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The perimeter of a triangular field is 420 m and its sides are in the ratio 6:7:8. Find the area of the triangular field.

Convert the following equations in the general form given by:
$a_{1}x+b_{1}y+c_1=0and$
$a_{2}x+b_{2}y+c_2=0$,
and find $a_1,b_{2}and{c}_2$ respectively.
(1) 4x + 9y = 11
(2) 3x + 3y = 0

Write a alinear equation such that the point (1,2) lies on its graph.

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

Meenakshi cycles to her school at an average speed of 12 km/hr and takes 20 minutes to reach her school. If she wants to reach her school in 12 minutes, her average speed should be:

Hardeep went to a bank and deposited Rs 80000 at the rate of simple interest of 7% per annum. After some years, he withdrew 91200 and closed the account.

The adjacent sides of a parallelogram PQRS measure 34 cm and 20 cm and the diagonal QS measures 42 cm. Then, the area of parallelogram is:

At a certain rate of interest, the interest after 3 years on Rs. 5000 principal is Rs.1200. What would be the interest on Rs. 12000 for the same time period?

Nikita had 60 balloons on her birthday.She kept 12 balloons and distributed the remaining equally among her 8 friends.

a)How many balloons did each of her friends get?

b)What value does Nikita show by this gesture?

A parallelogram with equal sides and equal angles will be:

If A={1,2,3,4,5,6}, B={1,2}, then $\frac{A}{\left(\frac{A}{B}\right)}$ is equal to

In the above figure, ACDF, ABEF and BCDE are parallelograms. Analyse the given figure and choose the correct option(s).

What is the length of arc of a circle whose radius is 14 cm and which subtends an angle of 135^o at the centre?

(1) Story-telling should speak first to the heart and only second to the intellect.
(2) It should, in Isaac Bashevis Singer’s words, “be both clear and profound,” and it should also entertain.
(3) Many fine writing programs have sprung up across the United States.
(4) The new writer should avoid creating pieces that are deliberately obscure and impossible to understand except by a small, elite group of other writers.

Solve

$3^{x^2}:3^x=9:1$.

The point (3, – 5) lies in the ……… quadrant

In the figure, AB || CD and ∠F = 30^o the value of ∠ECD is

Given, ABCD is a rectangle and BD and AC are the two diagonals as shown. Which of the following statement is correct?

In the given figure, AB is the chord to the circle having centre at O. If AC = CB and $\angle AOC={50}^{\circ }$, then $\angle CAO$ is equal to__.

What Will be the height (AO) of the triangle if $\angle$ ABO given is changed from ${45}^{\circ }$ to ${60}^{\circ }$?

If Anish is moving along the boundary of a triangular field of sides 35m, 53m and 66m and you are moving along the boundary of a circular field whose area is double the area of the triangular field, then the radius of the circular field is :

(Take $pi=\frac{22}{7}$)

If in $△ABC$, $AB=10cm$, $\angle CAB$ = ${30}^{\circ }$ and $\angle CBA$ = ${60}^{\circ }$ and in $△DEF$, $FE=10cm$, $\angle DFE={30}^{\circ }$, $\angle DEF={60}^{\circ }$; then, select the correct statement.

(a) Draw an angle ${115}^{\circ }$ and construct its bisector. [2 MARKS]
(b) Suppose an angle (whose measure we do not know) is given and you have to make a copy of this angle. How will you do it? [2 MARKS]

In the given figure, PQ>PR. QS and RS are the bisectors of $\angle Q$ and $\angle R$, respectively then which of the following is true?

In a $\Delta ABC,\angle C=3\angle B=2(\angle A+\angle B)$.

Choose the correct options.

The height of a cone is 21 cm.Find the area of the base if the slant height is 28 cm.

The probability expressed as a percentage of a particular occurrence can never be
(a) less than $100$
(b) less than $0$
(c) greater than $1$
(d) anything but a whole number

Factorize using suitable identities:

2x^2+11x-21

. How many square metres of canvas is required for a conical tent whose height is 3.5 m and the radius of whose base is 12 m?

Mr. Siddhant opened a recurring deposit account in a bank. He deposited in the installment of Rs. 2500 per month for two years. At the time of maturity he received an amount of Rs. 67,500. Calculate the rate of interest per annum.

Is zero is rational number where q=o

Area of a face of a cuboid is of the form xy, where x and y are length and breadth respectively.

In the solution this statement is shown true.But area of one face of cuboid can also be breadth x height or length x height

In the given figure, AB = BC and AC = CD. Find the ratio of ∠BAD: ∠ADB.

In order to draw a frequency polygon by using a histogram, which of the following statements is incorrect?

The equation of the circumcircle of the triangle formed by the lines x = 0, y = 0, 2x + 3y = 5 is

The area of a sector of a circle with radius 12 cm and angle 60° is .

If f (x) be a quadratic polynomial such that f (2)=-3 and f (-2)=21. Find the coefficient of x in f (x)

A= {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} write the sets using rule method

All the angles of a convex quadrilateral are congruent. However, not all its sides are congruent. What type of quadrilateral is it?

Pentacontagon is the name given to a polygon which has 50 sides. What will be the measure of one side of a regular pentacontagon if its perimeter is 1250 cm?

Match column B to column A

$$\begin{array}{cc}ColumnA& ColumnB\\ \left(a\right)sin(90-A)& \left(i\right)cosA\\ \left(b\right)tan(90-A)& \left(ii\right)cosecA\\ \left(c\right)sec(90-A)& \left(iii\right)cotA\end{array}$$

In a right triangle $\Delta$ ABC with right angle at B, BD is a perpendicular, dropped onto the hypotenuse. Which of the following statements are true?

Construct a $\Delta$PQR with QR = 8 cm, PQ = 6 cm, PR = 4 cm. Construct the incircle of the triangle and find the radius of the incircle.