(English Medium) ICSE Class 9 - CISCE Question Bank Solutions

If sin(θ - 15°) = cos(θ - 25°), find the value of θ if (θ-15°) and (θ - 25°) are acute angles.

If A, B and C are interior angles of ΔABC, prove that sin`(("A" + "B")/2) = cos  "C"/(2)`

If P, Q and R are the interior angles of ΔPQR, prove that `cot(("Q" + "R")/2) = tan  "P"/(2)`

If cosθ = sin60° and θ is an acute angle find the value of 1- 2 sin²θ

If secθ= cosec30° and θ is an acute angle, find the value of 4 sin²θ - 2 cos²θ.

Prove the following: tanθ tan(90° - θ) = cotθ cot(90° - θ)

Prove the following: sin58° sec32° + cos58° cosec32° = 2

Prove the following: `(tan(90° - θ)cotθ)/("cosec"^2 θ)` = cos²θ

Prove the following: sin²30° + cos²30° = `(1)/(2)sec60°`

If A + B = 90°, prove that `(tan"A" tan"B" + tan"A" cot"B")/(sin"A" sec"B") - (sin^2"B")/(cos^2"A")` = tan²A

Find the value of 'a' and 'b' if
a. (a + 2,5 + b) = (1, 6)
b. (2a + b, a - 2b) = (7, 6)

Each of the equal sides of an isosceles triangle is 4 cm greater than its height. If the base of the triangle is 24 cm; calculate the perimeter and the area of the triangle.

A sum is invested at compound interest, compounded yearly. If the interest for two successive years is Rs. 5,700 and Rs. 7,410. calculate the rate of interest.

A certain sum of money is put at compound interest, compounded half-yearly. If the interest for two successive half-years are Rs. 650 and Rs. 760.50; find the rate of interest.

A certain sum amounts to Rs. 5,292 in two years and Rs. 5,556.60 in three years, interest being compounded annually. Find : the rate of interest.

A certain sum amounts to Rs. 5,292 in two years and Rs. 5,556.60 in three years, interest being compounded annually. Find: the original sum.

The compound interest, calculated yearly, on a certain sum of money for the second year is Rs. 1,089 and for the third year it is Rs. 1,197.90. Calculate the rate of interest and the sum of money.

Mohit invests Rs. 8,000 for 3 years at a certain rate of interest, compounded annually. At the end of one year it amounts to Rs. 9,440. Calculate: 

1. the rate of interest per annum.
2. the amount at the end of the second year.
3. the interest accrued in the third year.

Geeta borrowed Rs. 15,000 for 18 months at a certain rate of interest compounded semi-annually. If at the end of six months it amounted to Rs. 15,600; calculate :
(i) the rate of interest per annum.
(ii) the total amount of money that Geeta must pay at the end of 18 months in order to clear the account.

Ramesh invests Rs. 12,800 for three years at the rate of 10% per annum compound interest. Find:

1. the sum due to Ramesh at the end of the first year.
2. the interest he earns for the second year.
3. the total amount due to him at the end of the third year.