Explore topic-wise InterviewSolutions in Current Affairs.

Find the sum of $\frac{x+1}{x+2}$ and $\frac{x^2-1}{x^2+1}.$

Rohan has a recurring deposit account in State Bank of India of ₹2000 per month at the rate of 10% per annum. He receives ₹83100 at the time of maturity. What was the time period for which he held the account?

Consider two sets A and B, which of the following is always true?

In a survey of 200 students from 7 different schools, 50 people do not play only NFS, 40 people do not play only Dota and 10 people play no online games. Then find the no. of people out of 200 people who do not play both the games.

Two chords AP and QM of a circle intersect internally at a point R. If AR = 14 cm, RP = 9 cm, and RQ = 21 cm, then find MR.

Solve : $\frac{2x+3}{5}>\frac{4x-1}{2},xϵW.$

For solving each pair of equations, use the method of eliminations by equating coefficients:

$3-(x-5)=y+2$

$2(x+y)=4-3y$

$\frac{1}{x-2}+\frac{2}{x-1}=\frac{6}{x}$

Find the value of 'x'

If the equation $x^2-px+216=0$ has one root as a square of the other, find the value of p

If 3/5 of a number exceeds it's 2/7 by 44, find the number.

The solution is blank in this question "

Euclid's division lemma states that for any positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy

(a) 1 < r < b (b) 0<r≤b (c) 0≤r<b (d) 0 < r < b

Please sort this for me

By investing Rs 45,000 in 10% Rs 100 shares, Shared gets Rs 3,000 as dividend. Find the market value of each share.

The figure below shows a histogram of heights of cherry trees. Find the correct statement(s) among the options.

The total number of trees under 85 feet is ?

Write $x^2$ +10x+16 =0 in the form $x^2$ + px + qx + 16 = 0 such that p x q = 16

Show that the following points are the vertices of a rectangle:

(i) A(-4, -1), B (-2, -4), C(4, 0) and D(2, 3)
(ii) A(2, -2), B(14, 10), C(11, 13) and D(-1, 1)
(iii) A(0, -4), B(6, 2), C(3, 5) and D(-3, -1)

Find the roots of the equation $x^2–18x+12=0$ by the method of completing the square.

If $a_n$ denotes the nth term of the AP 3, 8, 13, 18, ... then what is the value of $(a_{30}-a_{20})$
(a) 40 (b) 36 S(c) 50 (d) 56

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of the two of the balls are 1.5 cm and 2 cm respectively. Determine the diameter of the third ball.

Find the common difference of an AP whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.

In a circle of radius 6 cm, a chord of length 10 cm makes an angle of ${110}^{\circ }$ at the centre of the circle. Find

(i) The circumference of the circle.

(ii) The area of the circle

(iii) The length of the arc AB

(iv) The area of the sector OAB.

If A (-1, 3), B (1, -1) and C (5, 1) are the vertices of a triangle ABC, find the length of the median through A.

Given $a=1\frac{5}{7},b=\frac{1}{4},c=\frac{1}{9}andd=(-1\frac{1}{4})$, Evaluate $a(b-c)÷d$.

Which of the following should be the THIRD sentence after rearrangement?

Every natural number is a

Prove that if a positive integer is of the form 6q+5, then it is of the form 3q+2 for some integer q but not conversely.

In an AP of 50 terms the sum of the first 10 terms is 210 and the sum of the last 15 terms is 2565. find the AP.

Solve:

(i)$x^4-2x^2-3=0$ (ii) $x^4-10x^2+9=0$

A colour T.V. is marked for sale at Rs.17,600 which includes sales tax at 10%. Calculate the sales tax in Rs.

If x = 2sin² θ, y = 2cos² θ + 1, then the value of x + y is:

Let $T_r$ be the rth term of an AP, for r = 1, 2, . . . . . If for some positive integers m, n, we have $T_m=\frac{1}{n}and{T}_n=\frac{1}{m}$
then $T_{mn}$ equals

Solve $5x^2-6x-2=0$

Prove that:

(i) $sin\theta cos({90}^{\circ }-\theta )+sin({90}^{\circ }-\theta )cos\theta =1$

(ii) $\frac{sin\theta }{cos({90}^{\circ }-\theta )}+\frac{cos\theta }{sin({90}^{\circ }-\theta )}=2$

