List of top Mathematics Questions

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{sin\,x+cos\,x}{sin\,x-cos\,x}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{cos\,x}{1+sin\,x}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): cosec x cot x

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): sin (x + a)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): (ax +b)ⁿ (cx + d)^m

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): (ax +b)ⁿ

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{px^2+qx+r}{ax+b}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers):\(\frac{ax+b}{px^2+qx+r}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers):\(\frac{1}{ax^2+bx+c}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{1+\frac{1}{x}}{1-\frac{1}{x}}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers):\(\frac{(ax+b)}{(cx+d)}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): (ax + b) (cx + d)²

Find the derivative of the following functions from first principle:
(i) −x (ii) (-x)-1 (iii) sin (x + 1) (iv) cos (x – \(\frac{\pi}{8}\))

A die is thrown once. Find the probability of getting 
(i) a prime number; 
(ii) a number lying between 2 and 6;
(iii) an odd number.

A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see the given figure), and these are equally likely outcomes. What is the probability that it will point at
(i) 8?
(ii) an odd number? 
(iii) a number greater than 2?
(iv) a number less than 9?

How many terms of the AP : 9, 17, 25, ..... must be taken to give a sum of 636?

Find the sum of the odd numbers between 0 and 50.

Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish (see the given figure).What is the probability that the fish taken out is a male fish?

Find the sum of the first 15 multiples of 8.

Find the sum of the first 40 positive integers divisible by 6.

If the sum of the first n terms of an AP is \(4n – n^2 \), what is the first term (that is \(S_1\))? What is the sum of first two terms? What is the second term? Similarly, find the \(3^{rd}\), the \(10^{th}\) and the \(n^{th}\) terms.

A box contains 5 red marbles,8 white marbles and 4 green marbles.One marble is taken out of the box at random.What is the probability that the marble taken out will be
(i) red?  (ii) white?  (iii) not green?

Show that \(a_1, a_2, . . ., a_n, .....\) form an AP where an is defined as below:

1. \(a_n = 3 + 4n\)
2. \(a_n = 9 – 5n\)

Also find the sum of the first 15 terms in each case.

Form the pair of linear equations in the following problems, and find their solutions graphically. (i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.(ii) 5 pencils and 7 pens together cost Rs50, whereas 7 pencils and 5 pens together cost Rs46. Find the cost of one pencil and that of one pen.

It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?