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Find the value of |x+b| + |x + a| + |a-b| ___

A projectile is thrown with speed $u$ making angle $\theta$ with horizontal at $t=0.$ It just crosses two points of equal height, at time $t=1\text{s}$ and $t=3\text{s}$ respectively. Calculate the maximum height attained by it?

$(g=10{\text{m/s}}^2)$

The value of constants $m$ and $c$ for which $y=mx+c$ is a solution of the differential equation $D^{2}y+3Dy+4y=4x$

$(D^{2}y=\frac{d^{2}y}{d{x}^2},Dy=\frac{dy}{dx})$

The distance between the parallel lines $\frac{x}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\overrightarrow{r}=2\hat{i}-\hat{j}+3\hat{k}+\lambda (\hat{i}+2\hat{j}+3\hat{k})$ is

The surface area of a cube increases at a uniform rate of $0.5\text{cm}{}^2\text{/sec}$. The rate of increase in the volume of the cube when the side is $20$ cm is ____

Let $\ast$ be a binary operation on the set of natural numbers N defined by a$\ast$b = $a^b$ for all a and b $ϵ$ N , then $\ast$ is

If$H_1,H_2,....H_{20}$be 20 harmonic means between 2 and 3, then$\frac{H_1+2}{H_1-2}+\frac{H_{20}+3}{H_{20}-3}=$

The radius of gyration of a uniform rod of length $l$ about an axis passing through a point $\frac{l}{4}$ away from the centre of the rod and perpendicular to it is

If $-4\le 8x-2\le 4$, then the minimum value of $\frac{1}{x^2}$ is

Express the following matrix as the sum of a symmetric and a skew-symmetric matrices;

$\left[\begin{array}{ccc}3& 3& -1\\ -2& -2& 1\\ -4& -5& 2\end{array}\right]$

If $\underset{0}{\overset{4}{\int }}\sqrt{\left\{x\right\}}dx=\alpha$, then the value of $3\alpha$ is

(where $\{\cdot \}$ denotes fractional part function)

The value of $\underset{x\to \infty }{lim}\frac{(x+1{)}^{10}+(x+3{)}^{10}+(x+5{)}^{10}+\cdots +(x+49{)}^{10}}{(x+2{)}^{10}+(x+4{)}^{10}+(x+6{)}^{10}+\cdots +(x+26{)}^{10}}$ is

Statements: T $ G, K P, M # T, P + M

Conclusions:

I. K T

II. G $ P

Find the sum of the
products of the corresponding terms of the sequences 2, 4, 8, 16, 32
and 128, 32, 8, 2,
.

The value of ${\cos }^{-1}\left(\frac{15}{17}\right)+2{\tan }^{-1}\left(\frac{1}{5}\right)$ is

Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ be three vectors such that $|\overrightarrow{a}|=|\overrightarrow{b}|=|\overrightarrow{c}|=4$ and angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\pi /3$ angle between $\overrightarrow{b}$ and $\overrightarrow{c}$ is $\pi /3$ and angle between $\overrightarrow{c}$ and $\overrightarrow{a}$ is $\pi /3.$

The volume of trianglular prism whose adjacent edges are represented by the vectors $\overrightarrow{a},\overrightarrow{b}$and$\overrightarrow{c}$

$\int \frac{x-sinx}{1+cosx}dx=xtan\left(\frac{x}{2}\right)+plog\left|sec\left(\frac{x}{2}\right)\right|+c\Rightarrow p=$

The value of $\underset{n\to \infty }{lim}\frac{1}{n^3}\sum _{k=1}^n\left(k^{2}x\right)$ is

For the sequence $1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,\dots ,$ the ${1025}^{\text{th}}$ term is

If the area of a triangle with vertices (-3,0), (3, 0) and (0, k) is 9 sq. units, then, the value of k will be:

(a) 9
(b) 3
(c) -9
(c) 6

Integrate the following functions.
$\int \frac{x^2}{\sqrt{x^6+a^6}}dx.$

Find the
angle between the vectors

if the second largest side of quadrilateral is of length 10 then what is the length of largest side

State the types of the underlined phrases.

The arrogant and vain man had been taught a lesson.

For every positive integer n, $2^n$ < n! when

Suppose $\alpha ,\beta$ and $\theta$ are angles satisfying $0<\alpha <\theta <\beta <\frac{\pi }{2}$, then $\frac{\sin \alpha -\sin \beta }{\cos \beta -\cos \alpha }=$

The perpendicular distance of the point $P(6,7,8)$ from $XY-$plane is

The sum of first 20 terms of the sequence 0.5, 0.55, 0.555,...., is ___.

If X follows a binomial distribution with parameters $n=8$ and $p=\frac{1}{2}$, then $P(|X–4|\le 2)$ equals.