(iii) $\frac{sin\theta cos({90}^{\circ }-\theta )cos\theta }{sin({90}^{\circ }-\theta )}+\frac{cos\theta sin({90}^{\circ }-\theta )sin\theta }{cos({90}^{\circ }-\theta )}=1$

(iv) $\frac{cos({90}^{\circ }-\theta )sec({90}^{\circ }-\theta )tan\theta }{cosec({90}^{\circ }-\theta )sin({90}^{\circ }-\theta )cot({90}^{\circ }-\theta )}+\frac{tan({90}^{\circ }-\theta )}{cot\theta }=2$

(v) $\frac{cos({90}^{\circ }-\theta )}{1+sin({90}^{\circ }-\theta )}+\frac{1+sin({90}^{\circ }-\theta )}{cos({90}^{\circ }-\theta )}=2cosec\theta$

(vi) $\frac{sec({90}^{\circ }-\theta )cosec\theta -tan({90}^{\circ }-\theta )cot\theta +co{s}^2{25}^{\circ }+co{s}^2{65}^{\circ }}{3tan{27}^{\circ }tan{63}^{\circ }}=\frac{2}{3}$

(vii) $cot\theta tan({90}^{\circ }-\theta )-sec({90}^{\circ }-\theta )cosec\theta +\sqrt{3}tan{12}^{\circ }tan{60}^{\circ }tan{78}^{\circ }=2$

If the central angle of a sector is greater than ${180}^{\circ }$, then it is the _____.

The area of a circle inscribed in an equilateral triangle is 154 $c{m}^2$ . Find the perimeter of the triangle. [ Take $\sqrt{3}=\mathrm{1.73.}$]

Write the $n^{th}$ term of odd numbers.

A (5, –1), B(–3, –2) and C(–1, 8) are the vertices of triangle ABC. Find the length of median through A and the coordinates of the centroid.

Fill in the blanks:
(i) The common point of a tangent and the circle is called___
(ii)A circle may have___ parallel tangents.
(iii)A tangent to a circle intersects it in___ point(s).
(iv)A line intersecting a circle in two points is called a___
(v)The angle between tangent at a point on a circle and the radius through the points is___

Given that $p,q,r,s$ are in an arithmetic progression, which of the following condition(s) can be used to verify this?

In a swimming race 3 swimmers compete . The probability of A and B wining is same and twice that of C. What is the probability that B or C wins. Assuming no two finish the race at the same time.

Question 117

Match the following :
$\begin{array}{cc}& \\ \text{Column I}& \text{Column II}\\ \text{(a) a}\times 1& \text{(i) Additive inverse of a}\\ \text{(b) 1}& \text{(ii) Additive identity}\\ \text{(c) (-a)}÷\text{(-b)}& \text{(iii) Multiplicative identity}\\ \text{(d) a}\times (-1)& \text{(iv) a}÷\text{(-b)}\\ \text{(e) a}\times 0& \text{(v) a}÷\text{b}\\ \text{(f) (-a)}÷\text{b}& \text{(vi) a}\\ \text{(g) 0}& \text{(vii) -a)}\\ \text{(h) a}÷\text{(-a)}& \text{(viii) 0}\\ \text{(i) -a}& \text{(ix) -1}\end{array}$

A circus artist is climbing a 20m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. The height of the pole is ___ (in m)

if the angle made by the rope with the ground level is ${30}^{\circ }$ ^.

$3tan\theta$ + $cot\theta$ = 5 $cosec\theta$. Solve for $\theta$, 0 < $\theta$ ≤ 90. __

Question 118

You have Rs, 500 in your saving account at the beginning of the month. The record below, shows all of your transactions during the month. How much money is in your account after these transactions ?
$\begin{array}{ccccc}& & & & \\ \text{Cheque no.}& \text{Date}& \text{Transaction description}& \text{Payment}& \text{Deposit}\\ 384102& 4/9& \text{Jal Board}& \text{Rs.}120& \text{Rs.}200\\ 275146& 12/9& \text{Deposit}& & \\ 384103& 22/9& \text{LIC India}& \text{Rs.}240& \text{Rs.}150\\ 801351& 29/9& \text{Deposit}& & \end{array}$
How much money is in your account after these transactions ?

Question

Prove that n^2-n is divisible by 2 for every positive integer n

If A and B together invest Rs. 12,000 in a business such that A's investment is twice more than that of B. The investment of A is -

If $5x-2y=7$ and $xy=2$ , then find the value of $(5x+2y{)}^2$