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Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number of vehicles arriving on this highway follows Poisson distribution, the probability (round off to 2 decimal places) that the headway between successive vehicles lies between successive vehicles lies between 6 and 10 seconds in

1. 0.18

The fractional value of $2.357$ is

How many diagonals are there in a nonagon?

The solution of the differential equation $x^2\frac{dy}{dx}+2xy-x+1=0$ given that at x = 1, y = 0 is

The values of $x$ for which the angle between the vectors $\overrightarrow{a}=x\hat{i}-3\hat{j}-\hat{k}$ and $\overrightarrow{b}=2x\hat{i}+x\hat{j}-\hat{k}$ is acute and the angle between the vector $\overrightarrow{b}$ and the axis of ordinates is obtuse, are

​​​​​​$\begin{array}{cc}ColumnI& ColumnII\\ \text{a. If}I=\underset{-2}{\overset{2}{\int }}(\alpha x^3+\beta x+\gamma )dx,\text{then}I\text{is}& \text{p.}\text{independent of}\alpha \\ \text{b. Let}\alpha ,\beta \text{be the distinct positive roots}& \\ \text{of the equation}\tan x=2x,\text{then}& \\ \gamma \underset{0}{\overset{1}{\int }}(\sin \alpha x\cdot \sin \beta x)dx(\text{where}\gamma \ne 0)\text{is}& \text{q.}\text{independent of}\beta \\ \text{c. If}f(x+\alpha )+f\left(x\right)=0,\text{where}\alpha >0,& \\ \text{then}\underset{\beta }{\overset{\beta +2\gamma \alpha }{\int }}f\left(x\right)dx,\text{where}\gamma \in N,\text{is}& \text{r.}\text{independent of}\gamma \\ & \text{s.}\text{depends on}\alpha \end{array}$
Then which of the following is correct ?

The solution of the differential equation $x\frac{dy}{dx}+y=x^2+3x+2$ is

The set of values of $a$ for which the function $f:R\to R$ given by $f\left(x\right)=x^3+(a+2)x^2+3ax+5$ is one-one, is

Let $z_1=2+3i$ and $z_2=3-4i$. If $z_3$ and $z_4$ are the points which divides the line segment joining the points $z_1$ and $z_2$ internally and externally in the ratio of $1:2$ respectively, then which of the following is/are correct?

In a triangle ABC,
$a^3\cos (B-C)+b^3\cos (C-A)+c^3\cos (A-B)=$

Effective capacity between A and B is (in $\mu F$)

If the sum of two numbers $p$ and $q$ is $\sqrt{10}$ and their difference is $\sqrt{6}$, then the value of ${\log }_{q}p$ is

Find the sum of the following series :

(i) 5 + 55 + 555 + ... to n terms.

(ii) 7 + 77 + 777 + ... to n terms.

(iii) 9 + 99 + 9999 + ... to n terms.

(iv) 0.5 + 0.55 + 0.555 + ... to n terms.

(v) 0.6 + 0.66 + 0.666 + ... to n terms.

If $e^{sinx}-e^{-sinx}=a$ has alteast one real solution, then

The number of value(s) of $x$ satisfying ${\sin }^{-1}(1-x)-2{\sin }^{-1}x=\frac{\pi }{2}$ is

Two sets $A\&B$ are disjoint sets, if

Set of values of ${}^{\prime }{a}^{\prime }$ for which the equation $\sqrt{a}\cos x-2\sin x=\sqrt{2}+\sqrt{2-a}$ possesses a solution is

Given below are the runs scored by five players. If the average runs scored by them is $146$, then find the runs scored by Kuldeep.​

Name
Runs

Match the conditions/expressions in Column I with statement in Column II.



Let $f_1:R\to R,f_2:[0,\infty ]\to R,f_3:R\to R$ and $f_4:R\to [0,\infty )$ be defined by $f_1\left(x\right)=\{\begin{array}{c}|x|,ifx<0\\ e^x,ifx\ge 0\end{array}{f}_2\left(x\right)=x^2;f_3\left(x\right)=\{\begin{array}{c}sinx,ifx<0\\ x,ifx\ge 0\end{array}$ and $f_4\left(x\right)=\{\begin{array}{c}{f}_2\left[f_1\right(x\left)\right],ifx<0\\ f_2\left[f_1\right(x\left)\right]-1,ifx\ge 0\end{array}$

$\begin{array}{cc}\text{Column I}& \text{Column II}\\ a.f_{4}is& p.\text{onto but not one-one}\\ b.f_{3}is& q.\text{neither continuous nor one-one}\\ c.f_{2}of{f}_{1}is& r.\text{differentiable but not one-one}\\ d.f_{2}is& s.\text{continuous and one-one}\end{array}$

Let f(x) be a function defined on [0,2] by:

where a, b and c are constants such that f(x) has second derivative at x = 1. Then a equals

If $p{x}^2$ + qx + r = 0 has no real roots and p, q, r are real such that p + r > 0 then

In the following question, two equations I and II are given. You have to solve both the equations and choose the appropriate answer.

I. 4a${}^2$ = 1

II. 4b${}^2$ - 12b + 5 = 0

You are asked to construct a distance chart representing distances between cities given in a set with all the cities of the same set. What kind of matrix will come out of it?

The area (in $\text{sq.units}$) enclosed by the curve $|x^2-4x+y^2-6y|<12$ is equal to