Explore topic-wise InterviewSolutions in Current Affairs.

A (1, 4), B (3, 2) and C (7, 5) are vertices of a triangle ABC. Find :

(i) the co-ordinates of the centroid of triangle ABC.

(ii) the equation of a line, through the centroid and parallel to AB.

At $\theta ={90}^{\circ }$ which of the two angles are not defined?

AB is a fixed line. State the locus of the point P so that AB${}^2$= AP${}^2$+ BP${}^2$

M/s Saniya Sports Equipment does not keep proper records. From the following information, find out profit or loss and also prepare balance sheet for the year ended December 31, 2005.

$\begin{array}{ccc}\text{Items}& \text{Jan 1, 2005 (Rs.)}& \text{Dec 31, 2005 (Rs.)}\\ \text{Cash in hand}& 6,000& 24,000\\ \text{Bank Overdraft}& 30,000& \underset{–}{}\\ \text{Stock}& 50,000& 80,000\\ \text{Sundry Creditors}& 26,000& 40,000\\ \text{Sundry Debitors}& 60,000& 1,40,000\\ \text{Bills Payable}& 6,000& 12,000\\ \text{Furniture}& 40,000& 60,000\\ \text{Bills Receivable}& 8,000& 28,000\\ \text{Machinery}& 50,000& 1,00,000\\ \text{Investment}& 30,000& 80,000\end{array}$

Drawing Rs. 10,000 p.m. for personal use, fresh capital introduced during the year Rs. 2,00,000. Outstanding salary Rs. 2,400, prepaid insurance Rs. 700, depreciation charged on furniture and machinery 10% pa.

A clay ball was split in half and its insides is scooped out. If the hollow shape formed is a hemisphere of radius 7 cm, and has a thickness of 2 cm. Find the volume of the clay remaining in both the halves.

In the following passage, there are some numbered blanks. Fill in the blanks by selecting the most appropriate word for each blank from the given options.

At markets or at county fairs in the old days, the customer had to be on guard against a dishonest trader. A house wife, for example, wanting (1) ___ buy a live piglet might be (2) ___ a discount if she bought (3) ___ packed one, tied up in a small sack (4) ___ a poke. Anyone who agreed to (5) ___ a pig in a poke was naturally (6) ___ a risk. The pig might be ill (7) ___ even dead: Or it might turn (8) ___ to be not a piglet at all. Which of the following words will be most appropriate for blank (3)?

Wasim asked her sister to estimate the surface area of a conical funnel. Which of the following is the best method to estimate the area?

1. 40

If x^3+x^2-ax+b is divisible by (x^2-x), write the values of a and b.

If two of the zeroes of the polynomial f (x) = x⁴ - 3x³ - x² + 9x - 6 are - √3 and √3 then all the zeroes are

If the median of the following data is 166.79, then the mean and mode are

In fig., two concentric circles of radii a and b (a > b) are given. The chord AB of larger circle touches the smaller circle at C. The length of AB is:

If m,n are the roots of a quadratic equation $p{x}^2+qx+s$, then what is value of (m)$\times$(n)?

Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him $Rs.50$ per metre and trouser material that costs him $Rs.90$ per metre. For every $3$ meters of the shirt material he buys $2$ metres of the trouser material. He sells the materials at $12\%$ and $10\%$ profit respectively. His total sale is $Rs.36,600$. How much trouser material did he buy?

It the roots of the quadratic equation x²+2px+mn=o are the real and equal

A cylindrical boiler, 2 m high, is 3.5 m in diameter. It has a hemispherical lid. Find the volume of its interior, including the part covered by the lid.

Water is flowing through a cylindrical pipe of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m per second. Determine the rise in level of water in the tank in half an hour.

Four equal circles, each of radius a, touch each other. Show that the area between them is $\frac{6}{7}{a}^2$ (Take $\pi =\frac{22}{7}$)

Find the number which bears the same ratio to $\frac{7}{33}$ that $\frac{8}{21}$ does to $\frac{4}{9}$.

