Arts (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

The line lx + my + n = 0 will touch the parabola y² = 4ax if ln = am².

The equation of the parabola having focus at (–1, –2) and the directrix x – 2y + 3 = 0 is ______.

If the focus of a parabola is (0, –3) and its directrix is y = 3, then its equation is ______.

If the vertex of the parabola is the point (–3, 0) and the directrix is the line x + 5 = 0, then its equation is ______.

The equation of the ellipse whose focus is (1, –1), the directrix the line x – y – 3 = 0 and eccentricity `1/2` is ______.

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.