10th Maths Periodic Test I (2018-19)

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

1. 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.
2. Find the nature of roots of ax² + bx + c = 0, a > 0, b = 0, c > 0.
3. 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
4. Given 2 cos 3θ = √3, find the value of θ.
5. 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.
6. For what value of   k  will the following pair of linear equations have no solution?
   2x + 3y = 9
   6x + (k – 2)y = (3k – 2)
7. Find a quadratic polynomial with zero 3 + √2 and 3 – √2.
8. 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.
9. Find the zeroes of the polynomial 5x² – 8x – 4 and verify the relationship between the zeroes and the coefficients.
10. 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.
11. Solve the equation  + 6 = 0 by method of completing the square.
12. Simplify
    tan 28°                 1
    ————- + ——– (tan 20°. tan 60°. tan 70°)
    cot 62° + 1         √3
13. Find the positive value of   k   for which x² + kx + 64 = 0 and x² – 8x + k = 0 will have real roots.
14. Prove that:
    cot³ θ. sin³ θ                tan³ θ. cos³ θ           sec θ cosec θ – 1
    ——————- +  ——————— = ———————-
    (cos θ. + sin θ)²          (cos θ. + sin θ)^{2           cosec θ + sec θ}
15. 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.
16. 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.