The angels of elevation of the top of a tower from two points at a distance of 4m and 9m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6m.

33- Prove that the tangent down from an external point to a circle are equal.

(Question No. 34 to 37 are of 5 marks each)

34- A triangle ABC is down to circum scribe a circle of radius 4 cm such that the segment BD and DC into Which BC is divided by the point of contact D are of length 8 cm and 6 cm respectively. Find the sides AB and AC.

35- A Straight highway leads to the foot of a tower. A man standing at the top of the tower observe a car at an angle of depression of 30^{0}, which is approaching. The foot of tower with a uniform speed. Six second later, the angle of depression of the car is found to be 60^{0}. Find the time taken by car to reach the foot of the tower from this point.

36- Prove that = Cosec A + Cot A.

37- In an equilateral triangle ABC, D is point on side BC such that BD = Prove that 9AD^{2} = 7AB^{2}.