List of top Mathematics Questions asked in CBSE Class XI

How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

Find the derivative of x² – 2 at x = 10

Find \((a + b)^4 - (a - b)^4\). Hence, evaluate \((\sqrt3 + \sqrt2)^4 - (\sqrt3 - \sqrt2)^4\).

In the triangle ABC with vertices A (2, 3), B (4, –1) and C (1, 2), find the equation and length of altitude from the vertex A.

In Class XI of a school 40% of the student's study Mathematics and 30% study Biology. 10% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.

Find the distance between parallel lines
(i) \(15x + 8y – 34 = 0\) and \(15x + 8y + 31 = 0\)
(ii) \(l (x + y) + p = 0\) and \(l (x + y) – r = 0.\)

Prove that cos 4x =1-8 sin² x cos² x

Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that

1. A x (B ∩C) = (A x B) ∩(A x C)
2. A x C is a subset of B x D

The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio (3+2√2) : (3-2√2).

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 ...}

Find \((x + 1)^6 - (x - 1)^6\). Hence or otherwise evaluate \((\sqrt2 + 1)^6 + (\sqrt2 - 1)^6.\)

If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:
(i) A = {a, b, c}
(ii) B = {d, e, f, g}
(iii) C = {a, c, e, g}
(iv) D = {f, g, h, a}

Write the following as intervals:
(i) {\(x: x ∈ R, -4 < x ≤ 6\)}
(ii) {\(x: x ∈ R, -12 < x < -10\)}
(iii) {\(x: x ∈ R, 0 ≤ x < 7\)}
(iv) {\(x: x ∈ R, 3 ≤ x ≤ 4\)}

Prove that sin x+sin 3x+sin 5x+sin 7x=4 cos x cos 2x sin 4x.

Fill in the blanks to make each of the following a true statement:
(i) \(A ∪ A' = ...\)
(ii) \(\phi' ∩ A = ...\)
(iii) \(A ∩ A' = ...\)
(iv) \(U' ∩ A = ...\)

Find the sum to indicated number of terms in each of the geometric progressions in 1, – a, \(a^2\), –\(a^3\), ... n terms (if a ≠ – 1).

In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that
(i)The student opted for NCC or NSS.
(ii)The student has opted neither NCC nor NSS.
(iii)The student has opted NSS but not NCC

A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. Determine

1. P(not A)
2. P (not B)
3. P(A or B)

If f is a function satisfying \(f (x +y) = f(x) f(y)\text{ for all}\, x, y ∈ N\) such that f(1) = 3 and \(∑_{x = 1}^n f(x) = 120 \), find the value of n.

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.

Let R be the relation on Z defined by R = {(a, b): a, b ∈ Z, a - b is an integer}. Find the domain and range of R.