Explore topic-wise InterviewSolutions in Current Affairs.

Savera Club decided to impart Marshal training and safety tips to all girls and women of the city to protect them against rising crime and empowering them to protect themselves in dangerous situations. Following is the information relating to subscriptions for the year ended 31st March 2016 of the club:

Rs

Subscriptions received during 2015-16 70,000

Subscriptions outstanding on 31st March 2015 17,000

Subscriptions received in Advance on 31st March 2015 3,250

Subscriptions received in Advance on 31st March 2016 4,670

Subscriptions outstanding on 31st March 2016 11,250

(i) Identify the value highlighted above.

(ii) Show the subscription in Income and Expenditure A/c for the year ended or 31st March 2016 and in the Balance Sheet as at that date.

The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then the eccentricity $e$ is ,

Evaluate: ${lim}_{x\to 0}\frac{ax+b}{cx+d},d\ne 0$

Integrate the function.
$\int x^{2}logxdx.$

The perpendicular distance from $(0,0)$ to any normal of the curve $x=a(\cos \theta +\theta \sin \theta ),y=a(\sin \theta -\theta \cos \theta )$ is

Suppose $A$ is any $3\times 3$ non-singular matrix and $(A-3I)(A-5I)=O$, where $I=I_3$ and $O=O_3$. If $\alpha A+\beta A^{-1}=4I$, then $\alpha +\beta$ is equal to :

The area of the director circle of the ellipse $\frac{x^2}{5}+\frac{y^2}{4}=1$ is

The coefficient of $x^3{y}^4{z}^5$ in the expansion $(xy+yz+xz{)}^6$ is

The value of $sin{78}^{\circ }-sin{66}^{\circ }-sin{42}^{\circ }+sin{60}^{\circ }$ is

The 10th common term between the A.P.s 3, 7, 11, 15, .... and 1, 6, 11, 16, ... is

The value of $A=(1+\tan 1^{\circ })(1+\tan 2^{\circ })(1+\tan 3^{\circ })\cdots (1+\tan {45}^{\circ })\text{is}$

If $f\left(x\right)=\sin x+{\int }_0^x{f}^{\prime }\left(t\right)(2\sin t-{\sin }^{2}t)dt$ then $f\left(x\right)$ is

Circles $C_1$ and $C_2$, of radii r and R respectively, touch each other as shown in figure. The line l, which is parallel to the line joining the centres of $C_1$ and $C_2$, is tangent to $C_1$ at P and intersects $C_2$ at A,B. If $R^2=2r^2$, then $\angle AOB$

In how many ways can be letters of the word ASSASSINATION' be arranged so that all S's are together?

If $f\left(x\right)=lo{g}_e(1-x)$ and $g\left(x\right)=[x$, then determine each of the following functions :

(i) $f+g$
(ii) $fg$
(iii) $\frac{f}{g}$
(iv) $\frac{g}{f}$
Also, find $(f+g)(-1),\left(fg\right)\left(0\right),\left(\frac{f}{g}\right)\left(\frac{1}{2}\right),\left(\frac{g}{f}\right)\left(\frac{1}{2}\right)$

If $\sum _{r=1}^n{T}_r=\frac{n}{8}(n+1)(n+2)(n+3)$, and $\sum _{r=1}^n\frac{1}{T_r}=\frac{n^2+3n}{4\sum _{k=1}^{p}k}$, then $p$ is equal to

Find the sum of first $10$ terms of following series
$S=\frac{3\left(1\right)}{1}+\frac{5(1^3+2^3)}{1^2+2^2}+\frac{7(1^3+2^3+3^3)}{1^2+2^2+3^2}+....$

The sum of m terms of an A.P. to the sum of n terms of the same A.P. is $m^2:n^2$ . Provethat the ratio of the $m^{th}and{n}^{t}h$ term is 2m – 1 : 2n – 1.

