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A concrete pillar has a radius of 3.5 cm and a length of 15 cm. The total surface area of the pillar is ______.

Draw the perpendicular bisector of a line segment of length 10 cm. Find the point on the bisector, which along with the line segment forms an equilateral triangle.

1.666666...... is a rational number and can be expressed in $\frac{p}{q}$ form. Then p + q is ______.

In the given figure, D and E are mid points of sides AB and AC respectively of $\Delta$ABC. Which of the following is true ?

In the figure, if $PQ\parallel RS,\angle MXQ={135}^{\circ }$ and $\angle MYR={40}^{\circ }$. The measure of $\angle XMY$ is.

If each edge of a cube is increased by $50\%$, then its surface area is increased to .

Write the truth value (T/F) of each of the following statements :

(i) Two lines intersect in a point.

(ii) Two lines may intersect in two points.

(iii) A segment has no length.

(iv) Two distinct points always determine a line.

(v) Every ray has a finite length.

(vi) A ray has one end-point only.

(vii) A segment has one end-point only.

(viii) The ray AB is same as ray BA.

(ix) Only a single line may pass through a given point.

(x) Two lines are coincident if they have only onepoint in common.

What is the radius (in cm) of the tyre in a car, if it covers 0.396 km in 300 rotations? (Use π = $\frac{22}{7}$)

In the figure if AB ||CD, ∠APQ = 50^o and ∠PRD = 127^o then y is equal to

In the figure, two lines intersect at O. If x = ${75}^{\circ }$, find $\angle$u + $\angle$y.

By grouping the terms in xyz - xy - z + 1, we get

An exterior angle of triangle is ${80}^{\circ }$ and the interior opposite angles are in the ratio $1:3$. The measure of each interior opposite angle is

The perimeter of a right triangle is 144 cm and its hypotenuse measures 65 cm. The other sides and its area are

There are two numbers. If 2490 is subtracted from one number then we get the other number. The algebraic expression depicting this information is:

Which of the following statement is correct?

If the sides of a triangle is 20cm,24cm and 25cm.Find the semi perimeter of the triangle. [1 MARK]

In the following figure, ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect DC at P, then:

What is the solution to the system: 2x + 3y = 1 and -x + y = -3?

Two dice are thrown simultaneously. Find the probability of getting a sum of 12.

The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period 6: 05 am and 6: 40 am.

What is the difference between the number of edges and number of faces of a cube?

A rectangular paper is $44cm$ long and $20cm$ wide. A cylinder is formed by rolling the paper along its length. The volume of the cylinder will be

The value of the polynomial q(t) = 3t³ - 4t + √33 at t = 2 is

A principle of Rs. 40,000 is deposited in a bank which offers a simple interest at a rate of 10% a year. The amount at the end of 2 years is ___

Let $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ be three non -zero vectors such that no two of these are collinear. If the vector $\overrightarrow{a}+2\overrightarrow{b}$ is collinear with $\overrightarrow{c}$ and $\overrightarrow{b}+3\overrightarrow{c}$ is collinear with $\overrightarrow{a}$ $(\lambda$ being some non -zero scalar) then $\overrightarrow{a}+2\overrightarrow{b}+6\overrightarrow{c}$ equals

The Mean of 5 observations is 25. If one of the observations , 27 is removed from it, what will be the new mean?

If $cos(\frac{x}{2}+{10}^{\circ })=\frac{\sqrt{3}}{2}$, then x = ___

Two parallel chords of lengths 30 cm and 16 cm are drawn on the opposite sides of the centre of a circle of radius 17 cm. Find the distance between the chords.

Add (i) $(2\sqrt{3}-5\sqrt{2})and(\sqrt{3}+2\sqrt{2})$

(ii) $(2\sqrt{2}+5\sqrt{3}-7\sqrt{5})and(3\sqrt{3}-\sqrt{2}+\sqrt{5})$

(iii) $(\frac{2}{3}\sqrt{7}-\frac{1}{2}\sqrt{2}+6\sqrt{11})and(\frac{1}{3}\sqrt{7}+\frac{3}{2}\sqrt{2}-\sqrt{11})$

Find the mean of 994,996,998,1002 and 1000.

If $A_1,A_{2}and{A}_3$ denote the areas of three adjacent faces of a cuboid, then its volume is

If $25$ meters of cloth costs $Rs.337.50$ then
What will be the length of the cloth bought for $Rs.810$ ?

If any point on a perpendicular bisector is used to form a triangle along with the given line segment. The triangle formed will be a ___ triangle.

Read the bar graph given in figure and answer the following questions:
(i) What information is given in by the bar graph?
(ii) What was the crop-production if rice in 1970-71?
(iii) What is the difference between the maximum and minimum production of rice?

$Ina\Delta ABC,if3\angle A=4\angle B=6\angle CthenA:B:C=?$

(a) 3:4:6 (b) 4:3:2 (c) 2:3:4 (d) 6:4:3

In the given figure, AOB is a straight line. If $\angle AOC=4x^{\circ }$ and $\angle BOC=5x^{\circ }$ then $\angle AOC=?$

(a) ${40}^{\circ }$

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

(c) ${80}^{\circ }$

(d) ${100}^{\circ }$

In the given figure ABCD is a parallelogram. If P is a point on the diagonal, which of the following is true?

The shopkeeper shows an item of Rs. 551.50. He says there is a discount of 10%. What is the approximate amount I should pay?

Though a^3+b^3 is totally positive, (a+b)(a^2-ab+b^2) has​ a negative term in it.How is this possible?

A foot path of uniform width runs all around inside of a rectangular field 45m long and 36m wide. If the area of the path is 234m^2,find the width of the path

The cost of 3 cricket bats and 6 balls is ₹ 3900. The cost of one bat and 3 balls of the same kind is ₹ 1700. Select the equations that represent this situation algebraically.

Question 3 (ii)
Given below are the seats won by different political parties in the polling outcome of a state assembly elections:
$\begin{array}{ccccccc}\text{Political Party}& A& B& C& D& E& F\\ \text{Seats Won}& 75& 55& 37& 29& 10& 37\end{array}$
(ii) Which political party won the maximum number of seats?

Imagine a picture of a scoop of ice-cream in a cone. Draw a picture, considering the cone to be in the shape of an equilateral triangle and the scoop, to be in the shape of a semi circle, to fit exactly on the side of the equilateral triangle. What is the area of the picture if the side of the equilateral triangle is, a = 6 cm?

Calculate the circumference of a circle having its diameter as 28 cm.