List of top Mathematics Questions

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
(i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes \(\frac{1}{2}\) if we only add 1 to the denominator. What is the fraction?
(ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
(iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
(iv) Meena went to bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Find how many notes of Rs 50 and Rs 100 she received.
(v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out
(i) an orange flavoured candy?
(ii) a lemon flavoured candy?

The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

If P(E) = 0.05, what is the probability of 'not E'?

Solve the following pair of linear equations by the elimination method and the substitution method :
(i) x + y = 5 and 2x – 3y = 4
(ii) 3x + 4y = 10 and 2x – 2y = 2
(iii) 3x – 5y – 4 = 0 and 9x = 2y + 7
(iv)\( \frac{x}{2} + \frac{2y}{3} = -1 \) and \(x- \frac{y}{3} = 3\)

The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Which of the following cannot be the probability of an event?

Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

State whether the following quadrilaterals are similar or not:

Which of the following experiments have equally likely outcomes? Explain.
(i) A driver attempts to start a car. The car starts or does not start.
(ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.
(iii) A trial is made to answer a true-false question. The answer is right or wrong.
(iv) A baby is born. It is a boy or a girl.

Complete the following statements:
(i) Probability of an event E + Probability of the event 'not E' = _______.
(ii) The probability of an event that cannot happen is _________. Such as event is called _________.
(iii) The probability of an event that is certain to happen is _________. Such as event is called ________.
(iv) The sum of the probabilities of all the elementary events of an experiment is _________.
(v) The probability of an event is greater than or equal to _______ and less than or equal to _______.

On comparing the ratios\( \dfrac{a_1}{a_2},\) \(\dfrac{b_1}{b_2}\), and \(\dfrac{c_1}{c_2}\), find out whether the following pair of linear equations are consistent, or inconsistent.(i) \(3x + 2y = 5 ; 2x – 3y = 7\) (ii) \(2x – 3y = 8 ; 4x – 6y = 9\) (iii) \(\dfrac{3}{2x} + \dfrac{5}{3y} =7\) ; \(9x – 10y = 14\) (iv) \(5x – 3y = 11 \) ;\( – 10x + 6y = –22\) (v)\( \dfrac{4}{3x} +2y =8; 2x + 3y = 12\)

On comparing the ratios \(\dfrac{a_1}{a_2}\), \(\dfrac{b_1}{b_2}\), and \(\dfrac{c_1}{c_2}\), find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:
(i) \(5x – 4y + 8 = 0\) , \(7x + 6y – 9 = 0\) (ii) \(9x + 3y + 12 = 0\), \(18x + 6y + 24 = 0\) (iii) \(6x – 3y + 10 = 0\), \(2x – y + 9 = 0\)

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (i)\(\dfrac{1}{4} , 1\) (ii) \(\sqrt 2 , \dfrac{1}{3}\) (iii) \(0, \sqrt5\) (iv) \(1, 1\) (v) \(-\dfrac{1}{4} ,\dfrac{1}{4}\)(vi) \(4, 1\)

Show that the points (5, –1, 1), (7, – 4, 7), (1 – 6, 10) and (–1, – 3, 4) are the vertices of a rhombus.

Find the following integral: \(\int (2x^2+e^x)dx\)

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): \(\frac{x}{sin\,n^x}\)

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): \((x+sec\,x)(x-tan\,x)\)

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): \(\frac{x}{1+tan\,x}\)

Evaluate\( ( √3 +√2) ^6 - ( √3 -√2) ^6.\)

If a and b are distinct integers, prove that a - b is a factor of \(a^n - b^n\) , whenever n is a positive integer.
[Hint: write\( a ^n = (a - b + b)^n\) and expand]

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): sinⁿ x

Check whether the following probabilities P(A) and P(B) are consistently defined
(i) P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6
(ii) P(A) = 0.5, P(B) = 0.4, P(A ∪ B) = 0.8

If E and F are events such that P(E)=\(\frac{1}{4}\) ,P(F)=\(\frac{ 1}{2}\) and P(E and F)=\(\frac{1}{8}\) ,find: (i) P(E or F),(ii) P(not E and not F).

The number lock of a suitcase has 4 wheels, each labelled with ten digits i.e., from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?