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

Prove that:

(cosec A – sin A) (sec A – cos A) sec² A = tan A

Prove that: 
(cosec θ - sinθ )(secθ - cosθ ) ( tanθ +cot θ) =1

Simplify 

sin A `[[sinA   -cosA],["cos A"  " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`

Using the remainder theorem, find the remainders obtained when x³ + (kx + 8 )x + k is divided by x + 1 and x − 2. 

Hence, find k if the sum of the two remainders is 1.

Shekhar had a fixed deposit of Rs 24000 for 3 years . If he received interest at 10% p.a compounded annually, find the amount received by him at the time of maturity.

Prashant borrowe Rs. 35000 at 12% p.a. compounded semi-annually. Find the amount he needs to pay back at the end of `1 1/2` years

Amita wanted to start a business for which she needed Rs, 40000. She borrowed this from Dolly at 10% p.a compounded semi-annually. Find the extra amount that she needs to pay at the end of two years to clear her debt. 

Pradeep gave Rs.16000 to a friend for 1.5 years at 15% p.a. compounded semi-annually. Find the interest earned by him at the end of 1.5 years. 

Mr.Mohan invested Rs. 12500 at 16 % p.a. compounded annually. If the duration of the deposite was 1.5 years , find the amount Mr.Mohan received at the end of 1.5 years.

Rajeev borrowed Rs 15,000 from Sanjay at 12% p.a. compound interest. After 2 years Rajeev gave Rs 7,500 and a scooter to clear the account. Find the cost of the scooter.

Manoj borrowed Rs 25,000 from Sohan at 8.4 % p.a. compound interest. After 2 years Manoj cleared Rs 17,500 and a motorcycle. Find the cost of the motorcycle.

Mr. Chatterjee borrowed Rs 50,000 in compound interest from Mr. Patel for 2 years when the rates of interest for the successive years were `7 1/2 %` and `9 1/4 %`. If Mr. Chatterjee returned Rs 27, 750 at the end of the first year, find the amount he needs to return at the end of the seoond year to clear the loan. 

What sum of money will amount to Rs 9,447.84 in 3 years at 8% p.a. compound interest?

What sum of money will amount to Rs 16,637.50 in 3 years at 10 % p.a. compound interest?

What sum of money will amount to Rs 7,128 in 2 years at compound interest, if the rates of interest are 8% and 10% for successive years?

What sum of money will amount to Rs 3,326.40 in 3 years at compound interest, if the rates of interest are 8%, 10% and 12% for the successive years?

What sum of money will amount to Rs 13,675.20 in 3 years at compound interest, if the rates of interest are 10%, 11% and 12% for the successive years?

The value of a machine depreciates by 15% in the first year and by 12% in the second year. Find the value of the machine if its depreciation in the second year was Rs 1,632.

The value of a 'Honda' bike depreciated by 16% in the first year and by 13% in the second year. Find the value of the bike if it depreciated by Rs 7,098 in the second year.

The interests on two successive years for a sum invested at compound interest compounded annually are Rs 840 and Rs 940.80. Calculate the rate of interest and the sum invested.