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A sphere of radius 4 cm is melted and recast into the shape of a cylinder of radius 8 cm. What is the height of the cylinder formed?

In the figure , ABCD is a parallelogram. If AB = 12 cm, AE = 7.5 cm, CF = 15 cm, then AD =

Find the supplement of each of the following angles:

(i) ${42}^{\circ }$

(ii) ${90}^{\circ }$

(iii) ${124}^{\circ }$

(iv) $\frac{3}{5}$ of a right angle

Is the product of a rational and an irrational number always irrational? Give an example

P = $\frac{7}{8}$ and Q = $\frac{8}{7}$ ; Which is greater in P and Q?
Ans: ___.

The lateral surface area of a cylinder is

$\left(a\right){\pi }^{2}h\left(b\right)\pi rh\left(c\right)2\pi rh\left(d\right)2\pi r^2$

Factorize $a^3-3a^{2}b+3a{b}^2-b^3+8$

Show that :

$\frac{{(a+\frac{1}{b})}^m\times {(a-\frac{1}{b})}^n}{{(b+\frac{1}{a})}^m\times {(b-\frac{1}{a})}^n}={\left(\frac{a}{b}\right)}^{m+n}$

Factorise

a⁶+b⁶

If f(x) =2x - 1 , what is f(-5)

Draw a circle with centre at point O. Draw its two chords AB and CD such that AB is not parallel to CD. Draw the perpendicular bisectors of AB and CD. At what point do they intersect ?

A three-wheeler scooter charges Rs 15 for first kilometre and Rs 8 each for every subsequent kilometre. For a distance of x km, an amount of Rs y is paid. Write the linear equation representing the above information.

A solid cylinder has a total surface area of $462c{m}^2$, if its curved surface area is one third of its total surface area. find the radius and height of the cylinder

Factorize $(a-3b{)}^3+(3b-c{)}^3+(c-a{)}^3$

ABCD is a parallelogram such that its diagonals are equal.What is the measure of angle ABC?

The equation of the line shown in the figure is.

If AB || CD, CD || EF and y:z = 3:7 then x is

The corresponding angles of a quadrilateral are 48°, 72°, 120° and 120°

If the given figure is a parallelogram, find the values of x and y.

In the figure, AOC is a line, find x.

Match the following columns:

$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \left(a\right)\text{Angle bisectors of a parallelogram form a}& \left(p\right)\text{parallelogram}\\ \left(b\right)\text{The quadrilateral formed by joining the}& \left(q\right)\text{rectangle}\\ \text{midpoints of the pairs of adjacent sides}& \\ \text{of a square is a}& \\ \left(c\right)\text{The quadrilateral formed by joining the}& \left(r\right)\text{square}\\ \text{midpoints of the pairs of adjacent sides of}& \\ \text{a rectangle is a}& \\ \left(d\right)\text{The figure formed by joining the}& \left(s\right)\text{rhombus}\\ \text{mid-points of the pairs of adjacent sides}& \\ \text{of a quadrilateral is a}& \end{array}$

The correct answer is:

(a) ___ $\cdots$,

(b) ___ $\cdots$,

(c) ___ $\cdots$,

(d) ___​​​​​​​ $\cdots$

Question 10 (i)
A piggy bank contains hundred 50 p coins, fifty Re. 1 coins, twenty Rs. 2 coins and ten Rs. 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin will be a 50 p coin?

What is the value of p if x-2 is a factor of x² - 6x + p ?

If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is

If $△$ABC $\cong$ $△$DEF by SSS congruence, then, which of the following options is correct?

The outer diameter of a spherical shell is 12 cm and its inner diameter is 8 cm,Find the volume of metal contained in the shell. Also find its outer surface area.

Find the value of $\frac{6}{\sqrt{5}-\sqrt{3}}$, it being given that $\sqrt{3}=1.732and\sqrt{5}=2.236$.

If (4, 19) is a solution of the equation $y=ax+3$, then a =

$\sqrt[5]{56}\times \sqrt[5]{56}$ is equal to

In the figure, O and O' are centres of two circles intersecting at B aand C. ACD is a straight line, find x.

A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percentage is:

The length of a rectangular notebook is 15 cm and the perimeter is 50 cm. Find the width and area of the notebook.

A Cuboid has length, breadth and height of 6 cm, 4 cm and 2 cm respectively. Find the total surface area of Cuboid.

What is the perimeter of the triangle?

A juice seller fills glasses from a big cylindrical container of height 35.2cm and radius 10cm. He charges Rs10 for each glass of height 10cm and 4cm radius. The amount of money he earns by selling juice is(Take $\pi$= $\frac{22}{7}$)

Find the negation of the statement - 'There exists a rational number x such that its square is 2 '.

What is the perimeter of the triangle ABC in the given figure ABCD? ( Take $\sqrt{2}$ = 1.4 )

In the adjoining figure, ABCD is a parallelogram in which $\angle BAD={75}^{\circ }and\angle CBD={60}^{\circ }$. Then, $\angle BDC=$ ?

(a) ${60}^{\circ }$

(b) ${75}^{\circ }$

(c) ${45}^{\circ }$

(d) ${50}^{\circ }$

In the figure, if $l_1\left|\right|l_2$ the value of x is

Question 25

If 12 pumps can empty a reservoir in 20 hours, then the time required by 45 such pumps to empty the same reservoir is___hours.

A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients ?

Let $ABC$ be an isosceles triangle in which $AB=AC.$ If $D,E,F$ be the midpoints of the sides $BC,CA,$ and $AB$ respectively, show that the segment $AD$ and $EF$ bisect each other at right angles.

Construct a triangle XYZ in which $\angle Y={30}^{\circ },\angle Z={90}^{\circ }andXY+YZ+ZX=11.$

For a triangle ABC, the true statement is –

Question 4 (ii)
The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:
$\begin{array}{cc}\text{Length (in mm)}& \text{Number of leaves}\\ 118-126& 3\\ 127-135& 5\\ 136-144& 9\\ 145-153& 12\\ 154-162& 5\\ 163-171& 4\\ 172-180& 2\end{array}$
(ii) Is there any other suitable graphical representation for the same data?

Which of the following is true for a matrix A.

Consider the marks obtained by 20 students out of 100 marks in a science quiz

30 40 50 35 55 60 40 30 60 75

75 60 30 40 60 55 35 50 40 30

What is the frequency of 60 marks?