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The coefficient of $x^{2}in(1+x)(1+2x)(1+4x)....(1+2^{n}x)$ is

$\frac{sinA+\sqrt{3}cosA}{2}$ equals to

The coefficient of $x^3$ in $(2x-\frac{3}{x^2}{)}^9$ is

If tan $\theta$ = $\frac{-4}{3}$ then sin$\theta$ is

The equation of the set of points which are equidistant from (1,2,3) and (3,2,-1).

If the lines represented by the equation $a{x}^2-bxy-y^2=0$ make angles $\alpha$ and $\beta$ with the x - axis, then $\tan (\alpha +\beta )$ =

The number of values of y in $[-2\pi ,2\pi ]$ satisfying the equation |sin 2x| = |cos 2x| = |sin y| is

If $z$ and $\omega$ be two non-zero compex numbers such that $|z|=|\omega |$ and $arg\left(z\right)+arg\left(\omega \right)=\pi$, then $z$ equals

Plot the graph of $f(x-1)$ if the graph of $f\left(x\right)$ looks like

$x=n\pi +\frac{3\pi }{4}$ or $x=m\pi +ta{n}^{-1}\frac{1}{2}$, where m, $n\in I$

A woman has m $\$20$ notes and n $\$50$ notes. The total amount of money in her possession cannot be less than $\$800$. Represent this as an inequality.

From the given options, the truth values of p,q and r respectively for which $(p\wedge q)\vee (\sim r)$ has a truth value F are

Match the following:

Given sin x = $\frac{2}{5}$ and x $ϵ$ $(0,\frac{\Pi }{2})$

$\begin{array}{cc}\text{(p) cos x}& \text{(1)}\frac{5}{2}\\ \text{(q) tan x}& \text{(2)}\frac{\sqrt{21}}{2}\\ \text{(r) cosec x}& \text{(3)}\frac{\sqrt{21}}{5}\\ & \text{(4)}\frac{2}{\sqrt{21}}\end{array}$

If two different numbers are taken from the set {0, 1, 2, 3,.... 10}, then the probability that their sum as well as absolute difference are both multiple of 4, is ?

If $Li{m}_{x\to 0}\frac{4+sin2x+Asinx+Bcosx}{x^2}$ exists, then the values A and B are

Given that the standard potential ($E^{\circ }$) of $C{u}^{2+}/Cu$ and $C{u}^{+}/Cu$ are $0.340\text{V}$ and $0.522\text{V}$ respectively. The $E^{\circ }$ of $C{u}^{2+}/C{u}^{+}$ is:

If $a_1,a_2,a_3,\dots ,a_n$ are in arithmetic progression, where $a_1>0$ for all i.
Prove that $\frac{1}{\sqrt{a_1}+\sqrt{a_2}}+\frac{1}{\sqrt{a_2}+\sqrt{a_3}}+\dots +\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_n}}=\frac{n-1}{\sqrt{a_1}+\sqrt{a_n}}$

A combination lock on a suitcase has 3 wheels, each labelled with nine digits from 1 to 9. If an opening combination is a particular sequence of three digits with no repeats, what is the probability of a person guessing the right combination ?

Let A, B and C be the sets such that $A\cup B=A\cup C$ and $A\cap B=A\cap C$. Show that B = C

Or

A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all three sports? How many received medals in exactly two of the three sports?

Out of 100 students, two sections of 40 and 60 students are formed, if you and your friends are among the 100 students. What is the probability that

(i) you both enter the same section?

(ii) you both enter the different section?

Enter the following transaction in Simple cahs book for December 2010.

$\begin{array}{ccc}\text{Date}& \text{Particulars}& \text{Rs.}\\ 1& \text{Cash in hand}& 7,750\\ 6& \text{Paid to Sonu}& 45\\ 8& \text{Purchased goods}& 600\\ 15& \text{Received cash from Prakash}& 960\\ 20& \text{Cash Sales}& 500\\ 25& \text{Paid to S Kumar}& 1,200\\ 30& \text{Paid rent}& 600\end{array}$

Identify the function from the given options?

Three distinct real numbers, a, b, c are in G.P. such that a + b+ c= x b, then

If 1,$\alpha$,${\alpha }^2$,${\alpha }^3$,............,${\alpha }^{n-1}$ are roots of unity.What is the value of If 1 $\times$ $\alpha$ $\times$ ${\alpha }^2$ $\times$ ${\alpha }^3$, $\times$ ............,${\alpha }^{n-1}$.

If z be a complex number satisfying $z^4$ + $z^3$ +$2z^2$ + z + 1 = 0 Then the value of $\left|z\right|$.

Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that $P^2{R}^n=S^n$

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incorrect and why?

