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

Prove that:

`cosA/(1 + sinA) = secA - tanA`

Prove that:

cos A (1 + cot A) + sin A (1 + tan A) = sec A + cosec A

Prove that:

`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`

Prove that:

`sqrt(sec^2A + cosec^2A) = tanA + cotA`

Prove that:

(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A

Prove that:

(tan A + cot A) (cosec A – sin A) (sec A – cos A) = 1

Prove that

`cot^2A-cot^2B=(cos^2A-cos^2B)/(sin^2Asin^2B)=cosec^2A-cosec^2B`

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?