Explore topic-wise InterviewSolutions in Current Affairs.

A line segment having its end points on the circle is called a

Write the product of n geometric means between two numbers a and b.

If $\alpha$, $\beta$ are the roots of the equation $x^2-5x+6=0$, the value of ${\alpha }^2-{\beta }^2$ is:

In a $\Delta ABC$, AD is the bisector of $\angle A$, meeting side BC at D.
(i) If BD= 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC.
(ii) If BD= 2 cm, AB = 5 cm and DC = 3 cm, find AC.
(iii) If AB= 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.
(iv) If AB =10 cm, AC =14 cm and BC = 6 cm, find BD and DC.
(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm, find AB.
(vi) If AD= 5.6 cm, AC = 6 cm and DC = 3 cm, find BC.
(vii) If AB= 3.6 cm, BC e 6 cm and BD = 32 cm, find AC.
(viii) If AB =10 cm, AC = 6 cm and BC = 12 cm, find BD and DC

Find the ratio of the areas of two similar triangles shown in the figure.

The sum of probabilities of all outcomes in an experiment is__.

How to identify two points P and Q on a line segment AB such that AP:PQ = 1:2 and PQ:QB = 4:5?

Find the co-ordinate of the mid point of the line segment joining the points ( 2 ,1) (4,7)

AB is a chord of a circle. AB divides the circumference of the circle into two parts. The part with the longer length is called ____ and the part with shorter length is called ____.

6/x+y =7/x-y +3

1/2(x+y) =1/3(x-y)

If area(ΔAOB) = area(ΔCOD)

And ΔAOC~ΔBOD

Then does

area(ΔAOC) + ΔAOC ~ area(ΔCOD) + ΔBOD

Still true, above equation is true?

The height of a tree is $\sqrt{3}$ times the length of its shadow. Find the angle of elevation of the sun.

Construct a $3\times 3$ matrix whose elements $a_{ij}$ are given by $a_{ij}=0$ if $i<j$ and $a_{ij}=i+j$ if $i\ge j$.

Prove That:

In the given frequency distribution where the marks are ordered, which 2 observations (students) are the median observations?

$$\begin{array}{cc}Marksobtained& Numberofstudents\left(Frequency\right)\\ 20& 6\\ 25& 20\\ 28& 24\\ 29& 28\\ 33& 15\\ 38& 4\\ 42& 2\\ 43& 1\end{array}$$

Look at the following table below.
$\begin{array}{cc}\text{Class interval}& \text{Class mark}\\ 0-5& --\\ 5-10& --\\ 10-15& \\ 15-20& \end{array}$

Fill in the blanks with the class marks of the corresponding class intervals.

Nandhini Iyer standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60°. When she moves 50m away from the bank she finds the angle of elevation to be 30°, find: the height of the tree.

If 2 sin 2 θ = √3 then θ is

sin70/cos20+cosec20/sec70-2cos70cosec20.Simplify

A milk container is made of metal sheet in the shape of frustum of a cone whose volume is $10459\frac{3}{7}c{m}^3.$ The radii of its lower and upper circular ends are 8 cm and 20 cm respectively. Find the cost of metal sheet used in making the container at the rate of Rs 1.40 per $c{m}^2$.

A square water tank has its side equal to 40 m. There are four semi-circular grassy plots all round it. Find the cost of turfing the plot at Rs. 1.25 per square metre. (Take $\pi =3.14$)

In the given figure, there are two circles with the centres O and O' touching each other internally at P. Tangents TQ and TP are drawn to the larger circle and tangents TP and TR are drawn to the smaller circle . Find TQ : TR.

How many circles can be made with two points?

Question 3 (i)
On comparing the ratios $\frac{a_1}{a_2}$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$ find out whether the following pairs of linear equations are consistent, or inconsistent.
3x + 2y = 5 ; 2x - 3y = 7

In a $\Delta ABC$; the value of $\frac{co{s}^2\frac{B-C}{2}}{(b+c{)}^2}+\frac{si{n}^2\frac{B-C}{2}}{(b-c{)}^2}$ is

Find the value of: $ta{n}^2\theta +co{t}^2\theta +2$

The following data gives the marks obtained by students in an exam.

$\begin{array}{cc}\text{Class interval}& \text{Frequency}\\ Below10& 5\\ Below20& 10\\ Below30& 23\\ Below40& 31\\ Below50& 45\\ Below60& 49\end{array}$

(i)Convert the cumulative distribution to a regular distribution.

(ii)Calculate the mode. [3 MARKS]

A juice seller fills glasses from a big cylindrical container of height 35.2 cm and radius 10 cm . He charges Rs. 10 for each glass of height 10cm and 4cm radius. The amount of money he earns by selling juice is = (Take $\pi$= $\frac{22}{7}$)

TA and TB are tangents to a circle with centre O from an external point T. OT intersects the circle at point P. Prove that AP bisects the angle TAB.

Question 1(d)

Fill in the blanks:
1 crore = _______________ million

Find the distance between the points (-1, 5), (2, 1) [2 MARKS]

A semicircle with AB as diameter passes through the point 'P' as shown in fig. Find the centre of the given semicircle.

Question 1(c)

Estimate the following using general rule:
12,904 + 2,888

Construct a line segment of 10 cm. Divide this line segment in the ratio 3:2. [2 MARKS]

From a point P on the ground, the angle of elevation of the top of a 20 m tall building is ${30}^{\circ }$. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff is ${45}^{\circ }$. Find the height of the flag. (You may take $\sqrt{3}$ = 1.732)

A chord of a circle of radius 12 cm subtends an angle of ${120}^{\circ }$ at the centre. Find the area in $c{m}^2$ of the corresponding segment of the circle. (Use $\pi =3.14$ and $\sqrt{3}=1.73$) [3 MARKS]

In fig., circles C(O,r) and $C(O{}^{\prime },\frac{r}{2})$ touch internally at a point A and AB is a chord of the circle C (O,r) intersecting $C(O{}^{\prime },\frac{r}{2})$ at C. Prove that AC = CB. [3 MARKS]

"There is a good chance that the Prime Minister of India will visit Australia". What does this statement imply?

If a sector of radius 9 cm with central 240⁰ is folded into a cone, the slant height of cone is

State, in each case, whether true or false.

$\left(i\right)\sqrt{2}+\sqrt{3}=\sqrt{5}$

$\left(ii\right)2\sqrt{4}+2=6$

$\left(iii\right)3\sqrt{7}-2\sqrt{7}=\sqrt{7}$

$\left(iv\right)\frac{2}{7}$ is an irrational number.

$\left(v\right)\frac{5}{11}$ is a rational number.

(vi) All rational numbers are real numbers.

(vii) All real numbers are rational numbers.

(viii) Some real numbers are rational numbers.

In a triangle ABC, if AB=2x-1, $AC=2\sqrt{2x}$ and BC=2x+1. Find the angle $\angle BAC$.