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The value of ${\sum }_{r=0}^n(-1{)}^r\left(\frac{{}^n{C}_r}{{}^{r+3}{C}_r}\right)$ is

If $z_1$ and $z_2$ are complex numbers and $u=\sqrt{z_1{z}_2},$ then $|\frac{z_1+z_2}{2}+u|+|\frac{z_1+z_2}{2}-u|$ is equal to

Equation of the circle on the latusrectum of $y^2=8x$ as ends of diameter is

Find the value of ${\int }_0^{\infty }x{e}^{-x}dx$

Construct a $3\times 4$ matrix whose elements are given by
$\left(i\right)a_{ij}=\frac{1}{2}|-3i+j|$

$\left(ii\right)a_{ij}=2i-j$.

Can I have the answers with steps for the differentiation topic of jee mains 2018 ?

In an increasing geometric progression, the sum of the first term and the last term is $66$, the product of the second terms from the beginning and the end is $128$ and sum of all terms is $126$. Then the number of terms in the progression is

From a group of 2 boys and 3 girls, two children are selected at random. Describe the events :

(i) A = event that both the selected children are girls

(ii) B = event that the selected group consists of one boy and one girl

(iii) C = event that at least one boy is selected

Which pairs of events are mutually exclusive ?

How to find the domain and range of the functions with all the steps.

And

Find the domain and range of the function f(x)=(9-x)^1/2

Find the second order derivative of the given functions.

log x.

Number of ways of selecting four letters from proportion

If ${}^n{P}_r=720$ and ${}^n{C}_r=120$, find the value of r.

The number of different straight lines that are formed with A (2,3), B(3,4), C(5,6), D(3,7) are

Integral of $\int \sqrt{\tan x}dx$

In a G.P. if the ${(m+n)}^{th}$ term be p and ${(m-n)}^{th}$ term be q , then its $m^{th}$ term is

If for a $△ABC,cotA.cotB.cotC>0$ then the triangle is

If a directed line L₁ passing through the origin makes angles α, β, and y with x, y and z-axes, respectively, then what are the direction cosines of a line L₂ , in the reverse direction of line L₁

A coin is tossed n times. What is the chance that the head will present itself an odd number of times?___

The underlined prefix in the following words mean ________.

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

A circle is tangent to the x and y axes in the first quadrant at the points $P$ and $Q$ respectively. $BC$ and $AD$ are parallel tangents to the circle with slope $-1$. If the points $A$ and $B$ are on the y- axis while $C$ and $D$ are on the x-axis and the area of the quadrilateral $ABCD$ is $900\sqrt{2}$ sq. units, then the radius of the circle is

If the coefficients of $X^7$and $X^6$ in ${(2+\frac{x}{3})}^n$ are equal, then n is

The average weight of 35 students in a class is 40kg. If the weight of the teacher is also included, the average rises by 0.5 kg. The weight of the teacher is

If $A$ is a matrix of order $m\times n$ and $B$ is a matrix such that $A{B}^{\prime }$ and $B^{\prime }A$ are both defined, the order of matrix $B$ is

If the last term in the binomial expansion of ${(2^{\frac{1}{3}}-\frac{1}{\sqrt{2}})}^{n}is{\left(\frac{1}{3^{5/3}}\right)}^{lo{g}_{3}8}$, then the 5th term from the beginning is

The slope of the tangent to the curve $x=t^2+3t-8,y=2t^2-2t-5$ at the point t = 2 is

The length of the perpendicular from (1, 0, 2) on the line ​$\frac{x+1}{3}=\frac{y+1}{-2}=\frac{z+1}{-1}$ is

Let O be the origin and A be a point on the curve $y^2=4x$ Then the locus of the midpoint of OA is

The vertex of the conic represented by $25(x^2+y^2)=(3x-4y+12{)}^2$ is

A rectangle ABCD is inscribed in a circle with a diameter lying along the line. 3y=x+10. If A = (-6,7), B=(4,7) then the area of rectangle is

If $\cos \alpha +2\cos \beta +3\cos \gamma =\sin \alpha +2\sin \beta +3\sin \gamma =0$, then the value of $\sin 3\alpha +8\sin 3\beta +27\sin 3\gamma$ is

Mohan posts a letter to Sohan. It is known that one letter out of $10$ letters does not reach its destination. It is certain that Sohan will reply if he receives the letter. If $A$ denotes the event that Sohan receives the letter and $B$ denotes the event that Mohan gets a reply, then

Equation of Plane which is parallel to XY plane is -

If $a\ne b\ne c$ such that
$\left|\begin{array}{ccc}{a}^3-1& b^3-1& c^3-1\\ a& b& c\\ a^2& b^2& c^2\end{array}\right|=0$ then,

Let $f\left(1\right)=–2$, and $f^{\prime }\left(x\right)\ge 4.2$ for $1\le x\le 6$. The possible value of f(6) lies in the interval

If $\frac{1}{{}^5{C}_r}+\frac{1}{{}^6{C}_r}=\frac{1}{{}^4{C}_r},$ then the value of $r$ equals to

If $tan\frac{\theta }{2}=\sqrt{\frac{1-e}{1+e}}.tan\frac{\alpha }{2},\text{then}cos\alpha$ =

Let $g\left(x\right)=logf\left(x\right)$ where f(x) is a twice differentiable positive function on $0,\infty$ such that $f(x+1)=xf\left(x\right)$ . Then, for $N=1,2,3,.....g^{\prime \prime }(N+\frac{1}{2})-g^{\prime \prime }\left(\frac{1}{2}\right)$=

In a bag, there are 2 blue balls, 5 green balls and 6 red balls. If a person took two balls without replacement, what is the probability that the second ball will be red given that the first ball is red?

f(x) = [x], the greatest integer less then or equal to x and k is an integer. Then, ${lim}_{x\to k}f\left(x\right)=$___