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

For a, b, c to be in G.P. the value of `(a - b)/(b - c)` is equal to ______.

The third term of a G.P. is 4, the product of the first five terms is ______.

The sum or difference of two G.P.s, is again a G.P.

Find the distance between the lines 3x + 4y = 9 and 6x + 8y = 15.

Show that the locus of the mid-point of the distance between the axes of the variable line x cosα + y sinα = p is `1/x^2 + 1/y^2 = 4/p^2` where p is a constant.

The distance of the point P(1, – 3) from the line 2y – 3x = 4 is ______.

A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16. The locus of the point is ______.

Find the points on the line x + y = 4 which lie at a unit distance from the line 4x + 3y = 10.

If the sum of the distances of a moving point in a plane from the axes is 1, then find the locus of the point.

The distance of the point of intersection of the lines 2x – 3y + 5 = 0 and 3x + 4y = 0 from the line 5x – 2y = 0 is ______.

The distance between the lines y = mx + c₁ and y = mx + c₂ is ______.

A point equidistant from the lines 4x + 3y + 10 = 0, 5x – 12y + 26 = 0 and 7x + 24y – 50 = 0 is ______.

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.