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Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two non-zero vectors perpendicular to each other and $|\overrightarrow{a}|=|\overrightarrow{b}|.$ If $|\overrightarrow{a}\times \overrightarrow{b}|=|\overrightarrow{a}|$, then the angle between the vectors $(\overrightarrow{a}+\overrightarrow{b}+(\overrightarrow{a}\times \overrightarrow{b}))$ and $\overrightarrow{a}$ is equal to:

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If the angles of a triangle are in the ratio 2: 3: 4, determine the angles.
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If $x,y$ are two positive numbers such that $x-y=10$ and square of the greater exceeds twice the square of the smaller by maximum value, then which of the following is/are true

Simplify: ${(xy+yz)}^2$ - ${(xy-yz)}^2$

In the figure below, AB is a diameter of the circle and PQ is a chord parallel to it.

Compute the area of the quadrilateral ABQP.

Which of the following should be the SECOND sentence after rearrangement?

Two sides of a triangle have lengths of 5 units and 6 units respectively. Which of the following is a possible length for the third side?

Find the area in $c{m}^2$ of the yellow region where the square has side measuring 14 cm.

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$\text{In the given figure, prove that}\text{(i) CD + DA + AB}>BC\text{(ii) CD + DA + AB + BC}>2AC.$

The volume of a cone whose height and radius is 6 cm and 5 cm respectively is:

In a triangle ABC, AB = AC then $\angle B=$.

The ages (in years) of 10 teachers in a school are
32, 44, 53, 47, 37, 54, 34, 36, 40, 50.
Find the median age.

The number of integral values of $\lambda$ for which $x^2+y^2+\lambda x+(1-\lambda )y+5=0$ is the equation of a circle whose radius cannot exceed 5, is

The vector which joins the point $A(4,5,6)$ to $B(10,11,12)$ is

If $2A+B^T=\left[\begin{array}{cc}2& -3\\ 4& 7\end{array}\right]$ and $A^T-B=\left[\begin{array}{cc}4& -5\\ 0& 1\end{array}\right]$, then $A$ is equal to

In the figure shown find the distance of point O from line AB and line CD.

Find three rational number between 1\5and 3\4

A line separates a plane into______parts namely the two____and the_____itself.

If three angles of a quadrlateral are ${76}^{\circ }$, ${104}^{\circ }$ and ${89}^{\circ }$.

Find its fourth angle.

The base of a prism is an equilateral triangle of perimeter 15 centimetres and its height is 5 centimetres. What is its volume?

Find the volume of a sphere whose radius is

(i) 7 cm (ii) 0.63 m

If the sets A and B are defined as

A = {(x, y) : $y=\frac{1}{x}$, 0 ≠ x ∈ R}

B = {(x, y) : y = -x, x ∈ R}, then

Without actual division, show that each of the following rational numbers is a nonterminating repeating decimal.

$\left(i\right)\frac{11}{(2^3\times 3)}\left(ii\right)\frac{73}{(2^2\times 3^3\times 5)}$

David opened a recurring deposit account in a bank & deposited Rs. 300 per month for two years. If he received Rs.7,725 at the time of maturity, find the rate of interest per annum.

If $5^{4a}=6^7$ and $36=5^b$, then the value of $\frac{a}{b}$ is equal to

Sand is poured at a rate of $1000\text{c.c/sec}$ on the ground(from a certain height), which is always in the form of cone whose height $\left(h\right)$ is equal to the base radius $r$. If $l$ is its slant height and $S$ is the curved surface area and $h=40\text{cm}$(at an instant), then which of the following(s) is/are true