Explore topic-wise InterviewSolutions in Current Affairs.

The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the centre of the circle is

(a) 8 cm (b) $\sqrt{104}$ cm (c) 12 cm (d) $\sqrt{1}25$ cm

The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3. Find the ratio of theri volumes.

A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: 200 for the first day, 250 for the second day, Rs. 300 for the third day, etc., the penalty for each succeeding day being Rs. 50 more than for the preceding day. How much money the contractor has to pay the penalty if he has delayed the work by 30 days?

Prove that:

(i) $tan{5}^{\circ }tan{25}^{\circ }tan{30}^{\circ }tan{65}^{\circ }tan{85}^{\circ }=\frac{1}{\sqrt{3}}$

(ii) $cot{12}^{\circ }cot{38}^{\circ }cot{52}^{\circ }cot{60}^{\circ }cot{78}^{\circ }=\frac{1}{\sqrt{3}}$

(iii) $cos{15}^{\circ }cos{35}^{\circ }cosec{55}^{\circ }cos{60}^{\circ }cosec{75}^{\circ }=\frac{1}{2}$

(iv) $cos{1}^{\circ }cos{2}^{\circ }cos{3}^{\circ }...cos{180}^{\circ }=0$

(v) ${\left(\frac{sin{49}^{\circ }}{cos{41}^{\circ }}\right)}^2+{\left(\frac{cos{41}^{\circ }}{sin{49}^{\circ }}\right)}^2=2$

In __ theorem, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Find the H.C.F. of $(x^2+x+1)$ and $(x^4+x^2+1)$ by using the division method.

The diameters of the top and bottom of a bucket are 40 cm and 20 cm respectively. If the depth of the bucket is 12 cm then its volume will be

In $\Delta ABC,\angle A={50}^{\circ },BC=8cm.$ Find the circumdiameter of the triangle $[sin{50}^{\circ }=0.77]$

Question 7
The runs scored by two teams A and B on the first 60 balls in a cricket match are given below:
$\begin{array}{ccc}\text{Number of balls}& \text{Team A}& \text{Team B}\\ 1-6& 2& 5\\ 7-12& 1& 6\\ 13-18& 8& 2\\ 19-24& 9& 10\\ 25-30& 4& 5\\ 31-36& 5& 6\\ 37-42& 6& 3\\ 43-48& 10& 4\\ 49-54& 6& 8\\ 55-60& 2& 10\end{array}$
Represent the data of both the teams on the same graph by frequency polygons.

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{15}{1600}$

In triangle ABC, points D and E lie on sides AB and AC respectively such that DE is parallel to BC.

If AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm, then AE is equal to ____.

Why is 1 + 1 = 2 ?

Find the greatest number of four digits which is exactly divisible by 15, 24 and 36.

The ratio between the radius of the base and the height of a cylinder is 2 : 3. If the volume of the cylinder is 12936 $c{m}^3$, find the radius of the base of the cylinder.

A chemist has one solution containing 50 % acid and a second one containing 25% acid.How much of each should be used to make 10 litres of a 40% acid solution?

Find the area of the shaded region in Fig. if AC = 24 cm, BC = 10 cm and O is the center of the circle. (Use $\pi =3.14$)

Compute the median from the following data:
$\begin{array}{cccccccc}\text{Marks}& 0-7& 7-14& 14-21& 21-28& 28-35& 35-42& 42-49\\ \text{Numbers of}& & & & & & & \\ \text{students}& 3& 4& 7& 11& 0& 16& 9\end{array}$

5 books and 7 pens together cost Rs.79 whereas 7 books and 5 pens together cost Rs.77.Find the total cost of 1 book and 2 pens.

Express $0.\overline{2}$ as a fraction in its lowest form.

Question 1

$\frac{2}{5}\times 5\frac{1}{5}$ is equal to
(a) $\frac{26}{25}$
(b) $\frac{52}{25}$
(c) $\frac{2}{5}$
(d) 6

Question 36

$4.7÷100=$ ___.

