Explore topic-wise InterviewSolutions in Current Affairs.

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, find the modal size of the surnames.

Solve for x and y:

$\frac{5}{x}+6y=13,\frac{3}{x}+4y=7(x\ne 0).$

A circle is drawn with AB as the diameter whose endpoints are $A(-4,2)$ and $B(8,10)$. If another circle with diameter one-third of the above circle is drawn with the same centre, what are the points that the circle cuts AB?

PT and PS are tangents drawn to a circle, with centre C, from a point P. If ∠TPS = 50^O, then the measure of ∠TCS is

if sec 3𝜃 = cosec(𝜃 − 2)where 3𝜃 and (𝜃 − 2) are acute angles, find 2𝜃.

Divide a line segment AB of length 9 cm in the ratio 4:4 at C. Now, divide the new line segment AC in the ratio 3:2 at M.

State the two properties which are necessary for given two triangles to be similar.

(i) Is the line 3x + 4y + 7 = 0 perpendicular to the line 28x - 21y + 50 = 0 ?

(ii) Is the line x - 3y = 4 perpendicular to the line 3x - y = 7 ?

(iii) Is the line 3x + 2y = 5 parallel to the line x + 2y = 1 ?

(iv) Determine x so that the slope of the line through (1, 4) and (x, 2) is 2.

In the figure above, DE and CE are the tangents through the point E. AF and AB are the tangents through the point F to the circle with centre M.

Also, $\angle DEM={30}^{\circ }$ and $\angle AFM={10}^{\circ }$

What is the value of $\angle MFB+\angle MEC=?$

Find the ${10}^{th}$ term of the AP : 2, 7, 12, . . .

If $2x,x+10,3x+2$ are in A.P, then $x$ = ___

Give an example of two rational numberthe product of which is a

1) rational number

2)irrational number

Find the smallest no. which when increased by 17is exactly divisible by 520 and468.

The image of a point P(x, y) when reflected in the X-axis is ___.

Question 2 (vi)
Write whether the given statement is true or false. Justify your answer.
If the coefficient of $x^2$ and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.

If $a\ne b\ne c$ prove that $(a,a^2),(b,b^2)(0,0)$ will not be collinear.

The decorative block shown in Fig. is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (Take $\pi =\frac{22}{7}$) [2 MARKS]

Question 87

Solve the following:

Find a number whose fifth part increased by 30 is equal to its fourth part decreased by 30.

A and B are two fixed points. What will be the locus of the point P such that $\angle APB={90}^{\circ }$

If $a\times cos\beta =cos\alpha$ and $b\times sin\beta =cos\alpha$, then value of $(a+b)cos\beta$ is

If $x-2$ is a factor of $2x^3-x^2-px-2$, then find the value of p.

There is a hollow cylinder as shown in the figure having outer radius 7 cm, height 21 cm and inner radius 6 cm, whose inner and outer surfaces are to be painted. Calculate the area to be painted.

The observations 29,32,48,50,x,x+2,72,78,84,95 are arranged in ascending order.What is the value of x if the median of the data is 63?

ABC is an isosceles triangle with AC = BC. If ${AB}^2=2{AC}^2$, prove that $\Delta ABC$ is right triangle. [1 MARK]

Question 43

2__ $\frac{5}{3}=\frac{10}{3}$

In $\Delta ABC$, $\angle A={60}^{\circ },\angle B={45}^{\circ }andAB=10cm$ as shown in the figure. Then the area of the triangle is equal to

For the two particles $P$ and $Q$ along the diametrically opposite end of a circle $(r=4\text{m})$ as shown in figure at time $t=0$, origin is taken at centre of the circle.

If Particle $P$ moves $6\text{m}$ towards $Q$, along line joining them. Then position of $P$ with respect to $Q$ will be:

Question 75

A typist has to type a manuscript of 40 pages. She has typed 30 pages of the manuscript. What is the ratio of the number of pages typed to the number of pages left?

In the given figure, AP and AQ are the tangents drawn to a circle from a point A outside the circle. If $\angle$PAQ = ${40}^{\circ }$ then, find $\angle$AQP.

Plot the points A(4, 6) and B (1, 2). If A' is the image of A when reflected in the X axis and B' is the image of B when reflected in the line AA'. then the figure ABA'B' so formed is a

Alpha and Beta are zeroes of polynomial x²-5x+k such that alha-beta=1 Find value of k

A solid metallic sphere of diameter 8 cm is melted and drawn into a cylindrical wire of uniform width. If the length of the wire is 12 m, find its width.

Graph of $y=x^2+7x+3$ intersects the x-axis at __ number of points

Question 93

If the price of petrol, diesel and LPG is slashed as follows

$\begin{array}{cccc}\text{Fuel}& \text{Old price/litre (in Rs)}& \text{New price/litre(in Rs)}& \%\text{Decrease}\\ \text{Petrol/L}& 45.62& 40.62& \_\_\_\\ \text{Diesel/L}& 32.86& 30.86& \_\_\_\\ \text{LPG/14.2 kg}& 304.70& 279.70& \_\_\_\end{array}$
Complete the above table.

Solve: 217X+131Y=913, 131X+217Y=827

Mark a point P outside the circle of radius 4 cm with centre O. Construct the two tangents to the circle from P which is at the distance of 7cm from centre. Measure the length of the tangents.

Given A = {a, b, c, d, e} B = {a, e, i, o, u} C = {c, d, e, u} . Show that A\ (B\C) $\ne$ (A\B)\C

A single 6-sided die is rolled. What is the probability of getting a 2 or 5?

The radius and height of a cone are in the ratio 3:4. Then the ratio of the total surface area to the curved surface area of the cone is

The number of possible pairs of numbers, whose product is 5400 and HCF is 30, is

Ans given:- 2 pairs

Rohan buys, 600, ₹ 200 share at ₹ 20 premium in a company paying 10% dividend. Then his annual income & percentage income will be

Given below are the weekly wages of 200 workers in a small factory.

Calculate the maean weekly wages of the workers.

2 tangents are drawn from a point P to a circle as shown . If PA : AB = 5:2 and the perimeter of triangle APB is 48 cm, the length of PB is:

A boy, standing on a 50 m tall building is looking at a stone on the ground. The distance between the stone and the building is equal to the height of the building. Find the angle of depression.

A cylindrical container of depth 20 m and radius 0.7 m is painted for Rs.8800. If the painter takes Rs.40 per sq. meter to paint the cylindrical container, then find the CSA of the cylindrical vessel.