Explore topic-wise InterviewSolutions in Current Affairs.

Question 23
If $a_n=3-4n$, then show that $a_1,a_2,a_3,\cdots$ form an AP. Also, find $S_{20}$.

Given a line ABCD in which AB = BC = CD, B= (0, 3) and C= (1, 8). Find the co-ordinates of A and D.

If the $p^{th}$ term of an AP is $q$ and the $q^{th}$ term is $p$, then $n^{th}$ term of the A.P is:

If a line segment of length 10 cm is reflected in a line of symmetry (mirror), then its reflection is a line of length ___ .

Question 3
The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency f.

$\begin{array}{cccccccc}\text{Daily pocket allowance (in Rs)}& 11-13& 13-15& 15-17& 17-19& 19-21& 21-23& 23-25\\ \text{Number of workers}& 7& 6& 9& 13& f& 5& 4\end{array}$

If $3sin\theta +4cos\theta =5$, then the value of $sin\theta$ is _____.

If A, B, C are the angles of a triangle, then
$\sin \left(\frac{B+C}{2}\right)=$ ___.

The diagonal of a rectangular field is 16m longer than the shorter side .the longer side is 14 more than the shorter side then find the length of the side of a field.

A survey was conducted on 20 families in a locality by a group of students .What will be the mode of the data?

$\begin{array}{cccccc}\text{Age of family member}& 0-20& 20-40& 40-60& 60-80& 80-100\\ \text{Number of students}& 7& 8& 2& 2& 1\end{array}$

A tangent to a circle is a line that intersects the circle in

If the median of the following frequency distribution is 40 and total frequency is 60, then find the missing frequencies.
$\begin{array}{cccccc}\text{Marks}& 0-10& 10-30& 30-60& 60-80& 80-90\\ \text{Number of students}& 5& f_1& 30& f_2& 2\end{array}$

(2014^2-2020)(2014^2+4028-3)(2015)/2011(2013)(2016)(2017)

Four Geometric means are inserted between 2 and 486. Find the common ratio of the resulting G.P.

In the given figure, AB & DE are ⏊ to BC.

If AB = 6 cm, DE = 4 cm & AC = 15 cm.

a well of diameter 6m and depth 30m is dug in a field.the earth taken out from the well is spread over a rectangular ground of dimensions 45m*22m .Find the level of ground rise

Simplify $2\sqrt{3}+4\sqrt{2}$

In a mango groove the trees are planted in horizontal rows. THERE ARE 6 TREES MORE IN EACH HORIZONTAL ROW. Altogether there are 720 trees. Find the number of trees in horizontal rows.

In the given figure, if $\angle B=\angle Q$, then _____.

Find the L.C.M and H.C.F. of 1296 and 2520 by applying the fundamental theorem of arithmetic method i.e. using the prime factorisation method. [3 MARKS]

Ten years later, A will be twice as old as B and five years ago, A was three times as old as B. What are the present ages of A and B ?

Match the value of standard deviation with respective method and their data.

Vijay inherits his father's wealth and squared it by starting a soft drinks company. He then starts a company which manufactures airplane toys and incurs losses amounting to $k(>0)$ times the wealth he inherits. If his total assets stand at the debt of 4 crores, then the equation representing the situation is ___.

Find the value of b if the equation $x^2-x+b=0$ does not possess real roots.

The equation of a straight line which passes through the point (3, 4) and whose intercept on y-axis is twice that of x-axis, is

If p,q are prime positive integers, prove that √p+ √q is an irrational number.

My doubt: how to find whether √p is an irrational number???

The sum of two irrational numbers is an irrational numbers(True/False). Give reason for your answer.

If $\Delta$ABC and $\Delta$PQR are two similar triangles shown in the figure. AM and AN are the medians on $\Delta$ABC and $\Delta$ PQR respectively. Then which of the following statements is true?

$Inthegivenfigure.ABandDEareperpendicularstoBC.IfAB=9cm.DE=3cmandAC=24cm,calculateAD.$

If Dividend = $3x^3-2x^2+4x-3$ and Divisor = $x^2+3x+3$ then find the remainder and quotient.

The above pie chart depicts the percentage of students being girls and boys in the mechanical branch of a college. If the red coloured portion represents the percentage of boys, and the total number of students is 100, then what is the probability of a student chosen at random is a girl?

Use graph paper for the question. Plot points A(4, 6) & B(1, 2).

A’ is the image of A when reflected in – axis.

B’ is the image of B when B is reflected in AA’.

Write the geometric name of the figure ABA’B’.

Calculate $\frac{\text{sin}{70}^{\circ }}{\text{cos}{20}^{\circ }}+\frac{\text{cosec}{36}^{\circ }}{\text{sec}{54}^{\circ }}-2\text{cos}{43}^{\circ }\text{cosec}{47}^{\circ }$.

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 3² – 7 – 6² = 0 find the value of : . Hence find the value of duplicate and triplicate ratio of : .

If a point A (0, 2) is equidistant from the points B (3, p) and C (p, 5), then find the value of p.

How many terms of the A.P. $-6,-\frac{11}{2},-5,\dots \dots$ are needed to give the sum -25 ?

If [1 2 3] A = [4 5], the order of matrix A is

Total surface area of a cylinder whose radius is 4 cm and height is 10 cm is .

Solve & give answers correct to 2 d.p. x²– 5 – 10 = 0

In the given figure, $\angle ACB={90}^{o}andCD\perp AB$.

Prove that $\frac{B{C}^2}{A{C}^2}=\frac{BD}{AD}$.

D and E are points on the sides AB and AC respectively of a $△$ABC such that DE || BC. Which of the following statement is true?

(i) $△$ ADE ~ $△$ ABC

(ii) $\frac{areaof△ADE}{areaof△ABC}$ = $\frac{A{D}^2}{A{B}^2}$

(iii) $\frac{areaof△ADE}{areaof△ABC}$ = $\frac{A{B}^2}{A{C}^2}$

Represent 0.333333…. in a rational form. [1 MARK]

Solve:

(a) Write a linear equation in two variables to represent the following information: The perimeter of a rectangle is 80.

(b) Find the point where 3x + 2y = 8 intersects the Y axis. [3 MARKS]

In a G.P., if the ${(m+n)}^{th}$ term be p and ${(m-n)}^{th}$ term be q , then its $m^{th}$ term is