Explore topic-wise InterviewSolutions in Current Affairs.

In the figure, AC > AB and D is a point on AC such that AB = AD, then

The interior angle of a regular polygon is double the exterior angle. The number of sides of the polygon is

The cost of a bike, purchased 2 years ago, depreciates at the rate of $20\%$ every year. If its present worth is ₹35600, find its purchase price.

If $lo{g}_a\left(ab\right)=x$, then $lo{g}_b\left(ab\right)$ is equal to

$O$ is the incentre of $△ABC$ and $\angle BOC={116}^{\circ }$. Then $\angle BAC=$

In the follow diagram, lines l, m and n are parallel to each other. Two transversals p and q intersect the parallel lines l, m and n at points A,B,C and P,Q,R respectively as shown below.
Which of the following is correct?

Which of the following line(s) would make a right-angled triangle with the coordinate axes?

A $3\times 3$ Rubik's cube has a total surface area of $54{\text{cm}}^2$. The area occupied by every single red tile of the cube is ___________ .

Question 6
The line represented by x = 7 is parallel to the X-axis. Justify whether the statement is true or not.

Among the observations, the value whose frequency of occurrence is maximum, is known as:

Find the number of lines of symmetry for the following figures.
(a)

(b)

[3 MARKS]

Which of the following is irrational number?

A number ‘s’ is called irrational if it cannot be written in the form of _____ , where p and q are integers and ______.

If the following numbers are represented on a number line, which number will be the rightmost?
5.6, -3, 0.5, 3

$997\times 998=$

.

If length, breadth and height of a cuboid are increased by 20%, what is the percentage increase in the the total surface area of cuboid? [3 MARKS]

How many lines can be drawn through a given point?

Diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD.If AB = CD, then show that:
(i) ar ($△$DOC) = ar ($△$AOB) (ii) ar ($△$DCB) = ar ($△$ACB) [4 MARKS]

Given $△$ DEF $\sim$ $△$ABC. If AB = 4 cm, BC = 2 cm, CA = 3 cm and EF = 4 cm, then the perimeter of $△$DEF is ____ cm.

Two triangles ABC and DEF are such that, AB = ED, BC = DF, AC = EF

The quotient obtained when we divide $a^6-b^6$ by the product of $a^2+ab+b^2$ and $a-b$.

Two equal circles intersect in P and Q. A straight line through P meets the circles in A and B. Prove that QA = QB.

Find the median of the following observations:

46,64,87,41,58,77,35,90,55,92,33

If 92 is replaced by 99 and 41 by 43 in the above data, what will be the new median?

The median of the following data: 1, 4, 7, 3, 9, 5, 3, 2, 7, 5.

Solve the following pair of equations:
2x + y = 7
3x + 2y = 12

In Fig. PQR is a triangle and S is any point in its interior, show that SQ + SR < PQ + PR. [3 MARKS]

$Ina\Delta ABC,sideBCisproducedtoD.If\angle ABC={50}^{\circ }and\angle ACD={110}^{\circ }then\angle A=?\left(a\right){160}^{\circ }\left(b\right){60}^{\circ }\left(c\right){80}^{\circ }\left(d\right){30}^{\circ }$

Assuming the earth to be a sphere of radius 6370 km, how many square kilometres is area of the land, if three fourth of the earths surface is covered by water?

$\text{A sphere of diameter 12.6 cm is melted and cast into a right circular cone of height 25.2 cm. The radius of the base of the cone is}\left(a\right)6.3cm\left(b\right)2.1cm\left(c\right)6cm\left(d\right)4cm$

Prove that :

$\left(i\right)(\sqrt{3\times 5^{-3}}÷\sqrt[3]{33^{-1}}\sqrt{5})\times \sqrt[6]{63\times 5^6}=\frac{3}{5}\left(ii\right)9^{\frac{3}{2}}-3\times 5^0-{\left(\frac{1}{81}\right)}^{\frac{-1}{2}}=15\left(iii\right){\left(\frac{1}{4}\right)}^{-2}-3\times 8^{\frac{2}{3}}\times 4^0+{\left(\frac{9}{16}\right)}^{\frac{-1}{2}}=\frac{16}{3}\left(iv\right)\frac{2^{\frac{1}{2}}\times 3^{\frac{1}{3}}\times 4^{\frac{1}{4}}}{{10}^{\frac{-1}{5}}\times 5^{\frac{3}{5}}}÷\frac{3^{\frac{4}{3}}\times 5^{\frac{-7}{5}}}{4^{\frac{-3}{5}}\times 6}=10\left(v\right)\sqrt{\frac{1}{4}}+(0.01{)}^{\frac{-1}{2}}-(27{)}^{\frac{2}{3}}=\frac{3}{2}\left(vi\right)\frac{2^n+2^{n-1}}{2^{n+1}-2^n}=\frac{3}{2}\left(vii\right){\left(\frac{64}{125}\right)}^{\frac{-2}{3}}+\frac{1}{{\left(\frac{256}{625}\right)}^{\frac{1}{4}}}+{\left(\frac{\sqrt{25}}{\sqrt[3]{364}}\right)}^0=\frac{61}{16}\left(viii\right)\frac{3^{-3}\times 6^2\times \sqrt{98}}{5^2\times \sqrt[3]{3\frac{1}{25}}\times (15{)}^{\frac{-4}{3}}\times 3^{\frac{1}{3}}}=28\sqrt{2}\left(ix\right)\frac{(0.6{)}^0-(0.1{)}^{-1}}{{\left(\frac{3}{8}\right)}^{-1}{\left(\frac{3}{2}\right)}^3+{\left(\frac{1}{3}\right)}^{-1}}=-\frac{3}{2}$

Question 33

State whether the given statements are true (T) or false (F).

If b : a = c : d, then a, b, c and d are in the proportion

A perpendicular bisector of a given line:

Find the value of ${27}^{\left(\frac{1}{{\log }_{4}3}\right)}+{16}^{{\log }_{4}2}+3^{\left(\frac{4}{{\log }_{7}9}\right)}$

Question 1(f)
Find the following product:
$(-12)\times (-11)\times \left(10\right)$

Write the supplement of an angle of measure $x^0$

A point is chosen in the given diagram .What is the probability that it is in the shaded area of the part of the circle? (Given that the diameter of the circle is equal to the measure of side of the square.)

A cricket coach noted the number of runs scored by a player over 8 matches. The data gathered is as follows:

In the given figure, ABCD is a parallelogram and ABEF is a rectangle, then

In the figure given above,
the ratio $\frac{AreaofDPQC}{AreaofABCD}$ =___.

The length of a rectangular wooden board is thrice its width. If the area of the board is 192 $c{m}^2$, find the cost of framing it at the rate of ₹.5 for 20 cm.

Which of the following is the coefficient of the given term?

$5x^4$

Find an irrational number between 3 & 5.

In $△$ABC if $\angle$B = $\angle$C = ${45}^{\circ }$, which of the following is the longest side?

Question 2 (i)
Find: $9^{\frac{3}{2}}$

In the adjoining figure, M is the midpoint of side BC of a parallelogram ABCD such that $\angle BAM=\angle DAM$. Prove that AD = 2CD.

Question 137(ii)

While studying her family's history, Shikha discovers records of ancestors 12 generations back. She wonders how many ancestors she had in the past 12 generations. She starts to make a diagram to help her figure this out. The diagram soon becomes very complex.



Write an equation for the number of ancestors in a given generation n.