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The radius of a wire is decreased to one third. If volume remains the same, the length will become

(a) 2 times (b) 3 times (c) 6 times (d) 9 times

Which of the following is a true statement ?

(a) (\pi\) and $\frac{22}{7}$ are both rationals.

(b) $\pi$ and $\frac{22}{7}$ are both irrationals.

(c) $\pi$ is rational and $\frac{22}{7}$ is irrational.

(d) $\pi$ is irrational and $\frac{22}{7}$ is rational.

$\text{The number of planks of dimensions}(4m\times 5m\times 2m)\text{that can be stored in a pit which is 40 m long, 12 m wide and 16 m deep,is}\left(a\right)190\left(b\right)192\left(c\right)184\left(d\right)180$

Let a be a rational number and b be an irrational number. Is ab necessarily an irrational number ? Justify your answer with an example.

A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in $m{m}^3$) is needed to fill this capsule?

If $x+\frac{1}{x}then{x}^2+\frac{1}{x^2}=$

A sphere of radius 5 cm is immersed in water filled in a cylinder, the level of water rises $\frac{5}{3}$ cm. Find the radius of the cylinder.

ABCD is a trapezium in which AB || DC. If $ar\left(△ABD\right)=24c{m}^2$ and AB = 8 cm, then height of$△ABC$ is

Question 1
A square is inscribed in an isosceles right triangle have one angle common. Show that the vertex of the square opposite the vertex of the common angle bisects the hypotenuse.

The coordinates of the point whose ordinate is 4 and which lies on the y-axis are?

The sum of the two angles in a triangle is ${95}^{\circ }$ and their difference is ${25}^{\circ }$. Then which of the following is/are true?

Prove that the diagonals of a parallelogram bisect each other.

Euclid's Axiom 1 is :

The sides of a triangular field are 325m, 300 m and 125 m. Its area is

Question 43

In the following question, fill in the blanks to make the statements true.

${[{\left(\frac{2}{13}\right)}^{-6}÷{\left(\frac{2}{13}\right)}^3]}^3\times {\left(\frac{2}{13}\right)}^{-9}=$ ___

Factorise: $2x^3-10x^2-4x+24$
using synthetic division.

Taylor purchased a rectangular plot of area 634$m^2$. The length of the plot is 2 more than thrice its breadth. Find the length and breadth (approximate values).

In the given triangle, the lines MN, PQ and BC are parallel to each other and AM = MP = PB. Which of the following statements is/are true?

Let $\overrightarrow{A}$ be vector parallel to line of intersection of planes $P_1$ and $P_2$ through origin. $P_1$ is parallel to the vectors $2\hat{j}+3\hat{k}$ and $4\hat{j}-3\hat{k}$ and $P_2$ is parallel to $\hat{j}-\hat{k}$ and $3\hat{i}+3\hat{j},$ then the angle between vector $\overrightarrow{A}$ and $2\overrightarrow{i}+\overrightarrow{j}-2\hat{k}$ is

If $a+b=10$ and $a-b=4,$ find the value of $a^2-b^2$

Which of the following is/are modes of cashless transactions?

Simplify (256)^8

If x= 1/2-√3 ,find the value of x³ - 2x² - 7x + 5

Simplify (√3+√11)²+(√3-√11)²

What is the perimeter of a regular heptagon if the length of one of its sides is 5 cm?

Find the area of an equilateral triangle whose perimeter is 60 cm

Factorise $(1-a^2)(1-b^2)+4ab$

Factorise: 1+64x³

A histogram, is a pictorial representation of the grouped data in which class intervals and frequency are respectively taken along

(a) vertical axis and horizontal axis

(b) vertical axis only

(c) horizontal axis only

(d) horizontal axis and vertical axis

A rectangular sheet of length 44 cm and breadth 10 cm is rolled up along the length to form a cylinder. So the volume of the cylinder is:

The length of the minute hand of a clock is $14cm.$ The area swept by the minute hand between $3:20$ and $3:45$ is

Find the area of the $△$AEF if EF = 1 m.

If the point P(2,1) lies on the line segment joining points A(4,2) and B(8,4) then

Question 15
A pole 6m high casts a shadow $2\sqrt{3}m$ long on the ground, then the Sun’s elevation is

(A) ${60}^{\circ }$
(B) ${45}^{\circ }$
(C) ${30}^{\circ }$
(D) ${90}^{\circ }$

Factorise:
$(x+1{)}^3+(x-1{)}^3$

Factorise:
$6-x-x^2$

If the perimeter of each face of a cube is 32 cm, find its lateral surface area. Note that four faces which meet the base of a cube are called its lateral faces.

Which of the following is an irrational number ?

(a) 3.14

(b) 3.141414......

(c) 3.14444....

(d) 3.141141114....

In the figure, CD || AE and CY || BA.
(i) Name a triangle equal in area of$△CBX.$
(ii) Prove that $ar\left(△ZDE\right)=ar\left(△CZA\right).$
(iii) Prove that ar (BCZY) = $ar\left(△EDZ\right)$

Choose the rational number which does not lie between $-\frac{2}{3}$ and $-\frac{1}{5}$

(a)$-\frac{3}{10}$

(b)$\frac{3}{10}$

(c)$-\frac{1}{4}$

(d)$-\frac{7}{20}$

$\text{Construct a}\Delta ABC\text{whose perimeter is 11.6cm and the base angles are}{45}^{\circ }and{60}^{\circ }$

Factorise:
$2x(p^2+q^2)+4y(p^2+q^2)$

There is a grouped data distribution for which mean is to be found by step deviation method.

A = assumed mean

B = class interval

C = sum of products of ‘u’ and frequency for each class interval

D = Total number of observations

Which of the following statements is true regarding mean(m) for the grouped distribution ?

For construction of a ${60}^{\circ }$ angle, which of the following instruments is not necessary.