Science (English Medium) Class 11 - CBSE Question Bank Solutions

Evaluate the following limit.

`lim_(x -> 0) (cos 2x -1)/(cos x - 1)`

Evaluate the following limit.

`lim_(x -> 0) (ax +  xcos x)/(b sin x)`

Evaluate the following limit.

`lim_(x → 0) x sec x`

Evaluate the following limit.

`lim_(x -> 0) (sin ax + bx)/(ax + sin bx) a, b, a+ b != 0`

Evaluate the following limit.

`lim_(x -> 0) (cosec x -  cot x)`

Evaluate the following limit.

`lim_(x -> (pi)/2) (tan 2x)/(x - pi/2)`

Which of the following statements are true and which are false? In each case give a valid reason for saying so.

p: Each radius of a circle is a chord of the circle.

Which of the following statements are true and which are false? In each case give a valid reason for saying so.

q: The centre of a circle bisects each chord of the circle.

Which of the following statements are true and which are false? In each case give a valid reason for saying so.

r: Circle is a particular case of an ellipse.

Which of the following statements are true and which are false? In each case give a valid reason for saying so.

s: If x and y are integers such that x > y, then –x < –y.

Which of the following statements are true and which are false? In each case give a valid reason for saying so.

t`sqrt11` is a rational number.

Check the validity of the statements given below by the method given against it.

p: The sum of an irrational number and a rational number is irrational (by contradiction method).

Check the validity of the statements given below by the method given against it.

q: If n is a real number with n > 3, then n² > 9 (by contradiction method).

Write the following statement in five different ways, conveying the same meaning.

p: If triangle is equiangular, then it is an obtuse angled triangle.

Find the mean and variance for the following frequency distribution.

Find the mean and variance for the following frequency distribution.

If the ordered pairs (x, −1) and (5, y) belong to the set {(a, b) : b = 2a − 3}, find the values of x and y. 

If a ∈ [−1, 2, 3, 4, 5] and b ∈ [0, 3, 6], write the set of all ordered pairs (a, b) such that a + b= 5.  

If a ∈ [2, 4, 6, 9] and b ∈ [4, 6, 18, 27], then form the set of all ordered pairs (a, b) such that a divides b and a < b.

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 × B, find A and B, where x, y, z are distinct elements.