Explore topic-wise InterviewSolutions in Current Affairs.

Express each one of the following with rational denominator :

(i) $\frac{1}{3+\sqrt{2}}$

(ii) $\frac{1}{\sqrt{6}-\sqrt{5}}$

(iii) $\frac{16}{\sqrt{41}-5}$

(iv) $\frac{30}{5\sqrt{3}-3\sqrt{5}}$

(v) $\frac{1}{2\sqrt{5}+\sqrt{3}}$

(vi) $\frac{3\sqrt{3}+1}{2\sqrt{2}-\sqrt{3}}$

(vii) $\frac{6-4\sqrt{2}}{6+4\sqrt{2}}$

(viii) $\frac{3\sqrt{2}+1}{2\sqrt{5}-3}$

(ix) $\frac{b^2}{\sqrt{a^2+b^2+a}}$

The blood groups of 30 students of class IX are recorded as follows:

$\begin{array}{ccccccccccccccc}& & & & & & & & & & & & & & \\ A,& B,& O,& O,& AB,& O,& A,& O,& B,& A,& O,& B,& A,& O,& O,\\ A,& AB,& O,& A,& A,& O,& O,& AB,& B,& A,& O,& B,& A,& B,& O,\end{array}$

A student is selected at random from the class from blood donation. Find the probability that the blood group of the students chosen is:

(i) A (ii) B (iii) C (iv) O

The mean of a, b is 8.5 and mean of a, b, c is 7. The value of c is:

What is a variable?where it is used?

Third power of $\frac{1}{4}\times$ fourth power of 4 equals to ______.

The following table shows the number of students participating in various games in a school.
$\begin{array}{ccccc}\text{Game}& \text{Cricket}& \text{Football}& \text{Basketball}& Tennis\\ \text{Number of students}& 27& 36& 18& 12\end{array}$
Draw a bar graph to represent the above data.

1. 8

Two circles, each of radius 5 units, touch each other at (1, 2). If the equation of their common tangent is 4x + 3y – 10 = 0 then equation of one such circle is

In a parallelogram, if diagonal PR bisects the ∠P, then it also bisects _____.

Which of the following statements best describes the organization of lines, "Thus, one impulse often ...abstractly” of the passage?

For a polynomial p(x) when divided by x+3 leaves a remainder of 2
So which of the following is true?

The batting average of Rohit Sharma ranges from 40 to 51 in a Calendar year.

If he starts in the month of March and increases his average by 1 every month, what will be his average in January next year?

Find the zero of the polynomial p(x)=ax, a≠0.

If x= 2 and y= 3 is a solution of 2x - 3y+ k = 0 find k value and write the resultant equation

Is every integer is a rational number?

Meena needs to serve mango juice to her guests in cylindrical tumblers of radius $7cm$ up to a height $10cm.$ If she wants to serve $25$ guests, how much juice does she need to prepare?

The y co-ordinate of the point is called its ………

Factorise $4xy-x^2-4y^2+z^2$

(X-y)^2 - 7(x^2-y^2) + 12(x+y)^2 factorise

Question 2
Determine the degree of each of the following polynomials.
(i) $2x-1$

(ii) $-10$

(iii) $x^3-9x+3x^5$

(iv) $y^3(1–y^4)$

PQRS is a parallelogram PO = 4cm and SO= 2.5 cm. Find the measure of RO and SQ.

For what value of $\frac{P}{Q}$ does A (a,a), B (-a,-a) and C (Pa,Qa) form the vertices of an equilateral triangle?

How is this simplified

1.6/(√3-1)

= 0.8(√3+1)

Please explain in brief how is this step done.

In a group of students,50 passed in english,60 passed in maths and 40 passed in

both.Find the number of students who passed in either English or Maths?

Question 88

Solve the following:

Divide 54 into two parts, such that one part is $\frac{2}{7}$ of the other.

The perimeter of an isosceles triangle is 42cm and base is 3/2 times each of the equal sides. Find length of each side of triangle, area of triangle, height of triangle

Two circles touch each other externally. The sum of their areas is $\left(106\pi \right)c{m}^2$ and the distance between their centers is 14 cm. Find the sum diameters of the circles.

A fair coin is tossed a number of times. If head appears on all the 4 tosses, what is the probability that a tail appears on the 5^th toss?

Taciturn is most nearly opposite in meaning to:

Simplify and express the result in power notation with positive exponent:

$(-3{)}^4\times {\left(\frac{5}{3}\right)}^4$

What length of tarpaulin 3 m wide will be required to make a conical tent of height 8 m and base radius 6m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately $20cm.[Use\pi =3.14]$

IF $S_n={\sum }_{r=0}^n\frac{1}{{}^n{C}_r}$ and $t_n={\sum }_{r=0}^n\frac{r}{{}^n{C}_r},$ then $\frac{t_n}{S_n}$ is equal to

Empirical probability P (E) of an event happening is defined as

Which among the following can be categorized as a mathematical statement?

Which of the following is an example of a dead object?

$-\frac{\sqrt{28}}{\sqrt{343}}$ is a/an ________ .

Question 9
In the figure, it is given that BDEF and FDCE are parallelogram. Can you say that BD = CD? Why or why not?

The value of tan θ in the given triangle is

1. 15

If $|y-3|=|y+1|$ then the value of y is

If $\Delta ABC\cong \Delta PQR$ and it is given that $\angle A={60}^{\circ },\angle B={70}^{\circ }.$Then the value of $\angle R$ is___.

What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?

The average speed of a bicycle, an athlete and a car are $18kmph$, $7m{s}^{-1}$ and $2kmmi{n}^{-1}$ respectively. Which of the three is the fastest and which is the slowest? [2 MARKS]

In a triangle ABC if ∠A = 53^o and ∠C = 44^o then the value of ∠B is:

Sum of the interior angles of a regular polygon is ${540}^{\circ }$.Then the polygon is

The bar graph shows the expenditure of Karan's monthly expenses on various things.

The percentage of salary that Karan spent on food is :