List of top Mathematics Questions

Write the relation R = {(x, x³ ): x is a prime number less than 10} in roster form.

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 image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.

The slope of a line is double of the slope of another line. If tangent of the angle between them is \(\frac{1}{3}\) , find the slopes of he lines.

If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4, find the value of m.

If sum of the perpendicular distances of a variable point P (x, y) from the lines x + y - 5 = 0 and 3x - 2y + 7 = 0 is always 10. Show that P must move on a line.

Find equation of the line which is equidistant from parallel lines 9x + 6y - 7 = 0 and 3x + 2y + 6 = 0.

A line passes through (x₁, y₁) and (h, k). If slope of the line is m, show that k-y₁=m(h-x₁)

A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.

Find the equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

Prove that the product of the lengths of the perpendiculars drawn from the points \(\left(\sqrt{a^2-b^2},0\right)\) and \(\left(-\sqrt{a^2-b^2},0\right)\) to the line \(\frac{x}{a}cosθ+\frac{y}{b}sinθ=1\) is \(b^2\).

A person standing at the junction (crossing) of two straight paths represented by the equations 2x - 3y + 4 = 0 and 3x + 4y - 5 = 0 wants to reach the path whose equation is 6x - 7y + 8 = 0 in the least time. Find equation of the path that he should follow.

Which of the following are sets? Justify our answer. 
(i) The collection of all months of a year beginning with the letter J. 
(ii) The collection of ten most talented writers of India. 
(iii) A team of eleven best-cricket batsmen of the world. 
(iv) The collection of all boys in your class. 
(v) The collection of all natural numbers less than 100. 
(vi) A collection of novels written by the writer Munshi Prem Chand. 
(vii) The collection of all even integers. 
(viii) The collection of questions in this Chapter. 
(ix) A collection of most dangerous animals of the world.

Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol \(∈\) or \(∉\) in the blank spaces: 
(i) 5…A  (ii) 8…A  (iii) 0…A  (iv) 4…A  (v) 2…A  (vi) 10…A

Write the following sets in roster form: 
(i) A = {x: x is an integer and \(-3 < x < 7\)}. 
(ii) B = {x: x is a natural number less than 6}. 
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8} 
(iv) D = {x: x is a prime number which is divisor of 60}. 
(v) E = The set of all letters in the word TRIGONOMETRY. 
(vi) F = The set of all letters in the word BETTER

Write the following sets in the set-builder form:
(i) (3, 6, 9, 12)  (ii) {2, 4, 8, 16, 32}
(iii) {5, 25, 125, 625}  (iv) {2, 4, 6 …}
(v) {1, 4, 9 … 100}

List all the elements of the following sets: 
(i) A = {x: x is an odd natural number} 
(ii) B = {x: x is an \(\frac{-1}{2} < x <\frac{ 9}{2}\)  integer,} 
(iii) C = {x: x is an \(x^2 ≤ 4 \) integer, 
(iv) D = {x: x is a letter in the word “LOYAL“} 
(v) E = {x: x is a month of a year not having 31 days} 
(vi) F = {x: x is a consonant in the English alphabet which proceeds k}.

Match each of the set on the left in the roster form with the same set on the right described in set-builder
form:
(i) {1, 2, 3, 6} (a) {x: x is a prime number and a divisor of 6}
(ii) {2, 3} (b) {x: x is an odd natural number less than 10}
(iii) {M, A,T, H, E, I,C, S} (c) {x: x is natural number and divisor of 6}
(iv) {1, 3, 5, 7, 9} (d) {x: x is a letter of the word MATHEMATICS}

Which of the following are examples of the null set
(i) Set of odd natural numbers divisible by 2
(ii) Set of even prime numbers
(iii) {x: x is a natural numbers, x < 5 and x > 7 }
(iv) {y: y is a point common to any two parallel lines}

Which of the following sets are finite or infinite
(i) The set of months of a year
(ii) {1, 2, 3 ...}
(iii) {1, 2, 3 ... 99, 100}
(iv) The set of positive integers greater than 100
(v) The set of prime numbers less than 99

State whether each of the following set is finite or infinite:
(i) The set of lines which are parallel to the x-axis
(ii) The set of letters in the English alphabet
(iii) The set of numbers which are multiple of 5
(iv) The set of animals living on the earth
(v) The set of circles passing through the origin (0, 0)

In the following, state whether A = B or not:
(i) A = {a, b, c, d}; B = {d, c, b, a}
(ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18}
(iii) A = {2, 4, 6, 8, 10}; B = {x: x is positive even integer and x ≤ 10} (iv) A = {x: x is a multiple of 10}; B = {10, 15, 20, 25, 30 ...}

Are the following pair of sets equal? Give reasons.
(i) A = {2, 3}; B = {x: x is solution of \(x^2+ 5x + 6 = 0\)}
(ii) A = {x: x is a letter in the word FOLLOW}; B = {y: y is a letter in the word WOLF}

From the sets given below, select equal sets:
A = {2, 4, 8, 12}, B = {1, 2, 3, 4}, C = {4, 8, 12, 14}, D = {3, 1, 4, 2}
E = {-1, 1}, F = {0, a}, G = {1, -1}, H = {0, 1}

Make correct statements by filling in the symbols \( ⊂ \) or \(⊄\) in the blank spaces:
(i) {2, 3, 4} … {1, 2, 3, 4, 5}
(ii) {a, b, c} … {b, c, d}
(iii) {x: x is a student of Class XI of your school} … {x: x student of your school}
(iv) {x: x is a circle in the plane} … {x: x is a circle in the same plane with radius 1 unit}
(v) {x: x is a triangle in a plane}…{x: x is a rectangle in the plane}
(vi) {x: x is an equilateral triangle in a plane}… {x: x is a triangle in the same plane} 
(vii) {x: x is an even natural number} … {x: x is an integer}