(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

If m = a sec A + b tan A and n = a tan A + b sec A, then prove that : m² – n² = a² – b²

If x = r sin A cos B, y = r sin A sin B and z = r cos A, then prove that : x² + y² + z² = r²

If sin A + cos A = m and sec A + cosec A = n, show that : n (m² – 1) = 2 m

If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x² + y² + z² = r²

If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m² + n²) cos² B = n².

How much money will be required to buy 200, Rs. 25 shares at a premium of Rs. 2?

How much money will be required to buy 125, Rs. 30 shares at a discount of Rs. 3?

Show that : tan 10° tan 15° tan 75° tan 80° = 1

Show that : `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec A cosec A`

Show that : `sinAcosA - (sinAcos(90^circ - A)cosA)/sec(90^circ - A) - (cosAsin(90^circ - A)sinA)/(cosec(90^circ - A)) = 0`

A man bought Rs. 40 shares at a discount of 40%. Find his income, if he invests Rs. 12,000 in these shares and receives a dividend at the rate of 11% on the face value of the shares.

Rajat buys Rs. 80 shares at 30% premium in a company paying 18% dividend. Find:
(i) The market value of 150 shares.
(ii) Rajat’s annual income from these shares.
(iii) Rajat’s percentage return from this investment.

Peter invests Rs. 5,625 in a company paying 7% per annum when a share of Rs. 10 stands from Rs. 12.50. Find Peter’s income from this investment.
If he sells 60% of these shares from Rs. 10 each, find his gain or loss in this transaction.

A company gives x% dividend on its Rs. 60 shares, whereas the return on the investment in these shares is (x + 3) %. If the market value of each share is Rs. 50, find the value of x.

Mr. Gupta has a choice to invest in ten-rupee shares of two firm at Rs. 13 or at Rs. 16. If the first firm pays 5% dividend and the second firm pays 6% dividend per annum, find:

1. which firm is paying better.
2. if Mr. Gupta invests equally in both the firms and the difference between the returns from them is Rs. 30, find how much, in all, does he invest?

Prove the following identities:

`1/(cosA + sinA) + 1/(cosA - sinA) = (2cosA)/(2cos^2A - 1)`

Prove the following identities:

`cosecA - cotA = sinA/(1 + cosA)`

Prove the following identities:

`1 - sin^2A/(1 + cosA) = cosA`

Prove the following identities:

`(1 - cosA)/sinA + sinA/(1 - cosA)= 2cosecA`

Prove the following identities:

`cotA/(1 - tanA) + tanA/(1 - cotA) = 1 + tanA + cotA`