Commerce (English Medium) इयत्ता ११ - CBSE Question Bank Solutions for Mathematics

The ratio in which the line 3x + 4y + 2 = 0 divides the distance between the lines 3x + 4y + 5 = 0 and 3x + 4y – 5 = 0 is ______.

A point moves so that square of its distance from the point (3, –2) is numerically equal to its distance from the line 5x – 12y = 3. The equation of its locus is ______.

The value of the λ, if the lines (2x + 3y + 4) + λ (6x – y + 12) = 0 are

Evaluate `lim_(h -> 0) ((a + h)^2 sin (a + h) - a^2 sina)/h`

Evaluate: `lim_(x -> 1) ((1 + x)^6 - 1)/((1 + x)^2 - 1)`

If `lim_(x -> 1) (x^4 - 1)/(x - 1) = lim_(x -> k) (x^3 - l^3)/(x^2 - k^2)`, then find the value of k.

`1/(ax^2 + bx + c)`

Let `f(x) = {{:((k cos x)/(pi - 2x)",", "when"  x ≠ pi/2),(3",", x = pi/2  "and if"  f(x) = f(pi/2)):}` find the value of k.

If `f(x) = {{:(x + 2",",  x ≤ - 1),(cx^2",", x > -1):}`, find 'c' if `lim_(x -> -1) f(x)` exists

Show that the following statement is true.
p: For any real numbers x, y if x = y, then 2x + a = 2y + a when a ∈ Z.

Which of the following is the converse of the statement?
“If Billu secure good marks, then he will get a bicycle.”

Write down the contrapositive of the following statements:

If x = y and y = 3, then x = 3.

Write down the contrapositive of the following statements:

If n is a natural number, then n is an integer.

Write down the contrapositive of the following statements:

If all three sides of a triangle are equal, then the triangle is equilateral.

Write down the contrapositive of the following statements:

If x and y are negative integers, then xy is positive.

Write down the contrapositive of the following statements:

If natural number n is divisible by 6, then n is divisible by 2 and 3.

Write down the contrapositive of the following statements:

If it snows, then the weather will be cold.

Write down the contrapositive of the following statements:

If x is a real number such that 0 < x < 1, then x² < 1.

Write down the converse of following statements:

If a rectangle ‘R’ is a square, then R is a rhombus.

Write down the converse of following statements:

If today is Monday, then tomorrow is Tuesday.