Explore topic-wise InterviewSolutions in Current Affairs.

Solve the following system of linear equations graphically and shade the region between the two lines and x-axis;

(i) 2x + 3y = 12,

x - y = 1

(ii) 3x + 2y - 4 = 0,

2x - 3y - 7 = 0

(iii) 3x + 2y - 11 = 0

2x - 3y + 10 = 0

Refer to the figure given. What is the length of the shadow that is formed by the stick AB of length $10\sqrt{3}$?

___

If $sin\theta =\frac{a}{b},$ show that $(sec\theta +tan\theta )$ = $\frac{b+a}{b-a}$.

A room 4.9 m long and 3.5 m broad is covered with carpet, leaving an uncovered margin of 25 cm all around the room. If the breadth of the carpet is 80 cm, find its cost at Rs.80 per metre.

Write the value of sin $\theta$ cos $({90}^o-\theta )$+cos $\theta$ sin$({90}^o-\theta )$.

In the given figure, PA and PB are two tangents drawn from an external point P. If $\angle APB={40}^{\circ }$, then $\angle AOB=$

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

$\begin{array}{cc}Marks& No.ofstudents\\ Above0& 80\\ Above10& 77\\ Above20& 72\\ Above30& 65\\ Above40& 55\\ Above50& 43\\ Above60& 23\\ Above70& 16\\ Above80& 10\\ Above90& 8\\ Above100& 0\end{array}$

(i) Convert to a regular distribution.

Using the FActor theroem, show that:
(i) (x-2) is a factor fo $x^3-2x^2-9x+18$ Hence factories the expression
(ii) (x+5) is a factor of$2x^3+5x^2-28x-15$ Hence factorise fthe expression $2x^3+5x^2-28x-18$ completely.
(iii) (3x+2) is a factor fo $3x^3+2x^2-3x-2.$ Hence factorise the expression
$3x^3+2x^2-3x-2$ completely

The shaded area in the adjoining diagram, between the circumferences of two concentric circles is 346.5 cm². The circumference of the inner circle is 88 cm; calculate the radius of the outer circle.

For what value of 'k' are the following points (7,-2), (5, 1), (3, k) collinear.

HCF of $(x^2-9)$ and $(x+3{)}^2$ is 'a'. HCF of $x^2+x-6$ and $x^2-4$ is 'b'. Then $a\times b$ is ____.

If the equation $x^2+2(k+2)x+9k=0$ has real equal roots, then values of $k$ are

A train covers a distance of 480 km at a uniform speed. If speed had been 8km /hr less then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train.

OACB is a quadrant of a circle with centre O and radius 7 cm. If OD = 4cm, then find the area of shaded region. [3 MARKS]

If a circle is drawn with centre C(0,4) and a radius of 5 cm as shown in below figure then find the coordinates of A and B.

At what point does the graph of the linear equation x + 2y = 7 meet a line which is parallel to the x-axis, at a distance 3 units from the origin and in the positive direction of y-axis? [3 MARKS]

Question 34

In the following question, fill in the blanks to make the statements true.

The multiplicative inverse of ${10}^{10}$ is ___

The volume of the two balls glued together of same radius 21 cm is

If two dice are thrown, what is the probability that the sum is neither 9 nor 12 ?

A takes 6 days less than the time taken by B to finish a piece of work. If both A and B together can finish it in 4 day, find the time taken by B to finish the work.
[4 MARKS]

Question 9
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

In a right angled triangle , if a perpendicular is drawn from right angle ti hypotenuse then prove that the area of the square of the perpendicular is equal to the area of the rectangle formed by the two segments of the hypotenuse .

A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be $345c{m}^3$ ^. Check whether she is correct, taking the above as the inside measurements, and $\pi =3.14$. [4 MARKS]

Find the quadratic polynomial whose zeroes are $\frac{6+\sqrt{3}}{3}\text{and}\frac{6-\sqrt{3}}{3}.$

If 3 or more parallel lines are interested by 2 non parallel lines then prove that their intercepts are in same proportion

Question 1
The graphs of y = p(x) are given in the following figure, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

A vertical stick 20 m long casts a shadow 10 m long on the ground. At the same time, a tower casts a shadow 50 m long on the ground. Find the height of the tower.

If a cone is cut into two parts by a horizontal plane passing through the mid-point of its axis, then the ratio of the volumes of the upper part and the cone is:

The angle between the minute hand and the hour hand of a clock when the time is 4.20, is

Are points A (−5, 4), B (−1, −2) and C (5, 2) the vertices of an isosceles right angled triangle? Find the coordinate of D. So that ABCD is a square.

Juice is filled upto a height of 64 cm in a cylindrical container of radius 30 cm. It is served in small cylindrical cups of radius 6 cm and height 16 cm. If each cup is sold at ₹ 3, how much money can be earned by selling the juice?

Pleased A and B are 100km apart on a highway . One car from A and another from B at the same time . If the cars travel in the same direction at different speeds ,the meet in 5 hrs . If they travel towards each ,the meet in 1 hr.. What are the speeds of the two car?

Number of zeroes of the polynomial shown in the figure?

A spherical ball of lead has been melted and made into identical smaller balls with radius equal to half of the radius of the original one. How many such balls can be made?

An ice-cream machine has two taps for filling ice-cream cones of height $6cm$ and radius $3cm$. If the rate of flow of ice-cream from both taps is equal to $2{cm}^3{s}^{-1}$. Find the maximum number of cones, the machine can fill in an hour.

During a practice match, a softball pitcher throws a ball, whose height can be modeled by the equation $h=-16t^2+24t+1$, where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?

If the zero of the polynomial x^3-3x^2+x+1 are a-b,a, a+b, find a and b.

Find the value of ‘k’ if x -1 is a factor of P(x) = 4$x^3$ + $x^2$ – 3x + k.