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

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

x² = – 16y

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

y² = 10x

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

x² = –9y

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

Find `lim_(x -> 0)` f(x) and `lim_(x -> 1)` f(x) where f(x) = `{(2x + 3, x <= 0),(3(x+1), x > 0):}`

Find `lim_(x -> 1)` f(x), where `f(x) = {(x^2 -1, x <= 1), (-x^2 -1, x > 1):}`

Evaluate `lim_(x -> 0) f(x)` where `f(x) = { (|x|/x, x != 0),(0, x = 0):}`

Find `lim_(x -> 0)` f(x), where `f(x) = {(x/|x|, x != 0),(0, x = 0):}`

Let a₁, a₂,..., a_n be fixed real numbers and define a function f ( x) = ( x − a₁ ) ( x − a₂ )...( x − a_n ).

What is `lim_(x -> a_1) f(x)` ? For some a ≠ a₁, a₂, ..., a_n, compute `lim_(x -> a) f(x)`

If f(x) = `{(|x| +  1,x < 0), (0, x = 0),(|x| -1, x > 0):}`

For what value (s) of a does `lim_(x -> a)`  f(x) exists?

If the function f(x) satisfies `lim_(x -> 1) (f(x) - 2)/(x^2 - 1) = pi`, evaluate `lim_(x -> 1) f(x)`.

if `f(x) = { (mx^2 + n, x < 0),(nx + m, 0<= x <= 1),(nx^3 + m, x > 1):}`

For what integers m and n does `lim_(x-> 0) f(x)` and `lim_(x -> 1) f(x)` exist?

Show that the statement

p: “If x is a real number such that x³ + 4x = 0, then x is 0” is true by

(i) direct method

(ii) method of contradiction

(iii) method of contrapositive

Show that the statement “For any real numbers a and b, a² = b² implies that a = b” is not true by giving a counter-example.

Show that the following statement is true by the method of contrapositive.

p: If x is an integer and x² is even, then x is also even.

By giving a counter example, show that the following statements are not true.

p: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.

By giving a counter example, show that the following statements are not true.

q: The equation x² – 1 = 0 does not have a root lying between 0 and 2.

Find the mean and variance for the data.

6, 7, 10, 12, 13, 4, 8, 12