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If an isosceles triangle has a perimeter of $20cm$ and base $4cm$, then its area is ___ .

Question 58

If $\frac{2}{3}$ of a number is 10, then what is 1.75 times of that number?

The curved surface area of cylinder is $1210c{m}^2$ and its diameter is 20 cm. Find its height and volume.

$\sqrt{10}\times \sqrt{15}=?$

(a)$\sqrt{25}$ (b)$5\sqrt{6}$ (c)$6\sqrt{5}$ (d) None of these

Factorize:6 X² + 5 x - 6

$\text{The sides BC,CA and AB of}\Delta ABC\text{have been produced to D ,E and respectively}\angle BAE+\angle CBF+\angle ACD=?.$

$\left(a\right){240}^{\circ }\left(b\right){300}^{\circ }\left(c\right){320}^{\circ }\left(d\right){360}^{\circ }$

The length of a string between a kite and a point on the ground is 60$\sqrt{3}$ m. If the string makes an angle of ${60}^{\circ }$ with the ground, how high is the kite? (Assume there is no slack in the string).

Find the HCF of 32 and 616 by prime factorisation method and Euclid division algorithm

A circle having radius 4 cm contains a chord of length 4 cm and subtends an angle of 60 degrees. Find the area of the minor segment of the chord.

Question 17

Fill in the blanks to make each statement true:

The solution of the equation 3x - 4 = 1 - 2x is ...................

If $p^{th},q^{th},r^{th}$ terms of a $G.P.$ are the positive numbers $a,b$ and $c,$ then the angle between the vectors $\left(\log a^2\right)\hat{i}+\left(\log b^2\right)\hat{j}+\left(\log c^2\right)\hat{k}$ and $(q-r)\hat{i}+(r-p)\hat{j}+(p-q)\hat{k}$ is

Find n if ${}^{n-1}{P}_3:{}^n{P}_4=1:9.$

a rhombus sheet , whose perimeter is 32 m and one of whose diagonal is 10 m long is painted on both sides at the rate of Rs 5 per m sq. find the cost of painting

Factorise:- x²+y-xy-x

In the figure, ABCD and AEFG are two parallelograms. If $\angle C={58}^{\circ }$, Find $\angle F$.

ABCD is a rectangle of area $40c{m}^2$. If X is any point on AB, then what is the area of $\Delta XCD$ ?

In the figure, if lines l and m are parallel lines, then x =

For x = 5, we can construct which of the following equation?

Express the order of magnitude of the following quantities

12578935m

In the adjoining figure, x : y : z = 5 : 5 : 6. If XOY is a straight line, find the values of x, y and z.

Question 78

In the following question, state whether the statement is True (T) or False (F):

The value of p for ${51}^2-{49}^2=100p$ is 2.

$\text{How many lead shots,each 0.3 cm in diameter, can be made from a cuboid of dimensions}9cm\times 11cm\times 12cm?\left(a\right)7200\left(b\right)8400\left(c\right)72000\left(d\right)84000$

The angles of quadrilateral are in ratio3.5.9.13. Find all the angles of the qluadrilateral.

The area (in sq. units) of the triangle formed by the points $A(1,1,2),B(2,3,5),C(1,15,5)$ is

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are vectors such that $|\overrightarrow{a}+\overrightarrow{b}|=\sqrt{29}$ and $\overrightarrow{a}\times (2\hat{i}+3\hat{j}+4\hat{k})=(2\hat{i}+3\hat{j}+4\hat{k})\times \overrightarrow{b},$ then a possible value of $(\overrightarrow{a}+\overrightarrow{b})\cdot (-7\hat{i}+2\hat{j}+3\hat{k})$ is

If D, E and F are the mid points of the sides BC, CA and AB of an equilateral triangle ABC, then triangle DEF is

A cube of side 4 $cm$ is cut into cubes of side 1 $cm$. Calculate the total surface area of all the small cubes.

Question 2

Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.