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A salesman sold 25 items, the number of sales increased at the rate of 20 items per day. Which of the given equations represent the correct number of sales the salesman made along with its domain?

1. 1.16

$\int \frac{x^2}{(x^2+a^2)(x^2+b^2)}dx=$

Match the following shaded regions in the venn diagram of two sets $A\&B$ to their corret representation.

4x
+ 3y
≤
60, y
≥
2x,
x
≥
3, x,
y
≥
0

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

If $\alpha ,\beta$ are the roots of $2x^2-3x+4=0$, then the equation whose roots are ${\alpha }^2$ and ${\beta }^2$ is

A line which makes an acute angle $\theta$ with the positive direction of x-axis is drawn through the point P(3, 4) to meet the line x = 6 at R and y = 8 at S, then

If three numbers $(x,y,z)=(\frac{2}{3},\frac{7}{6},\frac{8}{9}),$ then the L.C.M. of $x,y,z$ is

What is the maximum time to answer a question in jee maina?

, then c is equal to

The order of second IE of -O, N,F,C is?

The $6^{\text{th}}$ (from the beginning) term in the expansion of the ${[\sqrt{2^{\log (10-3^x)}}+\sqrt[5]{52^{(x-2)\log 3}}]}^m$
is equal to $21$. It is known that the binomial coefficient of the $2^{\text{nd}},3^{\text{rd}}$ and $4^{\text{th}}$ term in the expansion are in an $A.P.$, then the value of $x$ is/are

The function given by $f\left(x\right)=\frac{1}{|x|-1}-\frac{x^2}{2}$ is continuous in

Show that $\Delta ABC$ is an isosceles triangle, if the determinant
$\Delta =\left|\begin{array}{ccc}1& 1& 1\\ 1+cosA& 1+cosB& 1+cosC\\ co{s}^{2}A+cosA& co{s}^{2}B+cosB& co{s}^{2}C+cosC\end{array}\right|=0$

The coefficients of 2nd, 3rd and 4th terms in the expansion of $(1+x{)}^{2n}$ are in A.P., show that $2n^2-9n+7=0.$

If the angles $A,B$ and $C$ of a triangle are in an arithmetic progression and if $a,b$ and $c$ denote the lengths of the sides opposite to $A,B$ and $C$ respectively, then the value of the expression $\frac{a}{2}\sin 2C+\frac{c}{a}\sin 2A$ is

If y(t) is a solution of $(1+t)\frac{dy}{dt}-ty=1$ and y(0)=-1, then show that $y\left(1\right)=-\frac{1}{2}.$

Set of values for $p$ for which the function given by $f\left(x\right)=x^3-2x^2-px+1$ is one-one function $\forall x\in R$ is

The range of values of $a$ such that the angle $\theta$ between the pair of tangents drawn from $(a,0)$ to the circle $x^2+y^2=1$ satisfies $\frac{\pi }{2}<\theta <\pi$, lies in

If p is
the length of perpendicular from the origin to the line whose
intercepts on the axes are a and b, then show that.

Find
the values of k
so
that the function f
is continuous at the indicated point.

Select the possible graph(s) of the quadratic equation $y=a{x}^2+bx+c$ where $a<0,D>0.$

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ and $\overrightarrow{p},\overrightarrow{q},\overrightarrow{r}$ are sets of three non-coplanar unit vectors such that $\overrightarrow{a}\cdot \overrightarrow{p}+\overrightarrow{b}\cdot \overrightarrow{q}+\overrightarrow{c}\cdot \overrightarrow{r}=3,$ then vectors $\overrightarrow{p},\overrightarrow{q}$ and $\overrightarrow{r}$ respectively are given by the vectors

The set of all the critical points of $y=\underset{0}{\overset{x^2}{\int }}\frac{t^2-5t+4}{2+e^t}dt$ are

Integrate the following functions w.r.t. x.

$\int \frac{x^3}{\sqrt{1-x^8}}dx.$

If ${n+5}_{P_{n+1}}=\frac{11(n-1)}{2}{n+3}_{P_n}$, find n.

The equation $x^3-3x+\left[a\right]=0$ will have three real and distinct roots, then the set of all possible values of $a$ is

(where $[\cdot ]$ denotes the greatest integer function)

Find the next number in the sequence.

9, 11, 33, 13, 15, 33, 17, __