$(1+tan\theta +cot\theta )(sin\theta -cos\theta )=(\frac{sec\theta }{cose{c}^2\theta }-\frac{cosec\theta }{se{c}^2\theta })$

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$3x^2-2x+2=0$

A toy in the shape of a hemisphere of radius $7cm$ is surmounted by a cone of slant height $25cm$. The toy is placed in a cylindrical box of radius $70cm$ and height $1m$, which is to be packed and dispatched. Find how many such toys can be accommodated in the box. Assume packaging occupies a volume of $\frac{11}{3}(cm{)}^3$ for each toy and all toys need to be packed.(Take $\pi =\frac{22}{7}$)

Find the mode of the following data:

$$\begin{array}{ccccc}{x}_i& 10& 13& 16& 19\\ f_i& 2& 5& 7& 6\end{array}$$

The radius and height of a cylinder are increased by $10\%$, then what will be the percentage increase in volume?

Which of the following formulae correctly depicts the mode of a modal class?

$(secA+tanA)(1-sinA)=?$

(a) sin A (b) cos A (c) sec A (d) cosec A

Find the sum to n term of the A.P. 5,2,-1,-4,-7,...,

If the roots of the equation $(c^2-ab)x^2-2(a^2-bc)x+(b^2-ac)=0$ are real ane equal, show that either $a=0or(a^3+b^3+c^3)=3abc$.

How many students are there in the class?

I. There are more than 20 but less than 27 students in the class.

II. There are more than 24 but less than 31 students in the class. The number of students in the class can be divided into groups such that each group contains 5 students.

Solve each of the following systems of equations by using the method of cross multiplication:

$\frac{5}{(x+y)}-\frac{2}{(x-y)}+1=0,\frac{15}{(x+y)}+\frac{7}{(x-y)}-10=0.(x\ne y,x\ne -y).$

To receive grade 'A' in a course, one must obtain an average of 90 marks or more in five papers each of 100 marks.If Shikha scored 87,95,92 and 94 marks in first four papers, find the minimum marks that she must score in the last paper to get grade 'A' in the course.

In what ratio is the line joining (2,-4) and (-3, 6) divided by the y-axis ?

Find the slope of the line which is parallel to :

(i) x + 2y + 3 = 0

(ii) $\frac{x}{2}-\frac{y}{3}-1=0$

Define $x\%a$ as the remainder obtained when $x$ is divided by $a$.
Let $f:Z\to R$ be defined as $f\left(x\right)=x\%k$, where $kϵN$. If Y is the range of $f\left(x\right)$, then

If the sum of the zeroes of $k{x}^2-5x+2$ is $\frac{5}{2}$ find the value of k

The ages of 37 students in a class are given in the following table:

Find the Median

Find the value of x such that points (0, 3), (x, 9) and (12, 15) are collinear.

Square root of the expression $16a^2+9b^2-24ab+24a-18b+9$ is .

Find the maximum value of cos$\theta$ + 3$\sqrt{2}$ sin $(\theta +\frac{\pi }{4})$

Statement1: The polynomial $P\left(x\right)=4x^3–3x^2+5x–6$ when divided by $x–1$ gives zero as the remainder.

Statement2: $(x–1)$ is a factor of the polynomial $P\left(x\right)=4x^3–3x^2+5x–6$.

The condition that the point (x,y) may lie on the line joining (3,4) and (-5,-6) is

Find the value of k for which the lines k – 5y + 4 = 0 and 2 – y + 15 = 0 are ⊥ to each other.

In the given figure ΔA'BC' has been constructed similar to the fiven ΔABC.

The scale factor in this is

What is the meaning of total surface area of an object?

In triangle ABC, AB=m²-n², BC=2mn and AC=m²+n², the value of angle ABC is-

A)90°

B)30°

C)60°

D)45°

Two tangents PA and PB are drawn to the circle with centre O, such that $\angle$APB =${120}^{\circ }$what is the relation between OP and AP?