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

Determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If A ⊂ B and x ∉ B, then x ∉ A

Let f, g: R → R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and `f/g`

Let f = {(1, 1), (2, 3), (0, –1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.

Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b²}. Is the following true?

(a, a) ∈ R, for all a ∈ N

Justify your answer in case.

Find the principal and general solutions of the equation `tan x = sqrt3`

Find the principal and general solutions of the equation sec x = 2

Find the principal and general solutions of the equation  `cot x = -sqrt3`

Find the general solution of cosec x = –2

Find the general solution of the equation cos 3x + cos x – cos 2x = 0

Find the general solution of the equation sin 2x + cos x = 0

Find the general solution for each of the following equations sec² 2x = 1– tan 2x

Find the general solution of the equation  sin x + sin 3x + sin 5x = 0

If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are `A+- sqrt((A+G)(A-G))`.

The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2^nd hour, 4^th hour and n^th hour? 

What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?

If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.

The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum.

y² = 12x