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

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

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.