Explore topic-wise InterviewSolutions in .

Question 76

In the following question, state whether the statement is True (T) or False (F):

abc + bca + cab is a monomial.

Given ABCD is rectangle and E is the midpoint of BC and a line drawn from E meets the AD at G when extended. If DG = 2 and area of DFG = 40 and area of EFC = 10, find the area of the rectangle ABCD.

Which of the following is the mean of a set of observations?

Which all of the formula hold true for area of rhombus

Which of the following statements are true?

(i) Every natural number is a rational number.

(ii) Every integer is a rational number.

(iii) 0 is a whole number, but it is not a rational number.

The measures of interior angles of a quadrilateral are in the ratio 3:4:5:6. The measure of the largest angle is

In a triangle, exterior angle measures 100°. If one interior opposite angle is 55°, then the other interior angle is

Factorise:
$15x^2+2x-8$

Solve the following pair of linear equations.

$\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2$

$\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$



Here, x > 0 and y > 0.

Two parallel sides of trapezium are 12 cm and 8 cm long and the distance between them is 6.5 cm.The area of the trapezium is

(a) $74c{m}^2$

(b) $32.5c{m}^2$

(c) $65c{m}^2$

(d) $130c{m}^2$

Where does the point (-10, 0) lie?

Question 2 (iv)

Simplify $(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})$ .

$\text{Find the value for x, y for:}3x-7=\frac{1}{y},x+\frac{1}{y}=1$

Factorise:

$x^3+x-3x^2-3$

Question 9
Two chords AB and AC of a circle subtends angles equal to ${90}^{\circ }and{150}^{\circ }$ respectively at the centre. Find $\angle BAC$, if AB and AC lie on the opposite sides of the centre.

Suppose the vectors $X_1$, $X_2$ and $X_3$ are the solutions of the system of linear equations, $Ax=b$ when the vector $b$ on the right side is equal to $b_1$, $b_2$ and $b_3$ respectively. if

$X_1=\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right],X_2=\left[\begin{array}{c}0\\ 2\\ 1\end{array}\right],X_3=\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right],b_1=\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right],b_2=\left[\begin{array}{c}0\\ 2\\ 0\end{array}\right]$ and $b_3=\left[\begin{array}{c}0\\ 0\\ 2\end{array}\right]$, then the determinant of $A$ is equal to

1. 80

Find the area of the triangle if the sides of the triangle are in the ratio 12:17:25 and the perimeter of the triangle is 270 m.

I have 14 apples with me, out of which $\frac{2}{7}$ of them were spoilt. From the remaining good ones, I sold a few of them and was left with $\frac{1}{5}$ of the fresh apples. I gave half of the remaining apples to my friend. Find the total number of apples which are left with me.

If the lateral area of a cylinder of radius 13 cm and height 21 cm is to be covered with paper, then the area of the paper required is

The population of a town is increasing at the rate of 5% p.a. What will be the population of the town after 2 years, if the present population is 16,000?

A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.

Factorize: $4x^2-16xy$

A hemispherical bowl is made up of stones whose thickness is 7 cm. If the inner radius is 35 cm, find the total surface area of the bowl.

Twenty seven solid iron spheres, each of radius $r$ and surface area $S$ are melted to form a sphere with surface area $S^{\prime }$. Find the

(i) radius $r^{\prime }$ of the new sphere, (ii) ratio of $S$ and $S^{\prime }$.

If the height of a tower and the length of its shadow are in the ratio 1 : 1.73, then the angle of elevation of the sun is:

The height of the base of a conical tent is 16cm and 24cm. Find the cost of canvas required to make it at the rate of ₹210 per m^2

ABC is a right-angled triangle in which $\angle A={90}^{\circ }$ and AB = AC. Then, $\angle B$ equals

Expand each of the following, using suitable identities: [3 MARKS]
$1){(x+2y+4z)}^2$
$2){(3x-7y-z)}^2$