Explore topic-wise InterviewSolutions in Current Affairs.

Choose the area enclosed between the secant and the tangent.

Question 2

Only one of the four options is correct. Write the correct one.

The ratio of the number of sides of a square to the number of edges of a cube is

a) 1 : 2

b) 3 : 2

c) 4 : 1

d) 1 : 3

If $S_1,S_2,S_3$ are the sum of first n natural numbers, their squares and their cubes, respectively, show that $9S_2^2=S_3(1+8S_1)$

ABC is a triangle and DE is drawn parallel to BC cutting the other sides at D and E. If AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm, then AE equal to -

Below is a grouped data distribution for which mean is to be found by step deviation method.

$$\begin{array}{ccccc}ClassInterval& NumberofFrequency\left(f_i\right)& Classmark\left(x_i\right)& d_i=x_i-a& u_i=\frac{d_i}{h}\\ 0-100& 40& 50& -200& D......\\ 100-200& 39& 150& B.....& E.....\\ 200-300& 34& 250& 0& 0\\ 300-400& 30& 350& 100& 1\\ 400-500& 45& 450& C.....& F......\\ Total& A.\sum f_i=......& & & \end{array}$$

Find the value of A, B, C, D, E and F respectively.

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

A man wants to buy 120 shares available at ₹ 88 ( par value = ₹ 50)

i) How much should he invest ?

ii) If the dividend is 8.5 % , what will be his annual income ?

A pen cost ₹11 and a notebook cost ₹13. Find the number of ways in which a person can spend exactly ₹ 1000 to buy pens and notebooks.

What is the area of a triangle whose vertices are (a, b + c), (a, b - c) and (-a, c)?

Using the remainder Theorem, factorise each of the following completely:
(i) $3x^3+2x^2-19x+6$
(ii)$2x^3+x^2-13x+6$
(iii) $3x^3+2x^2-23x-30$
(iv) $4x^3+7x^2-36x-63$
(v) $x^3+x^2-4x-4.$

The sum of ages of A and B is 50 years. A said to B, “I am twice as old as you were when I was as old as you are. Find the present age of B.

The distance of the point P(-6, 8) from the origin is

(a) $8$ (b) $2\sqrt{7}$ (c)$6$ (d)$10$

If the point P(x, y) is equidistant from the points A(5, 1) and B(-1, 5) prove that 3x = 2y.

In the adjoining figure, $\Delta ABC$ is right-angled at B and $\angle A={45}^{\circ }.IfAC=3\sqrt{2}$ cm, find (i) BC, (ii) AB.

$co{t}^2{30}^{\circ }-2co{s}^2{30}^{\circ }-\frac{3}{4}se{c}^2{45}^{\circ }+\frac{1}{4}cose{c}^2{30}^{\circ }$

The sum of the 4th and the 8th terms of an AP is 24 and the sum of its 6th and 10th terms is 44. Find the sum of its first 10 terms.

The surface areas of two spheres are in the ratio of 4 : 25. Find the ratio of their volumes.

Which of the following statements is not true ?

(a) A tangent to a circle intersects the circle exactly at one point.

(b) The point common to the circle and its tangent is called the point of contact.

(c) The tangent at any point of a cricle is perpendicular to the radius of the circle through the point of contact.

(d) A straight line can meet a circle at one point only.

The radius of a circular garden is 100 m. There is a road 10 m wide, running all around it. Find the area of the road and the cost of levelling it at Rs 20 per $m^2$. [ Use $\pi$ = 3.14]

The minute hand of a clock is 10 cm long. Fnd the area of the face of the clock described by the minute hand between 8 AM and 8.25 AM.

In the following letter sequence, some of the letters are missing. These are given in order as one of the alternatives below. Choose the correct alternative. $\alpha \beta ...\alpha \alpha ...\beta \beta \beta ....\alpha \alpha \alpha ...\beta \beta$

The roots of the quadratic equation (x + 1)(x - 3) = 0

In fig, $\frac{QT}{PR}=\frac{QR}{QS}$ and $\angle 1=\angle 2$. Prove that $△PQS\sim △TQR$.

In figure, if $△ABE\simeq △ACD$, prove that $△ADE\sim △ABC$.

What is the angle of elevation of the sun when the length of the shadow of the pole is $\frac{1}{\sqrt{3}}$ times the height of the pole?

Find the zeroes of $49x^2-81$.

If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the ${20}^{th}$ term.

The vertices of $\Delta ABC=areA(4,6),B(1,5)andC(7,2)$. A line is drawn to intersect sides AB and AC at D and E respectively such that $\frac{AD}{AB}=\frac{AE}{AC}=\frac{1}{4}$ . Calculate the area of $\Delta ADE$ and compare it with the area of $\Delta ABC$

sin${30}^{\circ }$ $\times$ cos${60}^{\circ }$ has the numerical value :

Suppose there are two consumers in the market for a good and their demand functions are as follows:

$d_1\left(p\right)=20-p$ for any price less than or equal to 20 and $d_1\left(p\right)=0$ at any price greater than 20.

$d_2\left(p\right)=30-2p$ for any price less than or equal to 15 and $d_1\left(p\right)=0$ at any price greater than 15.

Find out the market demand function.

In the given figure, $XY$ and $X^1$$Y^1$ are two parallel tangents to a circle with centre O and another tangent $AB$ with point of contact C intersecting $XY$ at $A$ and $X^1$$Y^1$ at $B$ then $\angle AOB$ is ___.

1. 4

Find the value of the trigonometric functions in tan $\frac{19\pi }{3}$.

If x=3sec²A - 1 and y =3tan²A -2 then what is x -y

X Ltd purchased a machinery from Y for an agreed purchase consideration of Rs.4,40,000 to be satisfied by the issue of 12% Debentures of Rs.100 each at a premium of Rs.10 per Debenture. Journalise the transaction.

ABC is an equilateral triangle. A circle is drawn with centre A so that it cuts AB and AC at point M and N respectively. Prove that BN = CM

If $A=\left[\begin{array}{cccc}4& 3& 6& -8\end{array}\right],B=\left[\begin{array}{cccc}1& -3& -6& 2\end{array}\right]$
Find a matrix C such that C=A-2B

The perimeter of a rectangular field is 82m and its area is $400m^2.$ Find the breadth of the rectangle.

If sin $\theta$ =$\frac{a}{b}$ then cos $\theta$ = ?

(a) $\frac{b}{\sqrt{b^2-a^2}}$(b) $\frac{\sqrt{b^2-a^2}}{b}$(c) $\frac{a}{\sqrt{b^2-a^2}}$ (d) $\frac{b}{a}$

In Fig. 8.59, a circle touches all the four sides of a quadrilateral ABCD with AB =6 cm, BC =7 cm and CD =4 cm. Find AD.

Which side is equal to $sec\theta$ ?

In a given fraction,if 1 is subtracted from the numerator and 2 is added to the denominator,it becomes $\frac{1}{2}$.if 7 is subtracted from the numerator and 2 is subtracted to the denominator,it becomes $\frac{1}{3}$.The fraction is

(a) $\frac{13}{24}$ (b) $\frac{15}{26}$ (c) $\frac{16}{27}$ (d) $\frac{16}{21}$

The areas of two similar triangles ABC and PQR are in the ratio 9 : 16. If BC = 4.5 cm, find the length of QR.