If the sum of the roots of a quadratic equation is 5 and the product of the roots is also 5, then the equation can be:

Question 98(iii)

Solve the following:

$\frac{49\times z^{-3}}{7^{-3}\times 10\times z^{-5}}(z\ne 0)$

The following table shows data during a 1hr exam for a student.

$$\begin{array}{cc}\text{Time during exam(mins)}& \text{Total number of questions solved in the exam}\\ 0-10& 2\\ 10-20& 5\\ 20-30& 10\\ 30-40& 15\\ 40-50& 17\\ 50-60& 25\end{array}$$

Plot the less than type ogive curve

Statement 1: Square numbers can never end with 2, 3, 7 or 8.

Statement 2: If a number ends with 0, 1, 4, 5, 6 or 9, it must be a square number.

Which of these statement(s) is/are right?

In the given figure, PT is a common tangent to the circles touching externally at P and AB is another common tangent touching the circles at A and B. Prove that: [3 MARKS]

(i) T is the mid-point of AB

$\left(ii\right)\angle APB={90}^{\circ }$

(iii) If X and Y are centers of the two circles, show that the circle on AB as diameter touches the line XY.

A random variable X has the following probability distribution.

$\begin{array}{ccccccccc}\text{X}& 0& 1& 2& 3& 4& 5& 6& 7\\ \text{P(X)}& 0& k& 2k& 2k& 3k& k^2& 2k^2& 7k^2+k\end{array}$

$P(0<X<3)$

If $\frac{1}{x}+\frac{1}{y}=5$ and $\frac{2}{x}-\frac{3}{2y}=3$. Then value of $\frac{1}{y}-\frac{1}{x}$ is

What is the area of this trapezium?

ED and BC are perpendicular to DC. ED = a, BC = b, DC = c

If the matrix $A=\left[\begin{array}{ccc}2& 0& 0\\ 0& 2& 0\\ 2& 0& 2\end{array}\right]$, then $A^n=\left[\begin{array}{ccc}a& 0& 0\\ 0& a& 0\\ b& 0& a\end{array}\right],n\in N$ where

The probability of picking the letter K from the word TREKKING is $\frac{x}{4}$. Then the value of x is ___.

If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, express this in the form of an equation in two variables and draw a graph of the same by taking the constant force as 5 units. Also read from the graph the work done when the distance travelled by the body is: (i)2 units (ii)0 units

A random survey of the number of children of various age groups playing in park was found as follows:

$\begin{array}{cc}Age\left(inyears\right)& Numberofchildren\\ 1-2& 5\\ 2-3& 3\\ 3-5& 6\\ 5-7& 12\\ 7-10& 9\\ 10-15& 10\\ 15-17& 4\end{array}$

What are the adjusted frequency values for the classes of children in the age group 2-3, 5-7 and10-15?

The surface area of a box which is in the form of a cuboid whose dimensions are l $\times$ b $\times$ h is:

write the degree of zero polynomial?

The number of arcs to be made to divide a line segment in the ratio 5 : 7 using a single ray is ____.

Find the roots of the quadratic equation $6x^2-13x+6=0$ by using the quadratic formula.

Find the discriminant of the equation: $2x^2-3x-4=0$

A RIGHT TRIANGLE HAVING SIDES 15cm AND 20cm IS MADE TO REVOLVE AROUND THE HYPOTENESE .FIND THE VOLUME AND SURFACE AREA OF THE DOUBLE CONE FORMED. [ USE pie =3.14]

If the sum of $3^3$ + $7^3$ + ${11}^3$ + ${15}^3$ .........20 terms is $s_{20}$. Find the value of $\frac{s_{20}}{100}$.

A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap. [2 MARKS]

The sum of the squares of two positive integers is $208$. If the square of the larger number is $18$ times the smaller number, find the numbers.

D is the hcf of 45 and 27 find x and y satisfying d=27x+45y

Find the sum of the series $2^2$ + $4^2$ + $6^2$ + $8^2$ +................ 20 terms.