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A cone of height 20 cm and radius of base 5 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere.

In the given figure, a circle with centre O, is inscribed in a quadrilateral ABCD such that it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, $\angle$ = ${90}^o$ and DS = 5 cm then find the radius of the circle.

The three vertices of a parallelogram are (3, 4), (3, 8) and (9, 8). Find the fourth vertex.

What is the minimum rate prescribed under GST?

Find the value of $m$ so that the quadratic equation $mx(5x-6)+9=0$ has two equal roots.

Three vertices of a parallelogram are on a circle and the fourth vertex is at the center. Find $\angle$ ABC.

A box contains 3 black balls, 4 red balls, and 3 green balls. All the balls are identical in shape and size. Rohit takes out a ball from the bag without looking into it. What is the probability that the ball drawn is a black ball?

in figure A BC esd triangle in which L ABC > 90^{o and AD perpendicular to CB produced prove that AC sq. = AB sq. + BC sq . + 2BC × BD}

Write the equation y = 5x - 3 in the form ax + by + c = 0, and indicate the value of a b and c

The co-ordinate of the point which divides the line joining the points (–1, 7) and (4, –3) in the ratio 2:3 is ________.

Question 4
Given that HCF (306, 657) = 9, find LCM (306, 657).

The parallel sides of an isosceles trapezium are 10cm and 6cm respectively and one of the non-parallel sides is 8cm. If the angle between the non-parallel and parallel side is ${110}^{\circ }$, then the area of the trapezium is ___ $[sin{70}^{\circ }=0.93]$

From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle is drawn. Then, the area of the quadrilateral PQOR is
(A) 60 cm${}^2$
(B) 65 cm${}^2$
(C) 30 cm${}^2$
(D) 32.5 cm${}^2$

Match the following:

$$\begin{array}{cc}1.sin({90}^{\circ }-A)& a)cosecA\\ 2.tan({90}^{\circ }-A)& b)cotA\\ 3.sec({90}^{\circ }-A)& c)cosA\end{array}$$

A ladder 10 m long reaches the window of a house 8 m above the ground. Find the distance of the foot of the ladder from the base of the wall.

$cosecA+cotA=\frac{1}{cosecA-cotA}$

A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass(in $c{m}^3$).

A cube has dimension 6 cm $\times$ 6 cm $\times$ 6 cm. Find the lateral surface area of the cube.

A number of the form 4ⁿ cannot be divisible by

The probability of selecting a rotten apple from a heap of 900 apples is 0•18.What is the number of rotten apples in the heap?

The length of shadow of a tower on the plane ground is times the height of the tower. The angle of elevation of sun is :

In the given figure, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm with centre O. If $\angle POQ={30}^{\circ }$, find the area of the shaded region.

The radii of the circular ends of a conical curd container, 6 cm high are 16 cm and 24 cm. The volume of the container in litres will be

In the given figure, ABCD is a rectangle with AB = 80 cm and BC = 70 cm, $△AED={90}^{\circ }$ and DE = 42 cm. A semicircle is drawn, taking BC as diameter. Find the area of the shaded region.

The mean of the marks obtained by 7 students in a group is 226. If the marks obtained by six of them are 340, 180, 260, 56, 275, 307, then the marks obtained by the seventh student are

Give the approximate value of $\pi$ as given by Aryabhatta.

Question 17

On dividing 7 by $\frac{2}{5}$ the result is

The marks achieved by students in a class is given below:

$\begin{array}{cc}\text{Marks (more than)}& \text{Frequency}\\ 0& 0\\ 10& 15\\ 20& 2\\ 30& 12\\ 40& 30\\ 50& 24\\ 60& 18\\ 70& 14\\ 80& 18\\ 90& 16\\ 100& 0\end{array}$

The continuous grouped data with class interval 20 for the above table will be ___.

(a) The point P (2, -4) is reflected about the line x = 0 to get the image Q. Find the co-ordinates of Q.

(b) The point Q is reflected about the line y = 0 to get the image R. Find the co-ordinates of R.

(c) Name the figure PQR.

(d) Find the area of figure PQR.

Question 87

A floor is 4.5 m long and 3.6 m wide A 6 cm square tile costs Rs. 23.25.
What will be the cost to cover the floor with these tiles?

Find the sixth term of the series :

$2^2,2^3,2^4,.......................$

The area of triangle OAB with O (0, 0), A (4, 0) & B (0, 6) is ________________

Express the following in p/q form

(1)= 0. 23 23 23 23

(2)= 0. 98333

What are the conditions for a sequence to be an AP?

What is the condition for three line segments AB, BC and AC to form a triangle?

The ratio of milk is to water in the certain solution of 75 litres is 2 :1. How much water is to be mixed in solution so that ratio becomes 1:2 ?

Does the point (-2.5,3.5) lie inside, outside or on the circle $x^2+y^2=25?$

How many of the following statements are correct?
1. Graph of $-f\left(x\right)$ is obtained by taking the reflection of $f\left(x\right)$ about x-axis.
2. Graph of $f(-x)$ is obtained by taking the reflection of $f\left(x\right)$ about x-axis.

3. Graph of $-f(-x)$ is obtained by taking the mirror image of the graph of $f\left(x\right)$ about x-axis and then about y-axis.

Find the sum to $n$ terms of the AP: $5,2,-1,-4,-7,...$

The volume of a conical tent is 1232 m³ & the area of the bare floor is 154 m². Calculate the length of the canvas required to cover this conical tent if its width is 2 m.

If A is $3\times 4$ matrix and B is a matrix such that A'B and BA' are both defined. Then B is of the type

The perimeter of a certain sector of a circle of radius 6.5 cm is 31cm. The area of the sector will be

Tan45 tan13 tan77 tan85=1

Write all the other trigonometric ratios of $\angle A$ in terms of $\text{sec}A.$