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If the line passes through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24), find the value of x.

Convert the given complex number in polar form: $\sqrt{3}+i$

Show that the following four conditions are equivalent:

(i) $A\subset B$ (ii) $A-B=\Phi$

(ii) $A\cup B=B$ (iv) $A\cap B=A$

The Equation of the directrix to parabola $y^2=8x$ is _____

Two bodies of different masses $m_a$ and $m_b$ are dropped from two different heights a and b. The ratio of the time taken by the two to cover these distances are

Angle between the lines represented by the equation $x^2+2xysec\theta +y^2=0$ is

The coordinates of a point which is equidistant from the points $(0,0,0),(a,0,0),(0,b,0)and(0,0,c)$ are given by _____

If the line x=a+m, y=-2 and y=mx are concurrent , then least value of |a| is

$1+3+3^2+\cdots +3^{n-1}=\frac{(3^n-1)}{2}$

If tan A + tan B + tan C = tan A .tan B . tan C then

A point moves in such a way that the sum of square of its distance from the points A(2, 0) and B(-2, 0) is always

equal to the square of the distance between A and B. The locus of the point is

Let E denotes the event "India scores less than 300” in a cricket match between India and South Africa. How many elements are there in the sample space which will favor the event E?

If a,b,c are 3 unequal positive numbers, then (a+b+c) $(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})$ is

If A, B and C are three events such that P(B) =$\frac{3}{4},P(A\cap B\cap C^{\prime })=\frac{1}{3}andP(A^{\prime }\cap B\cap C^{\prime })=\frac{1}{3},$ then $P(B\cap C)$ is equal to

The value of $1.C_1+3.C_3+5.C_5+7.C_7+....where{C}_0,C_1,C_2.....C_n$ are binomial coefficients in the expansion of $(1+x{)}^n$ is:

The digit in the unit place of the number

(183!) + $3^{183}$ is

Find the set of real values of x for which ${\log }_{0.5}$ $\frac{3-x}{x+2}$ < 0

The centroid of a triangle is (2, 7) and two of its vertices are (4, 8) and (-2, 6). The third vertex is

The number of times the digit 3 will be written when listing the integers from 1 to 1000 is

Find the principal solution of cos 2x= sin x

A number is chosen from the numbers 1 to 100. Find the probability of its being divisible by 4 or 6.

Find the value of $si{n}^2\frac{\pi }{8}$ + $si{n}^2\frac{\pi }{4}$

The sum of the series $(\sqrt{2}+1)+1+(\sqrt{2}-1)+\cdots$ up to infinite term is

Find the value of the expression $co{s}^4\frac{\pi }{8}+co{s}^4\frac{3\pi }{8}+co{s}^4\frac{5\pi }{8}+co{s}^4\frac{7\pi }{8}$

Or

Find the value of $sin\frac{x}{2},cos\frac{x}{2}$ and $tan\frac{x}{2}$, if $sinx=\frac{1}{4}$, where x lies in ssecond quadrant.

The mean deviation about the mean for the following data :
$\begin{array}{cccccccc}{x}_i& 2& 3& 4& 5& 6& 7& 8\\ f_i& 5& 2& 3& 4& 5& 4& 2\end{array}$
is

Find the middle terms in the expansion of ${(3x-\frac{x^3}{6})}^7$

Or

Find the fourth term from the end in the expansion of ${(\frac{3}{x^2}-\frac{x^3}{6})}^7$

Among the complex number z satisfying the condition $|z+1-i|\le 1$, the complex number having the least positive argument is:

If the points (1,2) and (3,4) were to be on the same side of the line 3x-5y+a=0 then

The statement $\sim (p\Rightarrow q)$ is equivalent to

Random sampling is not Haphazard sampling. Comment.

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

1 + $\frac{3}{2}$ + $\frac{5}{2^2}$ + $\frac{7}{2^3}$ + ......... ∞ is equal to

Calculate the standard deviation by :

(A) Actual mean method

(B) Direct method

(C) Short cut method.

3, 4, 6, 7, 10

If the sum of the series $1+2r+3r^2+4r^3+\cdots \infty$ is $\frac{9}{4},$ then the value of $r$ is

Prove that $sinx+sin7x+sin3x+sin5x=4cosxcos2xsin4x$

Or

Solve $\sqrt{3}cosx-sinx=1$

Let the digits of a three digit number are in G.P. If $400$ is subracted from the number and the digits of the new number are in A.P., then the last digit of the original number is

A man running in a racecourse notes that the sum of the distances of the two flag posts from him is always 10 m, and the distance between the flag posts is 8 m. Find the equation of the path traced by the man.

A point R with x-coordinate 4 lies on the line segment joining the points $P(2,-3,4)$ and $Q(8,0,10).$ Find the coordinates of the point R.

The ratio of the AM and GM of two positive numbers a and b is m : n, show that $a:b=[m+\sqrt{(m^2-n^2)}]:[m-\sqrt{(m^2-n^2)}].$

Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular x-axis.

(i) $x-\sqrt{3}y+8=0$, (ii) y - 2 = 0, (iii) x - y = 4

How many outcomes are there in the sample space of throwing two dice?

If ${\alpha }_0,{\alpha }_1,{\alpha }_2,.........{\alpha }_{n-1}$ be the n, $n^{th}$ roots of unity, then value of $\sum _{i=0}^{n-1}$ $\frac{{\alpha }_i}{(3-{\alpha }_i)}$ is equal to

Find the derivative of $x^n+a{x}^{n-1}+a^2{x}^n-2+...+a^{n-1}x+a^n$ for some fixed real number a.

The shape of $d_{xy}$ is