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Which of the following points lie in the VII th octant?

In triangle ABC, right angled at B, if one angle is ${45}^{\circ }$, the values of sin A, cosC, cot A and tan C respectively are .

Team of four students is to be selected from a total of 12 students for a quiz competition. In how many ways it can be selected if two particular students do not wish to be together in the team.

The interval (2,4] written in set builder form is

The probability that a person will get an electrification contract is $\left(\frac{2}{5}\right)$ and the probability that he will not get a plumbing contract is $\frac{4}{7}.$ If the probability of getting at least one contract is $\left(\frac{2}{3}\right)$, what is the probability that he will get both ?

The sum of n terms of the series whose $n^{th}$ term is n(n+1) is equal to

The lines represented by the equation $x^2+2\sqrt{3}xy+3y^2-3x-3\sqrt{3}y-4=0$, are

Find the general solution for the following equation:

cos 3x+ cos x - cos 2x = 0

Find the value of $\underset{x\to 0}{lim}\frac{|x|}{x}$

Find the principal and general solutions of the following equation.

tan x = $\sqrt{3}$

In the expansion $(1+x{)}^5=1+5x+a{x}^2......x^5$, find the value of a.

If A and B are two sets containing 3 and 6 elements respectively, what can be the maximum number of elements in $A\cup B$ ?

Also, find hte minimum number of elements in $A\cup B$

In a class 6 students have to be arranged for a photograph. If the prefect and the vice must occupy the positions at either ends, how many ways the students can be arranged?

If $i{z}^3+z^2-z+i=0$, then $|z|$ equals

Let $f\left(x\right)$ be a twice differentiable function and $f^{\prime \prime }\left(0\right)=5$, then $\underset{x\to 0}{lim}\frac{3f\left(x\right)-4f\left(3x\right)+f\left(9x\right)}{x^2}$ is equal to:

For positive integers n₁,n₂ the value of the expression $(1+i{)}^{n_1}$+$(1+i^3{)}^{n_1}$+$(1+i^5{)}^{n_2}$ + $(1+i^7{)}^{n_2}$ where i=$\sqrt[2]{2-1}$ is a real number if and only if

Find the derivative of $x^2$ - 2 at x = 10.

${\sum }_{r=0}^n{5}^r{}^n{C}_r=a^n$. Find the value of a.

How will the graph of $y=f(x-1)$ look if the graph of $y=f\left(x\right)$ looks like

If 1 - $\frac{1}{3}$ + $\frac{1}{5}$ - $\frac{1}{7}$ +....... = $\frac{\pi }{4}$ then $\frac{1}{1.3}$ + $\frac{1}{5.7}$ + $\frac{1}{9.11}$ + ...... =

Let A(2, - 3) and B(-2, 1) be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y = 1

then the locus of the vertex C is the line

Percentage of lead in lead pencils is:

Find the value of ${\alpha }^2+{\beta }^2$ if $\alpha ,\beta$ are the roots of $x^2+5x+2=0$

Which one of the following will have the largest number of atoms? $($Molar mass of $Au=197g/mol)$

If $y=xlog\frac{x}{(a+bx)}$ , then $x^n\frac{d^{2}y}{d{x}^2}={(x\frac{dy}{dx}-y)}^m$, where:

In the expansion of ( $\frac{a}{x}+bx{)}^{12}$, the coefficient of $x^{-10}$ will be

If the sum of the n terms of G.P. is S product is P and sum of their inverse is R, than $P^2$ is equal to

Match the following.

In column 1, we are given a two dimensional projection of a right circular cone and a plane with dotted line. Match them with resulting conic given in column 2.

If $(1+x+x^2{)}^{100}=\sum _{r=0}^{200}{a}_r{x}^r$, then which of the following is/are true?

$\underset{x\to \infty }{lim}{\left(\frac{x^5+5x+3}{x^2+x+2}\right)}^x\text{equals}$

In a factory 70% of the workers like oranges and 64% likes apples. What is the maximum Percentage of people who can like both?

Which of the following are true statements.

The n arithmetic means between 20 and 80 are such that the first mean : last mean = 1 : 3. Find the value of n.

Prove that the line through the point $(x_1,y_1)$ and parallel to the line Ax + By + C = 0 is $A(x-x_1)+B(y-y_1)=0$.

$\underset{x\to 3}{lim}\left(\right[x-3]+[3-x]-x),\text{where[.]denote the greatest function, is equal to:}$

If $(asec\theta .btan\theta )$ and $(asec\Phi ,btan\Phi )$ are the ends of a focal chord of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ whose eccentricity is e,then $tan\frac{\theta }{2}\times tan\frac{\oslash }{2}$ equal to.

The length of the latusrectum of the parabola $2y^2+3y+4x-2=0$ is

which of the following is the graph of $y=lo{g}_{\frac{1}{2}}(x-\frac{1}{2})+\frac{1}{2}lo{g}_2(4x^2-4x+1)$

The latusrectum of the hyperbola $\frac{x^2}{4}-\frac{y^2}{12}=1$ is 4 $\frac{1}{2}$ . Its eccentricity e =

The focal distance of a point on the parabola $y^2=8x$ is 10. Its coordinates are

If A = {1, 3, 5, 7, 9, 11, 13, 15, 17}, B ={2, 4, ......, 18} and N, the set of natural numbers is the universal set, then $(A^{\prime }\cup [(A\cup B)\cap B^{\prime }\left]\right)$ is

The following points A(2a, 4a), B(2a, 6a) and C$(2a+\sqrt{3}a,5a)$, (a > 0) are the vertices of

A die is thrown twice. What is the probability that at least one of the two throws comes up with the number 4 ?

Find the derivative of $(9x^2+\frac{3}{x}+5sinx)$ with respect to x.

Find out the quartile deviation for the given individual observations 10, 20, 30, 40, 50, 60, 70.