Explore topic-wise InterviewSolutions in Current Affairs.

D is midpoint of side BC of $△ABC$ and E is the midpoint of BD.If O is the midpoint of AE,prove that $ar\left(△BOE\right)=\frac{1}{8}ar\left(△ABC\right)$

In the figure, if lines l and m are parallel, then the value of x is

Using ruler and compasses only, draw a right angle.

In the figure, ABCD is a cyclic quadrilateral, Find the value of x.

Examine, whether the following numbers are rational or irrational:

(i) $\sqrt{7}$ (ii) $\sqrt{4}$

(iii) $2+\sqrt{3}$ (iv) $\sqrt{3}+\sqrt{2}$

(v) $\sqrt{3}+\sqrt{5}$ (vi) $(\sqrt{2}-2{)}^2$

(vii) $(2-\sqrt{2})(2+\sqrt{2})$ (viii) $\sqrt{2}+\sqrt{3}{)}^2$

(ix) $\sqrt{5}-2$ (x) $\sqrt{23}$

(xi) $\sqrt{225}$ (xii) 0.3796

(xiii) 7.478478..... (xiv) 1.101001000100001.....

If $x-\frac{1}{x}=-1,$ find the value of $x^2+\frac{1}{x^2}$.

There were two sacks containing numbers, sack A contained the set of positive integers while sack B contained the set of whole numbers. Which sack contains more numbers?

Which economist defined inflation to be a state in which the value of money is falling?

In the above figure AB || CD. Also, ∠EAB = 84^o and ∠ECD = 126^o. Then, the value of "x" is

If the range of the data is 36 and the maximum value is 71, then the minimum value is

Area of the parallelogram $ABCD=1024$ sq. units. Find the area of $△AGH$. Here $E,F,G$ and $H$ are the mid points of $AB,AD,AE$ and $AF$ respectively.

The degree of a constant polynomial is ___ .

The roster form of the set $A=\{x:x=\frac{n}{2n+1},n\in N\text{and}n<4\}$ is ___. (Here, N stands for the set of natural numbers)

Factorise:

$12(3x-2y{)}^2-3x+2y-1$

1. 64000

Represent $\frac{5}{6}$ in decimal form.

The semi perimeter of a triangle is 132cm. The product of the difference of semi perimeter and it's respective side is 13200cm³. Find the area of triangle.

Range of the function $y=\frac{2^x-2^{-x}}{2^x+2^{-x}}$ is

Draw the graph of $y=|x|+2.$

$A,B,C$ are the three angles of a triangle. If $A-B={15}^{\circ }$, $B-C={30}^{\circ }$, find $\angle$A, $\angle$B and $\angle$C .

If two sides of a triangle are unequal then the smaller angle has the__ side opposite to it.

In the above triangle ABC, AB = BC. BD is perpendicular to AC and EC bisects the angle $\angle ACB$. Which of the following is correct?

The figure formed by joining the mid points of consecutive sides of a quadrilateral is

$\frac{3}{7}$ of $\frac{2}{5}$ is equal to

In a company, we need to find the central value of salaries of employees in all categories, i.e., I, II III, IV, then we must find

Volume of a sphere is directly proportional to the __ of the radius of the sphere.

Rationalise the denominator in $\frac{5}{3\sqrt{3}}$

Which of the following is a rational number between $\frac{5}{4}$ and $\frac{3}{2}$?

The area of an equilateral triangle is 16 root 3 cm^2.Find its perimeter.

Can you tell me the derivation of identity (a + b)3 = a3 + b3 + 3ab (a + b)

How many milli seconds are there in 1 nano seconds?

AN and CP are perpendiculars to the diagonal BD of a parallelogram ABCD. Choose the correct option

In the given figure arc AB and arc CD of a circle having centre at O are equal to 5cm.If $\angle AOB={30}^{\circ }$, then the $\angle COD$ is equal to__.

Find the area of the quarilateral ABCD if AB = 5 m, BC = 5 m, CD = 6 m and AD = 6 m.

What is the perimeter of $△$ ADE given in the figure?

$\text{In the given figure,}PQ>\text{PR and QS and RS are the bisectors of}\angle Qand\angle R\text{respectively. show that}SQ>SR.$

In each of the following, using the remainder Theorem, find the remainder when f(x) is divided by g(x) and verify the result y actual division.

f(x) = $9x^3-3x^2$ + x -5, g(x) = x -$\frac{2}{3}$

Which of the following is equivalent to $\frac{1}{\sqrt{6}}+\frac{1}{\sqrt{5}}$ ?

Two coin and one dice are rolled simultaneously. The outcomes obtained are listed below in the form of table given below.

Question 78 (ii)

If a and b vary inversely to each other, then find the values of x,y,z

Question 8
A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

Solution:

Side(a) of the cube = 12 cm

Volume of the cube =(a)3=(12 cm)3=1728 cm3

Let the side of the smaller cube be a1.

Volume of 1 smaller cube =(17288)cm3=216 cm3(a1)3=216 cm3⇒a1=6 cm

Therefore, the side of the smaller cubes will be 6 cm.

Ratio between surface areas of cubes =Surface area of bigger cubeSurface area of Smaller cube=6×1226×62=(12)2(6)2=41

Therefore, the ratio between the surface areas of these cubes is 4:1.

my doubt is how this a1 got 6cm

In the given figure, $\angle OAB={110}^{\circ }$ and $\angle BCD={130}^{\circ }$ then $\angle ABC$ is equal to

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

(b) ${50}^{\circ }$

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

(d) ${70}^{\circ }$

Find the mode of the following data.

$$\begin{array}{cccccccc}NumberofPlants& 0-2& 2-4& 4-6& 6-8& 8-10& 10-12& 12-14\\ Number& 1& 3& 2& 4& 5& 3& 2\end{array}$$

Prove that the diagonals of a rhombus are perpendicular. [3 MARKS]

In the given figure, O is the centre of the circle. Chord CD is parallel to the diameter AB. If $\angle$ABC = ${35}^0$, calculate $\angle$CED