List of top Questions asked in CBSE Class XI

How much copper can be obtained from 100 g of copper sulphate \((\text{CuSO}_4)\)?

A steel tape 1m long is correctly calibrated for a temperature of 27.0 °C. The length of a steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature is 45.0 °C. What is the actual length of the steel rod on that day ? What is the length of the same steel rod on a day when the temperature is 27.0 °C ? Coefficient of linear expansion of steel = 1.20 × 10\(^{-5}\) K\(^{-1}\).

Calculate the atomic mass (average) of chlorine using the following data:
% Natural Abundance Molar Mass
\(^{35}\text{Cl}\) 75.77 34.9689
\(^{37}\text{Cl}\) 24.23 36.9659

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): \(\frac{sin(x+a)}{cos\,a}\)

Evaluate the Given limit: \(\lim_{x\rightarrow 0}\) \((x+1)^5-\frac{1}{x}\)

Find the direction in which a straight line must be drawn through the point (-1, 2) so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point

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): x⁴(5sinx - 3cosx)

Evaluate the Given limit: \(\lim_{x\rightarrow 2}\) \(\frac{3x^2-x-10}{x^2-4}\)

\(If (a+ib) (c+id) (e+if)(g+ih)=A+iB, \text {then show that} (a^2+b^2 )(c^2+d^2) (e^2+f^2)(g^2+h^2)=A^2+B^2.\)

\(If (\frac{(1+i}{1-i})^m=1, \text{then find the least positive integral value of m.}\)

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): (x²+1) cosx

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

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): (ax²+ sin x)(p+qcos x)

If A x B = {(a, x), (a, y), (b, x), (b, y)}. Find A and 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): (4x+5sinx)(3x+7cosx)

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

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

Let A = {1, 2} and B = {3, 4}. Write A x B. How many subsets will A x B have? List them.

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): (4x+5sinx)(3x+7cosx)

Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A x B, find A and B, where x, y and z are distinct elements.

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): \(\frac{x^2cos(\frac{\pi}{4})}{sin\,x}\)

The Cartesian product A x A has 9 elements among which are found (-1, 0) and (0, 1). Find the set A and the remaining elements of A x A.

Let A = {1, 2, 3, ... ,14}. Define a relation R from A to A by R = {(x, y): 3x - y = 0, where x, y ∈ A}. Write down its domain, codomain and range.

Define a relation R on the set Non natural numbers by R = {(x, y): y= x+ 5, x is a natural number less than 4; x, y ∈ N}. Depict this relationship using roster form. Write down the domain and the range.

A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈A, y ∈B}. Write R in roster form.

The given figure shows a relationship between the sets P and Q. Write this relation

in set-builder form
in roster form.

What is its domain and range?