**10th Maths Periodic Test I (2018-19)**

**School Name: Venkateshwar Global School**, Sector 13, Rohini, Delhi 110085

**India**

**Class:**10

**Subject:**

**Mathematics**

**Time:**1 hour 30 minutes

**Maximum Marks:**40

**Date: 18/07/2018**

- The H.C.F of two number is 145 and their L.C.M is 2175. If one number is 725, then find the other number.
- Find the nature of roots of ax
^{2 }+ bx + c = 0, a > 0, b = 0, c > 0. - Find whether the given lines representing the following pair of liner equations intersect at a point, are parallel or coincident.

2x – 3y = 8

4x – 6y = 9 - Given 2 cos 3θ = √3, find the value of θ.
- Given that cos (A – B) = cos A cos B + sin A sin B, find the value of cos 15° by taking suitable values of A and B.
- For what value of k will the following pair of linear equations have no solution?

2x + 3y = 9

6x + (k – 2)y = (3k – 2) - Find a quadratic polynomial with zero 3 + √2 and 3 – √2.
- Without actually performing the long division, state whether 257/500 has a terminating decimal expansion or not. Also write the terminating decimal expansion if it exists.
- Find the zeroes of the polynomial 5x
^{2 }– 8x – 4 and verify the relationship between the zeroes and the coefficients. - Solve the following system of linear equations graphically
5x – 7y = 50

5x + 7y = 20

Also write the coordinates of the points where they meet x axis. - Solve the equation + 6 = 0 by method of completing the square.
- Simplify
tan 28° 1

————- + ——– (tan 20°. tan 60°. tan 70°)

cot 62° + 1 √3 - Find the positive value of k for which x
^{2 }+ kx + 64 = 0 and x^{2 }– 8x + k = 0 will have real roots. - Prove that:
cot

^{3 }θ. sin^{3 }θ tan^{3 }θ. cos^{3 }θ sec θ cosec θ – 1

——————- + ——————— = ———————-

(cos^{ }θ. + sin^{ }θ)^{2 }(cos^{ }θ. + sin^{ }θ)^{2 cosec θ + sec θ} - A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank is 60°. When he retires 40 metres from the bank, he finds the angle of elevation to be 30°. Find the width of the river.
- A man has certain notes of denomination of Rs. 20 and Rs. 5 which amount to Rs. 380. If the number of the each king are interchanged, they amount Rs. 60 less than before. Find the number of notes of each denomination.