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The perimeter of a triangle is 50cm.One side of a triangle is 4cm longer than the smaller side and the third side is 6cm less than twice the smaller side.Find the area of the triangle.

The curved area of a cone is 242 cm² and its radius and slant height are in the ratio 7:11. Calculate the radius of the cone.

In the rectangle ABCD, O is any point inside the rectangle. If area( ΔAOD) = 30 $c{m}^2$ and area( ΔBOC) = 60 $c{m}^2$, area of the rectangle ABCD is ___ $c{m}^2$.

Rationalising $\frac{\sqrt{2}+\sqrt{3}}{\sqrt{3}-\sqrt{2}}$ gives

In a cyclic quadrilateral ABCD, If $\angle A-\angle C={60}^o$, prove that the smaller of two is ${60}^o$.

Integers comprise of:

Construct a triangle ABC in which BC is 3.5 cm, Angle B is ${75}^{\circ }$ and AB+AC=6.5cm [4 MARKS]

The number of children in 10 families of a locality are
2, 4, 3, 4, 2, 0, 3, 5, 1, 6.
Find the mean number of children per family.

If $x=3+\sqrt{8}$ then $(x^2+\frac{1}{x^2})$ = ?

(a) 34 (b) 56 (c) 28 (d) 63

Factorize the following using appropriate identities: 9 $x^2$ + 6xy + $y^2$​

How many bullets can be made out of a cube of lead, whose edge measures 22 cm, each bullet being 2 cm in diameter?

Give an example of each, of two irrational numbers whose:

(i) difference is a rational number.

(ii) difference is an irrational number.

(iii) sum is a rational number.

(iv) sum is an irrational number.

(v) product is a rational number.

(vi) product is an irrational number.

(vii) quotient is a rational number.

(viii) quotient is an irrational number.

The shadow of a tower standing on a level ground is found to be 60 m longer when the Sun’s altitude is ${30}^{\circ }$ than when it is ${60}^{\circ }$. Find the height of the tower.

In the given figure, sides AB and AD of quad. ABCD are produced to E and F respectively. If $\angle CBE={100}^{\circ }then\angle CDF=?$

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

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

(c) ${130}^{\circ }$

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

Factorise:
$x^2-y^2+6y-9$

Using factor theorem, factorize each of the following polynomials

$2x^4-7x^3-13x^2$ + 63x - 45

The perimeter of a parallelogram is 22 cm. If the longer side measures 6.5 cm what is the measure of the shorter side ?

From a tap of inner radius 0.75 cm, water flows at the rate of 7 m per second. Find the volume in litres of water delivered by the pipe in one hour.

Two lines perpendicular to the same line are_______to each other.

The point from which distances are marked is called........................

The positive solution of equation ax + by + c = 0 always lie in the:

$(x+y)(x-y)(x^2+y^2)$ = ___________.

Arrange the following irrational numbers in decending order of magnitude,

5$\sqrt{5}$ , 3$\sqrt{7}$ , 8$\sqrt{2}$ , 8

$AB$ and $CD$ are two parallel chords of a circle such that $AB=10cm$ and $CD=24cm.$ If the chords are on the opposite sides of the centre and the distance between them is $17cm,$ find the radius of the circle.

If $a(x{)}^2+bx+c$ is a monomial in $x$ , what can be said about $a$, $b$ and $c$?

In order to find BD , the ratio which can be used is

In the figure, if AB = CD and $\angle$ABO = ${35}^{\circ }$. What is the value of $\angle$DCO in degrees?

The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of their surface areas.

The following 2 bar graphs shows the details of price distribution of making a car.One shows the amounts (in million Rs.) invested by a Lamborgini in purchasing raw materials for the production of a car over the years and the other shows the values (in million Rs.) of finished car sold by the Company over the years.

i)The difference between the amount invested in Raw materials and value of sales of finished car was maximum during which year?

ii) The value of sales of finished goods in 2009 was approximately what percent of the sum of amount invested in Raw materials in the years 2007, 2008 and 2009?

Question 50

Reshma prepared 18 kg of Burfi by mixing Khoya with sugar in the ratio 7 : 2. How much Khoya did she use?

The runs scored by 11 members of a cricket team are
15, 34, 56, 27, 43, 29, 31, 13, 50, 20, 0.
The median score is
(a) 27
(b) 29
(c) 31
(d) 20

The value of ${\{8^{\frac{-4}{3}}÷2^{-2}\}}^{\frac{1}{2}}$ is

If $x=log0.6;y=log1.25$ and $z=log3-2log2$, find the values of :

(i) $x+y-z$

(ii) $5^{x+y-z}$

Draw a histogram from the given data of a class students.

$\begin{array}{cc}Weight\left(kg\right)& Numberofstudents\\ 35.5-40.5& 4\\ 40.5-45.5& 15\\ 45.5-50.5& 12\\ 50.5-55.5& 13\\ 55.5-60.5& 6\end{array}$
[4 MARKS]

A technician has to repair a light on a pole of height 10 m. She needs to reach a point 2 m below the top of the pole to undertake the repair work. The length of the ramp that she should use which, when inclined at an angle of ${30}^{\circ }$ to the horizontal, would enable her to reach the required position, is ___ m

(You may take $\sqrt{3}$ = 1.73)

Write the value of ${25}^3-{75}^3+{50}^3.$

In the figure, if AC is bisector of $\angle BAD$ such that AB = 3 cm and AC = 5 cm, then CD =

Find the length of a chord which is at a distance of $5cm$ from the center of a circle of radius $10cm.$

Represent 23.43434343…. In a rational form.

In the figure, $AD\perp CDandCB\perp CD.IfAQ=BPandDP=CQ,\text{prove that}\angle DAQ=\angle CBP.$

In $△$ PQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. The value of cos R is .