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

While calculating the mean and variance of 10 readings, a student wrongly used the reading of 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance.

Calculate the mean, variance and standard deviation of the following frequency distribution. 

The perpendicular from the origin to the line y = mx + c meets it at the point (−1, 2). Find the values of m and c.

Find the equation of the straight line which cuts off intercepts on x-axis twice that on y-axis and is at a unit distance from the origin.

If p₁ and p₂ are the lengths of the perpendiculars from the origin upon the lines x sec θ + y cosec θ = a and x cos θ − y sin θ = a cos 2 θ respectively, then

If p be the length of the perpendicular from the origin on the line x/a + y/b = 1, then

If `(x/3+1, y-2/3)` = `(5/3,1/3),`find the values of x and y.

When A = Φ, then number of elements in P(A) is ______.

Power set of the set A = {1, 2} is ______.

Given A = {1, 2, 3, 4, 5}, S = {(x, y) : x ∈ A, y ∈ A}. Find the ordered pairs which satisfy the conditions given below:

x + y = 5

Given A = {1, 2, 3, 4, 5}, S = {(x, y) : x ∈ A, y ∈ A}. Find the ordered pairs which satisfy the conditions given below:

x + y < 5

Given A = {1, 2, 3, 4, 5}, S = {(x, y) : x ∈ A, y ∈ A}. Find the ordered pairs which satisfy the conditions given below:

x + y > 8

Express the following functions as set of ordered pairs and determine their range.
f : X → R, f(x) = x³ + 1, where X = {–1, 0, 3, 9, 7}

State True or False for the following statement.

The ordered pair (5, 2) belongs to the relation R = {(x, y) : y = x – 5, x, y ∈ Z}.

Prove that `(tanA + secA  - 1)/(tanA - secA + 1) = (1 + sinA)/cosA`

If `(2sinalpha)/(1 + cosalpha + sinalpha)` = y, then prove that `(1 - cosalpha + sinalpha)/(1 + sinalpha)` is also equal to y.
`["Hint": "Express" (1 - cosalpha + sinalpha)/(1 + sinalpha) = (1 - cosalpha + sinalpha)/(1 + sinalpha) * (1 + cosalpha + sinalpha)/(1 + cosalpha + sinalpha)]`

If m sinθ = n sin(θ + 2α), then prove that tan(θ + α)cotα = `(m + n)/(m - n)`

[Hint: Express `(sin(theta + 2alpha))/sintheta = m/n` and apply componendo and dividendo]

If cos(α + β) = `4/5` and sin(α – β) = `5/13`, where α lie between 0 and `pi/4`, find the value of tan2α.
[Hint: Express tan2α as tan(α + β + α – β)]

If tanx = `b/a`, then find the value of `sqrt((a + b)/(a - b)) + sqrt((a - b)/(a + b))`

Prove that cosθ `cos  theta/2 - cos 3theta cos  (9theta)/2` = sin 7θ sin 8θ.

[Hint: Express L.H.S. = `1/2[2costheta cos  theta/2 - 2 cos 3theta cos  (9theta)/2]`