Science (English Medium) कक्षा ११ - CBSE Question Bank Solutions

The expression 7⁹ + 9⁷ is divisible by 64.

If a, b, c are three consecutive terms of an A.P. and x, y, z are three consecutive terms of a G.P. Then prove that x^{b – c}. y^{c – a} . z^{a – b} = 1

If x, y, z are positive integers then value of expression (x + y)(y + z)(z + x) is ______.

If A is the arithmetic mean and G₁, G₂ be two geometric means between any two numbers, then prove that 2A = `(G_1^2)/(G_2) + (G_2^2)/(G_1)`

The minimum value of 4^x + 4^1–x, x ∈ R, is ______.

If the equation of the parabola is x² = – 8y, find coordinates of the focus, the equation of the directrix and length of latus rectum.

The area of the triangle formed by the lines joining the vertex of the parabola x² = 12y to the ends of its latus rectum is ______.

If the latus rectum of an ellipse with axis along x-axis and centre at origin is 10, distance between foci = length of minor axis, then the equation of the ellipse is ______.

If the eccentricity of an ellipse is `5/8` and the distance between its foci is 10, then find latus rectum of the ellipse.

If the parabola y² = 4ax passes through the point (3, 2), then the length of its latus rectum is ______.

The length of the latus rectum of the ellipse 3x² + y² = 12 is ______.

Evaluate: `lim_(h -> 0) (sqrt(x + h) - sqrt(x))/h`

Evaluate: `lim_(x -> 2) (x^2 - 4)/(sqrt(3x - 2) - sqrt(x + 2))`

Which of the following statements are compound statements 

“2 is both an even number and a prime number”

Which of the following statements are compound statements 

“9 is neither an even number nor a prime number”

Which of the following statements are compound statements 

“Ram and Rahim are friends”

Identify the component statements and the connective in the following compound statements.

It is raining or the sun is shining.

Identify the component statements and the connective in the following compound statements.

2 is a positive number or a negative number.

Translate the following statements in symbolic form

2 and 3 are prime numbers 

Translate the following statements in symbolic form

Tigers are found in Gir forest or Rajaji national park.