A number x is chosen at random from -4, -3, -2, -1, 0, 1, 2, 3, 4. The probability that \(\left| x \right| \le 3\) is ___________

If the co-efficient of variation and standard deviation of a data are 35% and 7.7 respectively then the mean is ___________

The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is 5 cm, then height of the cone is ___________

The angle of elevation of a cloud from a point h metres above a lake is b. The angle of depression of its reflection in the lake is 45^o. The height of location of the cloud from the lake is ___________

If the mid-point of the line segment joining \(A\left( \frac { x }{ 2 } ,\frac { y+1 }{ 2 } \right) \) and B(x + 1, y-3) is C(5, -2) then find the values of x, y ____________

In a triangle, the internal bisector of an angle bisects the opposite side. Find the nature of the triangle.

If \(A=\left[ \begin{matrix} y & 0 \\ 3 & 4 \end{matrix} \right] \) and \(I=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] \) then A² = 16 for ___________

\(\frac { { x }^{ 2 }+7x12 }{ { x }^{ 2 }+8x+15 } \times \frac { { x }^{ 2 }+5x }{ { x }^{ 2 }+6x+8 } =\_ \_ \_ \_ \_ \_ \_ \_ \_ \)

A square is drawn by joining the mid points of the sides of a given square in the same way and this process continues indefinitely. If the side of the first square is 4 cm, then the sum of the area of all the squares is ____________

If f is identify function, then the value of f(1) - 2f(2) + f(3) is: 

Let f(x) = x² - x, then f(x- 1) - (x + 1) is ___________

IF the probability of the non-happening of a event is q, then the probability of happening of that event is 

The radius of base of a cone 5 cm and height is 12 cm. The slant height of the cone ___________

(cosec²θ - cot²θ) (1 - cos²θ) is equal to ___________

Given that sin ∝ = \(\frac{1}{2}\) and cos β = \(\frac{1}{2}\), then the value of (∝ + β) is ___________

The sum of all deviations of the data from its mean is

Two persons are standing ‘x’ metres apart from each other and the height of the first person is double that of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the shorter person (in metres) is

tan \(\theta \) cosec²\(\theta \) - tan\(\theta \) is equal to 

The first term of an arithmetic progression is unity and the common difference is 4. Which of the following will be a term of this A.P.

The slope of the line joining (12, 3), (4, a) is \(\frac 18\). The value of ‘a’ is

In a \(\triangle\)ABC, AD is the bisector \(\angle\)BAC. If AB = 8 cm, BD = 6 cm and DC = 3 cm. The length of the side AC is

A frustum of a right circular cone is of height 16 cm with radii of its ends as 8 cm and 20 cm. Then, the volume of the frustum is

Let A = {1, 2, 3, 4} and B = {4, 8, 9, 10}. A function f: A ⟶ B given by f = {(1, 4), (2, 8), (3, 9), (4,10)} is a

Which of the following can be calculated from the given matrices A  = \(\left( \begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix} \right) \), B = \(\left( \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix} \right) \),
(i) A²
(ii) B²
(iii) AB
(iv) BA

\(\frac { x }{ { x }^{ 2 }-25 } -\frac { 8 }{ { x }^{ 2 }+6x+5 } \) gives