Explore topic-wise InterviewSolutions in Current Affairs.

The abcissa & ordinate of a point passing through 7x-4y + 6 = 0 , are equal . Find the point.

If ‘p’ and ‘q’ are the zeroes of the polynomial P(x) = $x^2$ + ax + b =0, then P(x) can be written as

The following is the Receipts and Payments Account of Ganga Club for the year ending on 31st Dec., 2012: Locker's Rent includes Rs 60 for 2011 and Rs 90 are still due. Rent includes Rs 1,300 for 2011 and Rs 1,300 are still outstanding; Printing and Stationery includes Rs 312 for 2011 while Rs 364 are still outstanding. Outstanding subscription for 2012 Rs 468 and Rs 350 are still receivable for special subscription for Governor's party. Prepare Income and Expenditure Account with the help of above information.

$\begin{array}{cccccc}\text{Receipts}& & \text{Amount}& \text{Payments}& & \text{Amount}\\ & & \text{(Rs)}& & & \text{(Rs)}\\ \text{Balance on Jan}1,2012& & 300& \text{Rent}& & 5,000\\ \text{Subscription:}2011& & 200& \text{Printing}\&\text{Stationery Exp}.& & 3,068\\ 2012& & 16,900& \text{Wages}& & 5,330\\ 2013& & 300& \text{Billiard Table}& & 5,900\\ \text{Locker's Rent}& & 500& \text{Interest}& & 1,500\\ \text{Received Special subscription for}& & & \text{Balance on 31st Dec.,}2012& & 396\\ \text{Governor's Party}& & 3,450& & & \\ & & \overline{\underset{–}{22,000}}& & & \overline{\underset{–}{22,000}}\end{array}$

For a rectangular field of area 3 sq. units, the length is one unit more than twice the breadth ‘x’. The quadratic equation representing the situation is:

If A (–2, –1), B (a, 0), C (4, b) and D (1, 2) are the vertices of a parallelogram. Find the values of a and b. [3 MARKS]

The age of 18 students of a class is reported below. Their modal age is

10, 17, 14, 10, 11, 12, 12, 13, 17, 13, 14, 14, 15, 16, 17, 15, 17, 16

Modal age of students in given distribution is

A man buys 75, Rs 100 shares paying 9 percent dividend. He buys shares at such a price that he gets 12 percent of his money. At what price did he buy the shares ?

Find the mean, variance and standard deviation using the short cut method

$\begin{array}{cc}Heightincm& No.ofchildren\\ 70-75& 3\\ 75-80& 4\\ 80-85& 7\\ 85-90& 7\\ 90-95& 15\\ 95-100& 9\\ 100-105& 6\\ 105-110& 6\\ 110-115& 3\end{array}$

$$\begin{array}{c}px-q\\ x^2+2x+13x^3+x^2+2x+6\\ \underset{–}{3x^3+6x^2+3x}2\\ -5x^2-x+5\\ \underset{–}{-5x^2-10x-5}\\ 9x+10\end{array}$$

Construct a 2 $\times$ 2 matrix by A = $\left[a_{ij}\right]$ whose elements are given by $a_{ij}$= 2i – j

If a cosθ + b sinθ = 4 and a sinθ - b cosθ = 3, then a² + b² is

Which of the following is/are not polynomial(s)?

Two lines, with slopes 'm' and 'n', are parallel to each other if ______.

Which of the following measures of central tendency takes into account all the observations?

If from any point on the common chord of two intersecting circles, tangents be drawn to the circles, prove that they are equal.

what must be added to the polynomial $f\left(x\right)=2x^3-2x^2+x-1$ so that the resulting polynomial is exactly divisible by $x^2+2x-3$?

D and E are points on the sides AB and AC respectively of a $\Delta ABC$. In each of the follwing cases, determine whether DE || BC or not.

(i) AD = 5.7 cm, DB = 9.5 cm, AE = 4.8 cm and EC = 8 cm.

(ii) AB = 11.7 cm, AC = 11.2 cm, BD = 6.5 cm and AE = 4.2 cm.