If the sequence $<a_n>$ is an A.P., show that $a_{m+n}+a_{m-n}=2a_m$

${lim}_{x\to \frac{\pi }{4}}\frac{2-cose{c}^{2}x}{1-cotx}$

The number of real solutions of the equation

cos(e^x) = 2^x + 2^-x is

(a) 0 (b) 1 (c) 2 (d) infinitely many

Solve the following systems of inequalities graphically:

$x+y\le 6,x+y\ge 4$

If $A=\left[\begin{array}{ccc}2& 2& -4\\ -4& 2& -4\\ 2& -1& 5\end{array}\right]$ and $B=\left[\begin{array}{ccc}1& -1& 0\\ 2& 3& 4\\ 0& 1& 2\end{array}\right]$, then find BA and use this to solve the system of equations y + 2z = 7, x - y = 3 and 2x + 3y + 4z = 17.

If the point diametrically opposite to point $P(1,0)$ on the circle $x^2+y^2+2x+4y-3=0$ is $(a,b)$, then

Z = $x+iy$, Where x,y are integers, then area of the rectangle whose vertices are roots of the equation

$Z(\overline{Z}{)}^3+Z^3\overline{Z}$ = 350 is

If the ratio of sum of m terms and n terms of an A.P. is , m²:n² then prove that the ratio of its mth and nth terms will be 2m-1 : 2n-1.

I know the answer for this, but i want to confirm if this method is right because everywhere, the other method is given!

S(m)÷s(n) = m²/n²
On solving till a point, we get this equation

2an + mnd -nd = 2am + mnd -dm
→ 2an-nd = 2am-dm
→ n(2a-d) = m(2a-d)
→ n=m. ......(1)

In the 'to prove' statement,

LHS →
a+(m-1)d / a+(n-1)d

Replacing n with m (using 1)

a+(m-1)d/a+(m-1)d = 1/1 = 1


RHS →

2m-1/2n-1
Replacing n with m (using 1)
2m-1/2m-1
= 1/1
=1

Hence, LHS=RHS.




IS THIS CORRECT?

sin (theta) = 3sin(theta +2alpha) then the value of [tan (theta+ alpha) + 2tan (alpha)] = please explain with proper steps elaborately

A survey shows that 67% of people like P1 whereas 73% like P2 if x% of people like both the P1 and P2 then the value of x is ?

If A = {3, 6, 9, 12, 15, 18, 21}

B = {2, 4, 6, 8, 10, 12, 14, 16}

C = {5, 10, 15, 20}

$$\begin{array}{cc}A& B\\ 1.B-C& A.\{5,10,20\}\\ 2.A-C& B.\{3,9,15,21\}\\ 3.C-(A-B)& C.\{3,6,9,12,18,21\}\\ 4.C\cap (A-B)& D.\{15\}\\ & E.\{2,4,6,8,12,14,16\}\end{array}$$

If the eccentricity of the hyperbola $x^2-y^{2}se{c}^2\alpha =5is\sqrt{3}$ times the eccentricity of the ellipse $x^{2}se{c}^2\alpha +y^2=25$, then the value of $\alpha$ is

The angle between a pair of tangents drawn from a point P to the circle $x^2+y^2+4x-6y+9si{n}^2\alpha +13co{s}^2\alpha =0is2\alpha .$ The equation of the locus of the point P is

If 1,$\alpha$,${\alpha }^2$,${\alpha }^3$,............,${\alpha }^{26}$ are the roots of the equation x = $(1{)}^{\frac{1}{27}}$.Find the product of the roots

There is a hole of area A at the bottom of cylindrical vessel. Water is filled up to a height h and water flows out in t second. If water is filled to a height 4h, it will flow out in time equal to

If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$ intersect, then the value of k is -

The value of $\sin \frac{\pi }{n}+\sin \frac{3\pi }{n}+\sin \frac{5\pi }{n}+\cdots \text{to}n\text{terms}$ is