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The angle of elevation of the Sun if the shadow of a 7 m long pole is $7\sqrt{3}$ m, is

From an aeroplane vertically above a straight horizontal road, the angles of depression of two stones on opposite sides of the aeroplane are observed to be $\alpha$ and $\beta$. The distance between the stones is 1m.Then the height in meters of the aeroplane above the road is

The table below shows the distance (in units) covered by 6 people.

Rosy covered three times the distance covered by all 6 people.

Calculate the distance covered by Rosy.

Let $\alpha \ne \beta$, ${\alpha }^2+3=5\alpha$ and ${\beta }^2=5\beta -3$. Which of the following is a quadratic equation whose roots are $\frac{\alpha }{\beta }$ and $\frac{\beta }{\alpha }$?

Which among the following represents the total surface area of the right circular cylinder?

Find the value of $x$ in the diagram below.

In the given diagram O is the center of the circle and CD is a tangent. $\angle$CAB and $\angle$ACD are supplementary to each other $\angle$OAC =

${30}^{\circ }$. Find the value of $\angle$OCB:

If $\alpha$ and $\beta$ are the zeros of the polynomial $f\left(x\right)=x^2+x-2$, find the value of $(\frac{1}{\alpha }-\frac{1}{\beta })$.

Question 45

Fill in the blanks to make the statement true.

If we multiply five positive integers and one negative integer, then the resulting integer is ___.

Question 126 (ii)

If $\Delta$ is an operation, such that for integers a and b. We have $a\Delta b=a\times b-2\times a\times b+b\times b(-a)\times b+b\times b,$ then find
$(-7)\Delta (-1)$
Also, show that $(-7)\Delta (-1)\ne (-1)\Delta (-7)$

Which of the following is an example of an arithmetic progression?

Evaluate

√(2017+2016√(2017+2016√(2017+2016√(.................................))

In an equilateral triangle ABC, the ratio of length of the perpendicular AD to side AB is

Consider the arithmetic sequence with first term and common difference. Is 1 a term of this sequence? What about 2?

Write the algebraic form of this sequence. Prove the no natural number occurs is this sequence.

If(x³+ax²+bc+6) has (x-2) as a factor and leaves a remainder 3 when divided by (x-3), find the value of a and b.

In the given diagram, find the area of segment PRQS. Sides OS and SQ have lengths a and b respectively. Let the area of circle be A.

The point at which two lines 3x + 4y = 30 and 7x – 2y = 35 cut each other is

Consider the figure where $\angle AOB={90}^{\circ }$ and $\angle ABC={30}^{\circ }.$ Then, $\angle CAO$ = ___.

If x, y and z are in continued proportion then $z:x::z^2:$.

The line $ax+by+c=0,$ is parallel to $x$ axis when $a$ = .

Look at the cumulative frequency distribution table given below:

$\begin{array}{cc}Monthlyincome& Numberoffamilies\\ MorethanRs.10000& 100\\ MorethanRs.14000& 85\\ MorethanRs.18000& 69\\ MorethanRs.20000& 50\\ MorethanRs.25000& 37\\ MorethanRs.30000& 15\end{array}$

Number of families having income range 20000 to 25000 is

(a) 19 (b) 16 (c) 13 (d) 22

The total cost to paint all the 4 walls of a room with length, breadth and height as 10 m, 20 m and 5 m respectively at the rate of Rs. 10 per sq. meter is Rs.7000. State with true or false.

Find the sum of first $24$ terms of the A.P. whose $n^{th}$ term is given by $a_n=3+2n$