Science (English Medium) इयत्ता १२ - CBSE Important Questions

If equal sides of an isosceles triangle with fixed base 10 cm are increasing at the rate of 4 cm/sec, how fast is the area of triangle increasing at an instant when all sides become equal?

The interval in which the function f(x) = 2x³ + 9x² + 12x – 1 is decreasing is ______.

The median of an equilateral triangle is increasing at the ratio of `2sqrt(3)` cm/s. Find the rate at which its side is increasing.

Sum of two numbers is 5. If the sum of the cubes of these numbers is least, then find the sum of the squares of these numbers.

The function f(x) = x³ + 3x is increasing in interval ______.

Find the interval/s in which the function f : R `rightarrow` R defined by f(x) = xe^x, is increasing.

If f(x) = `1/(4x^2 + 2x + 1); x ∈ R`, then find the maximum value of f(x).

Find the maximum profit that a company can make, if the profit function is given by P(x) = 72 + 42x – x², where x is the number of units and P is the profit in rupees.

Check whether the function f : R `rightarrow` R defined by f(x) = x³ + x, has any critical point/s or not ? If yes, then find the point/s.

Evaluate :`int_(pi/6)^(pi/3) dx/(1+sqrtcotx)`

Evaluate: `int(5x-2)/(1+2x+3x^2)dx`

Evaluate : `int_0^4(|x|+|x-2|+|x-4|)dx`

find : `int(3x+1)sqrt(4-3x-2x^2)dx`

Find : `int x^2/(x^4+x^2-2) dx`

Evaluate :`int_0^(pi/2)(2^(sinx))/(2^(sinx)+2^(cosx))dx`

Find:

`int(x^3-1)/(x^3+x)dx`

Find : `int((2x-5)e^(2x))/(2x-3)^3dx`

Find :`int(x^2+x+1)/((x^2+1)(x+2))dx`

Evaluate `int_(-2)^2x^2/(1+5^x)dx`

Evaluate:

`int x^2/(x^4+x^2-2)dx`