10th Maths Periodic Test I (2018-19)
Time: 1 hour 30 minutes
Maximum Marks: 40
- 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 ax2 + 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 5x2 – 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.
tan 28° 1
————- + ——– (tan 20°. tan 60°. tan 70°)
cot 62° + 1 √3
- Find the positive value of k for which x2 + kx + 64 = 0 and x2 – 8x + k = 0 will have real roots.
- 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
- 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.