List of top Mathematics Questions asked in CBSE Class XI

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)

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

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}

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

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

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.

Find the distance of the line \(4x + 7y + 5 = 0\)  from the point (1, 2) along the line  \(2x - y = 0\)

The hypotenuse of a right-angled triangle has its ends at the points (1, 3) and (-4, 1). Find the equation of the legs (perpendicular sides) of the triangle.

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

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 three lines whose equations are y = m₁x + c₁, y = m₂x + c₂ and y = m₃x + c₃ are concurrent, then show that m₁ (c₂ – c₃) + m₂ (c₃ – c₁) + m₃ (c₁ – c₂) = 0.

Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line  \(x -2y = 3.\)

Find the equation of the line passing through the point of intersection of the lines \(4x + 7y - 3 = 0\) and \(2x - 3y+ 1 = 0\)  that has equal intercepts on the axes.

Show that the equation of the line passing through the origin and making an angle θ with the line \(y=mx+c\) is \(\frac{y}{x}=\frac{m±tanθ}{1-+mtanθ}\)

In what ratio, the line joining (-1, 1) and (5, 7) is divided by the line x + y = 4?

Find the perpendicular distance from the origin to the line joining the points \((cosθ,sinθ) \) and \((cos\phi,sin\phi).\)

Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines  \(x - 7y+ 5 = 0\) and \(3x + y = 0.\)

Find the equation of a line drawn perpendicular to the line \(\frac{x}{4} +\frac{ y}{6} = 1 \) through the point where it meets the y-axis

Find the area of the triangle formed by the lines  \(y -x = 0, x + y = 0\) and \(x - k = 0.\)

If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that  \(\frac{1}{p^2}=\frac{1}{a^2}+\frac{1}{b^2}.\)

Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and – 6, respectively.

What are the points on the y-axis whose distance from the line  \(\frac{ x}{3} +\frac{ y}{4} = 1\) is 4 units?

Find the equation of the right bisector of the line segment joining the points (3,4) and (–1,2).

Find the coordinates of the foot of perpendicular from the point \( (–1, 3) \) to the line \(3x – 4y – 16 = 0.\)