If A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8} then state which of the following statement is true..

If f(x) = 2x² and g(x) = \(\frac{1}{3x}\), then f o g is

If the HCF of 65 and 117 is expressible in the form of 65m - 117 , then the value of m is

The sum of first n terms of the series a, 3a, 5a...is ____________

Find the matrix X if 2X + \(\left( \begin{matrix} 1 & 3 \\ 5 & 7 \end{matrix} \right) =\left( \begin{matrix} 5 & 7 \\ 9 & 5 \end{matrix} \right) \)

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

In the adjacent figure \(\angle BAC\) = 90^o and AD\(\bot \)BC then 

The point of intersection of 3x − y = 4 and x + y = 8 is

If sin \(\theta \) + cos\(\theta \) = a and sec \(\theta \) + cosec \(\theta \) = b, then the value of b(a² - 1) is equal to 

If the ratio of the height of a tower and the length of its shadow is \(\sqrt{3}: 1\), then the angle of elevation of the sun has measure

If x = a sec θ and = b tan θ, then b²x² - a²y² is equal to ___________

The volume (in cm³) of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

If the mean and coefficient of variation of a data are 4 and 87.5% then the standard deviation is

If are event occurs surely, then its probability is ___________

Represent the function f = {(1,2),(2,2),(3,2),(4,3),(5,4)} through
(i) an arrow diagram
(ii) a table form
(iii) a graph

Find the 19^th term of an A.P. -11, -15, -19,....

Prove that \(\sqrt { 3 } \) is irrational

Multiply \(\frac { { x }^{ 4 }{ b }^{ 2 } }{ x-1 } \) by \(\frac { { x }^{ 2 }-1 }{ { a }^{ 4 }{ b }^{ 3 } } \)

Solve the following system of linear equations in three variables.
x + y + z = 6; 2x + 3y + 4z = 20;
3x + 2y + Sz = 22

In the figure, AD is the bisector of \(\angle\)A. If BD = 4 cm, DC = 3 cm and AB = 6 cm, find AC.

In figure if PQ || RS Prove that \(\Delta POQ\sim \Delta SOQ\)

In each of the following, Find the value of ‘a’ for which the given points are collinear. (2, 3), (4, a) and (6, –3)

Show that the points (1, 7), (4, 2), (-1,-1) and (-4,4) are the vertices of a square.

The horizontal distance between two buildings is 70 m. The angle of depression of the top of the first building when seen from the top of the second building is 45°. If the height of the second building is 120 m, find the height of the first building.

A cone of height 24 cm is made up of modeling clay. A child reshapes it in the form of a cylinder of same radius as cone. Find the height of the cylinder.

Find the depth of a cylindrical tank of radius 28 m, if its capacity is equal to that of a rectangular tank of size 28 m x 16 m x 11 m.

Find the range and coefficient of range of the following data.
43.5, 13.6, 18.9, 38.4, 61.4, 29.8

Find the standard deviation for the following data. 5, 10, 15, 20, 25. And also find the new S.D. if three is added to each value.

Let A = {x \(\in \) W| x < 2}, B = {x \(\in \) N| 1 < x ≤ 4} and C = (3,5). Verify that
(A U B) x  C = (A x C) U (B x C)

A functionf: (1,6) \(\rightarrow\)R is defined as follows:

Find the value of f(3),

Find the least number that is divisible by the first ten natural numbers.

Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
-2, 2, -2, 2, -2

Iniya bought 50 kg of fruits consisting of apples and bananas. She paid twice as much per kg for the apple as she did for the banana. If Iniya bought Rs. 1800 worth of apples and Rs. 600 worth bananas, then how many kgs of each fruit did she buy?

BL and CM are medians of a triangle ABC right angled at A.
Prove that 4(BL² + CM²) = 5BC².

Find the equation of the median and altitude of Δ ABC through A where the vertices are A(6, 2), B(-5,-1) and C(1, 9)

If the points A(6, 1), B(8, 2), C(9, 4) and D(P, 3) are the vertices of a parallelogram, taken in order. Find the value of P.

prove the following identities.
sec⁶\(\theta \) = tan⁶\(\theta \) + 3tan²\(\theta \)sec²\(\theta \) + 1

If sin (A - B) = \(\frac12\),  cos (A + B) = \(\frac12\), 0^o < A + ≤  90°, A > B, find A and B.

If the radii of the circular ends of a frustum which is 45 cm high are 28 cm and 7 cm, find the volume of the frustum.

What is the ratio of the volume of a cylinder, a cone, and a sphere. If each has the same diameter and same height?

In a box there are 20 non-defective and some defective bulbs. If the probability that a bulb selected at random from the box found to be defective is \(\frac{3}{8}\) then, find the number of defective bulbs.

Find the co-efficient of variation for the following data: 16, 13, 17,21, 18.