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If sec 5A° = cosec (A-30)°, then the value of A is ___.

For what n , are the nth terms of two APs: 63,65,67,.. and 3,10,17,.. equal?

Given:

$A=\{x:11x-5>7x+3,x\in R\}$ and

$B=\{x:18x-9\ge 15+12x,x\in R\}$.

Find the range of set $A\cap B$.

If the angle of elevation of a cloud from a point 200 m above a lake is ${30}^{\circ }$ and the angle of depression of the reflection of the cloud in the lake from the same point is ${60}^{\circ }$, then the height of the cloud above the lake is:

A right angled triangle having its base and height equal to 24 $cm$ and 7 $cm$ respectively is rotated by 360⁰ along its base. Find the curved surface area of the resultant figure.

Find the square root of 324$(x+y{)}^{10}$

A cylindrical water flask has a hemispherical cap which exactly fits on the flask. The height and radius of the flask are 20 cm and 3 cm respectively. If the cap is used as the cup to drink water, how many cups of water can be served.

Construct a circle of radius 7cm. From a point 10 cm away from its centre, draw tangents to the circle. [4 MARKS]

A horse is placed for grazing inside a rectangular field 70 m by 52 m. It is tethered to one corner by a rope 21 m long. On how much area can it graze ? How much area is left ungrazed ?

If $\frac{1}{\sqrt{b}+\sqrt{c}},\frac{1}{\sqrt{c}+\sqrt{a}},\frac{1}{\sqrt{a}+\sqrt{b}}$ are in A.P., then the family of lines $ax+by+c=0$ will always passes through the fixed point:

The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.

(ii)





(iii)





(iv)





(v)

How many bricks each measuring $(25cm\times 11.25cm\times 6cm)$ will be required to construct a wall $(8m\times 6m\times 22.5cm)?$

(a) 8000 (b) 6400 (c) 4800 (d) 7200

$\begin{array}{cc}{x}_i& f_i\\ 4& 10\\ 8& 11\\ 5& 9\\ 2& 13\end{array}$
Find $\sum f_i{x}_i$ from the given table.

O is the centre of the circle and line XY shares one common point with the circle. A line segment OP is drawn from O to line XY such that P is a point on line XY. What happens if P lies on the circle?

In the figure, write the

(i) Corresponding vertices and

(ii) Corresponding sides of the ΔAPQ and ΔABC. Hence show that AP. AB = AQ.AC.

What is the area of a triangle whose vertices are (0,4), (0,0) and (3,0)?

If $(1,2),(4,y),(x,6)$ and $(3,5)$ are the vertices of parallelogram taken in order, find $x$ and $y$.

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:

(i) The length of the arc

(ii) Area of the sector formed by the arc

(iii) Area of the segment forced by the corresponding chord

Find the number of values of x satisfying

$3x-3\le 7x+5and5-x\ge \left(\frac{x}{4}\right)-\left(\frac{5}{4}\right),wherexϵN.$

Akshay’s income is 20% less than that of Ajay. What percent is Ajay’s income more than that of Akshay?

Q. Two water taps together can fill a tank in 6 hours. The tap of larger takes 9 hours less than the smaller one to fill the tank separately. Find the time in which each tap cam separately fill the tank.

Please give me full ezplanexpla of this question some Tell me some tips that how to create equation of hard word problems :)

Question 3
Draw a $\Delta$ABC in which BC= 6cm, CA = 5 cm and AB= 4 cm .Construct a triangle similar to it and of scale factor = $\frac{5}{3}$.
Thinking process
Here, scale factor = $\frac{m}{n}=\frac{5}{3}$ i.e m > n then the triangle to be construction is larger than the given through use this concept and then constant the required triangle.

1. 14

A cone of height h cm and base radius r cm is reshaped into a sphere. Then, which of the following is always correct?

In the figure, the $\angle ABC=30°$. If $CB=18m$ , then AB = and AC = .

In the given figure, $\Delta ODC\sim \Delta OBA,\angle BOC={115}^{o}and\angle CDO={70}^o$.

Find (i) $\angle DOC$

(ii) $\angle DCO$

(iii) $\angle OAB$

(iv) $\angle OBA$.

In which of the following goods, increase in the price of one causes an increase in demand of another?