(iii) AB = 10.8 cm, AD = 6.3 cm, AC = 9.6 cm and EC = 4 cm.

(iv) AD = 7.2 cm, AE = 6.4 cm, AB = 12 cm and AC = 10 cm.

Find the sum of first $n$ natural numbers.

AB is the diameter of a circle, centre O. C is a point on the circumference such that $\angle COB=\theta$. The area of the minor segment cut off by AC is equal to twice the area of the sector BOC. Prove that $sin\frac{\theta }{2}cos\frac{\theta }{2}=\pi (\frac{1}{2}-\frac{\theta }{120})$.

Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis:

2x-3y+4=0,x+2y-5=0.

A tent of height 77 dm is in the form of a right circular cylinder of diameter 36 m and height 44 dm surmounted by a right circular cone. Find the cost of the canvas at Rs. 3.50 per $m^2$.

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients :

$x^2+3x-10$

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

If A and B are acute angles such that tan $A=\frac{1}{2},tanB=\frac{1}{3}$ and tan $(A+B)=\frac{tanA+tanB}{1-tanAtanB}$,find A + B

How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid contact ?

Prove that following identities:

$co{s}^3\theta sin3\theta +si{n}^3\theta cos3\theta =\frac{3}{4}sin4\theta$

The sum of n terms of the series $2^2+4^2+6^2+..........is$

The shadow of a tower standing on a level ground is found to be $40m$ longer when the sun’s altitude is ${30}^{\circ }$ than when it is ${60}^{\circ }$. Find the height of the tower.

A = (7, -2) and C = (-1, -6) are the vertices of square ABCD. Find the equations of diagonals AC and BD.

Susan invested certain amount of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. She received Rs.1860 as annual interest. However, has she interchanged the amount of investment in the two schemes, she would have received Rs.20 more as annual interest. How much money did she invest in each scheme?

Solve each of the following systems of equations graphically:

$2x+3y+5=0,3x-2y-12=0.$

The $n^{th}$ terms of an A.P. is given by $(-4n+15)$. Find the sum of first $20$ terms of this A.P.

A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs. 500 per $m^2$ . (Note that the base of the tent will not be covered with canvas).

Find the value of 'm', if $m{x}^3+2x^2-3$ and $x^2-mx+4$ leave the same remainder when each is divided by x - 2.

Use figure shown above. In the given triangle ABC, AC = BC. Find AB and $\angle$ACB.

In parallelogram MODE, the bisectors of $\angle M$ and $\angle O$ meet at Q. Find the measure of $\angle MQO$

Draw a circle circumscribing a regular hexagon with side 5 cm.

Metallic spheres of radii 6cm, 8cm and 10cm, respectively are melted to form a single solid sphere. The radius of the resulting sphere(in cm) is

Rachel buys goods worth ₹ 5,500. She gets a rebate of 5% on it. After getting the rebate, sales tax 5% is charged. Find the amount she will have to pay for the goods.

Let a,b,c,d and e are positive integers such that abcde = a+b+c+d+e, then the maximum value of e is

c gayatri devi

The 4th term of an A.P. is 11 and the 8th term exceeds twice the 4th term by 5. Find the A.P. and the sum of first 50 terms.

A, B and C have co-ordinates (0, 3), (4, 4) and (8, 0) respectively. Find the equation of the line through A and perpendicular to BC.

In a cyclic quadrilateral ABCD,it is being given that $\angle A=(x+y+10{)}^{\circ },\angle B=(y+20{)}^{\circ },\angle C=(x+y-30{)}^{\circ },and\angle D=(x+y{)}^{\circ },Then\angle B=?\left(a\right){70}^{\circ }\left(b\right){80}^{\circ }\left(c\right){100}^{\circ }\left(d\right){110}^{\circ }$

Factorise:

2x²+7x+3

The cost of per litre of milk is Rs 15. Draw the graph for the relation between the quantity and cost. Hence, find

1. The proportionality constant

2. The cost of 3 litres of milk.

Find alpha, k , beta if the equation has equal roots ,

(K-4)x^{​​​​​​2} + 2(k-4)x+4=0.