(i) {3, 4} $\subset$ A (ii) {3, 4} $\in$ A

(iii) {{3, 4}} $\subset$ A (iv) $1\in A$

(v) $1\subset A$ (vi) {1, 2, 5} $\subset$ A

(vii) {1, 2, 5} $\in$ A (viii) {1, 2, 3} $\subset$ A

(ix) $\Phi \in A$ (x) $\Phi \subset A$

(xi) {$\Phi$} $\subset$ A.

Let n be a positive integer such that $sin\frac{\pi }{2^n}+cos\frac{\pi }{2^n}=\frac{\sqrt{n}}{2}$. Then

Find the modulus and the arguments of each of the complex numbers
$z=-\sqrt{3}+i$

The complex numbers z = x + iy which satisfy the equation $|$ $\frac{z-4i}{z+4i}$ $|$ = 1, lie on

If $\frac{\sin x}{a}=\frac{\cos x}{b}=\frac{\tan x}{c}=k$, then $bc+\frac{1}{ck}+\frac{ak}{1+bk}$ is equal to

If $\alpha$ and $\beta$ are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity Of the ellipse is

If $f\left(\theta \right)=si{n}^2\theta +si{n}^2(\theta +\frac{2\pi }{3})+si{n}^2(\theta +\frac{4\pi }{3}),thenf\left(\frac{\pi }{15}\right)$

If $\alpha ,\beta ,\gamma$ be the angles which a line makes with the positive direction of co-ordinate axes, then $si{n}^2\alpha +si{n}^2\beta +si{n}^2\gamma =$
[RPET 2000; AMU 2002; MP PET 1989, 98, 2000, 03, Pb. CET 2001]

The number of arrangements of the letters of the word ‘NAVA NAVA LAVANYAM’ which begin with N and end with M is :

Match the given angles with the corresponding slopes.
$\begin{array}{cc}\text{Positive x direction}& \text{Slope of line}\\ {\text{1.) 0}}^{\text{o}}& \text{p.) 0}\\ {\text{2.) 90}}^{\text{o}}& \text{q.) -}\sqrt{3}\\ {\text{3.) 120}}^{\text{o}}& \text{r.) -}\frac{1}{\sqrt{3}}\\ {\text{4.) 150}}^{\text{o}}& \text{s.) Not defined}\end{array}$

If $2^x+2^{f\left(x\right)}=2$ , then the domain of the function $f\left(x\right)$ is

The range of the function $f\left(x\right)=|x^2+2x-15|$ is

Evaluate: $\int \left(\cos \right(x)-\frac{3}{x^5})dx$

The $n^{th}$ term of a sequence of numbers is $a_n$ and given by the formula $a_n=a_{n-1}+2n$ for $n\ge 2$ and $a_1=1$.

Using the above information $a_n$ will be

In a triangle, the sum of lengths of two sides is $x$ and the product of the lengths of the same two sides is $y$. If $x^2-c^2=y$, where $c$ is the length of the third side of the triangle, then the circumradius of the triangle is:

Find the derivative of $\frac{2x+3}{3x+2}$ by first principle.

If ${}^{n-1}{C}_r=(k^2-3{)}^n{C}_{r+1}$, then $kϵ$

Match $\text{List I}$ with $\text{List II}$ and select the correct answer using the code given below the lists :

$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& \text{In a}△ABC,\text{if}{a}^2+b^2+c^2=ab+bc+ca,\text{then}& \text{(P)}& △ABC\text{is an equilateral triangle}\\ \text{(B)}& \text{In a}△ABC,\text{if}{a}^2+2b^2+c^2=2bc+2ab,\text{then}& \text{(Q)}& △ABC\text{is a right angled triangle}\\ \text{(C)}& \text{In a}△ABC,\text{if}{a}^2+b^2+c^2=\sqrt{2}a(b+c),\text{then}& \text{(R)}& △ABC\text{is a scalene triangle}\\ \text{(D)}& \text{In a}△ABC,\text{if}{a}^2+b^2+c^2=ca+\sqrt{3}ab,\text{then}& \text{(S)}& A={90}^{\circ },B={45}^{\circ },C={45}^{\circ }\end{array}$

Which of the following is the only CORRECT combination?

Find the set of values of $\alpha$ for which point the $P(\alpha ,-\alpha )$ is inside
$\frac{x^2}{16}+\frac{y^2}{9}=1$

Describe the sample space for the indicated experiment.
A Coin is tossed three times.

The number of solutions of the equation 5 sec$\theta$ - 13 = 12 tan$\theta$ in [0 , 2$\pi$] is

If ${}^{48}{C}_{3r-2}={}^{48}{C}_{2}r$ Find the value of r