Explore topic-wise InterviewSolutions in Current Affairs.

In what ratio does the line x-y-2 = 0 divide the linesegment joining the points A(3, -1) and B(8, 9) ?

Find the sum fo first forty positive integers divisible by 6.

Form the pair of linear equations in the followingproblems, and find their solution graphially:

(i) 10 students of class X took part in Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.

(ii) 5 pencil and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and a pen.

(iii) Champa went to a 'sale' to purchase some pants and skirts. When her friends asked her how many of each she had bought, she answered, "The number of skirts is two less than four times the number of pants purchased." Help her friends to find how many pants and skirts Champa bought.

Sushant has a vessel, of the form of an inverted cone, open at the top, of height 11 cm and radius of top as 2.5 cm and is full of water. Metallic spherical balls each of diameter 0.5 cm are put in the vessel due to which ${\left(\frac{2}{5}\right)}^{th}$ of the water in the vessel flows out. Find how many balls were put in the vessel. Sushant made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by Sushant?

If $S_n$ denotes the sum of the first n terms of an A.P., prove that $S_{30}=3(S_{20}-S_{10})$.

Find the sum of first n terms of an AP Whose nth term is (5-6n). Hence, find hte sum of its first 20 terms.

Find the median of the following data.

$$\begin{array}{cccccc}Classinterval& 0-10& 10-20& 20-30& 30-40& 40-50\\ Frequency& 10& 9& 8& 17& 6\end{array}$$

A letter is known to have come either from $TATANAGAR$ or from $CALCUTTA$. On the envelope, just two consecutive letter $TA$ are visible. What is the probability that the letter came from $TATANAGAR$.

If the fifth term of a G.P. is 2, then write the product of its 9 terms.

$IfA=\left[\begin{array}{ccc}cosx& sinx& 0\\ -sinx& cosx& 0\\ 0& 0& 1\end{array}\right]=f\left(x\right),then{A}^{-1}$ is equal to

Find the equation of the line passing through the point (3,2) and parallel to the line $4x+y=11$.

Question 3
Find the area of the shaded region in Fig. 12.21, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

If $f\left(x\right)=\frac{4^x}{4^x+2}\mathrm{for}\mathrm{all}x\in R.$
Which of the following is/are true?

Solve:
$\frac{9x}{7-6x}=15$

Solve the following systems of equations:

$\sqrt{2}x-\sqrt{3}y=0$

$\sqrt{3}x-\sqrt{8}y=0$

In a $△$ABC, right anged at B, if tan A = $\frac{1}{\sqrt{3}}$ , find the value of

1. sinA cosC + cosAsinC
2. cosAcosC – sinAsinC

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If a line is drawn parallel to the X-axis and (-3,5), (6,5) are two points on that line then find the coordinates of the point which is 5 units away from (6,5).

Match the two columns.
$\begin{array}{cc}Column-I& Column-II\\ \left(A\right)Thedistanceofapointfromthex-axisarecalled& \left(p\right)Coordinateaxes\\ \left(B\right)Thedistanceofapointfromthey-axisarecalled& \left(q\right)Ordinate\\ \left(C\right)Thelinesofacoordinateplanearecalled& \left(r\right)quadrants\\ \left(D\right)Thepartsofaplanemadebythecoordinateaxesarecalled& \left(s\right)abscissa\end{array}$
Choose the correct option:

If $(x+iy{)}^3=u+iv$, then show that $\frac{u}{x}+\frac{u}{y}=4(x^2-y^2)$

ABC is a right angled triangle with AB = 12 cm and AC = 13 cm. A circle, with centre O, has been inscribed inside the triangle.

Calculate the value of x, the radius of the inscribed circle.

The image of a point P under reflection in the x- axis is $(-3,2)$. The co-ordinates of P will be ?.

Which of the following functions are identical to f(x) =
$f\left(x\right)=\{\begin{array}{cc}x,& 1\le x<2\\ x^2,& 2\le x<3\end{array}$

(1 $\le$ x < 3)

The polynomial P($x$) = 4$x^3$ + 7$x^2$ – 5$x$ + t, when divided by $x$ + 1 gives 3 as the remainder. Find the value of ‘t’.

^{The sum of q terms of an AP is 162.The ratio of its 6th term to its 13th terms is 1:2 .find the first and 15th of the AP}

A right triangle is formed by connecting the 3 coordinates A, B and C as shown in the figure. Find the point B if AB and BC are parallel to the coordinate axes.

Renu wants to buy a washing machine whose printed price is ₹$10000$. $18\%$ GST is charged on this price. What amount should Renu pay to buy the washing machine?

In a G.P, the first term = 5 and common ratio = 3. Find its fourth term.

__

A tank with length,breadth and height of 5,6 and 3 units respectively is open at top.The cost of anti-microbial coating inside the tank if it is done at Rs.10 per sq. units is

If ax + 3y = 12 has an X intercept of 4, find the value of a. Hence find the Y intercept of the line. [4 MARKS]

A secant which meets the circle at A and B is dragged up until A and B concide at a point. What is that point of coincidence called?

Express in the form of a quadratic equation.
"Divide 32 into two parts whose product is 240". We would like to find each parts.

Question 1 (i)
Form the pair of linear equations in the following problems, and find their solutions graphically.
10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.

Question 1 (ii)

Find the roots of the quadratic equations by using the quadratic formula in the following question $5x^2+13x+8=0$.

Line L passes through the points (4, -5) and (3, 7). Find the slope of any line perpendicular to line L.

Simplify the expression-
$(cose{c}^2\theta -1)\times (se{c}^2\theta -1)$

The locus of a point equidistant from two intersecting lines is…………

Solve the following quadratic equation by factorization method: [4 MARKS]

$4x^2-4a^{2}x+(a^4-b^4)=0$

A can do $\frac{1}{2}$ of a work in 5 days. B can do $\frac{3}{5}$ of the same work in 9 days and C can do $\frac{2}{3}$ of that work in 8 days. In how many days can three of them together do the work?

$f\left(x\right)=a{x}^7+b{x}^3+cx-5$ where a,b,c are constants. If $f(-7)=7$ then $f\left(7\right)$ equals to

$\frac{tan{55}^{\circ }}{cot{35}^{\circ }}\times sin{30}^{\circ }=A$

Find the value of 2A.

Which of the following options is equal to $\sqrt{{\sec }^2\theta +cose{c}^2\theta }$ ?

Length of the altitude on the hypotenuse of a right angled triangle with area $A{\text{cm}}^2$ and one of the sides equal to $b\text{cm}$ is __ cm.

You have an eight-faced die. In this die, one of the faces contains '1', two faces contain '2', three faces contain '3' and other faces contain '4' and '5' respectively. What is the probability of getting '2' when the die is rolled? (All outcomes are equally likely).