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

(where $c$ is integration constant)

Factorie:x⁸-y⁸

The equation of the circle lying in first quadrant, which touches both the coordinates axes and the distance of it's centre from origin is $2$ units is

The length $\left(\text{in units}\right)$ of the projection of the line segment joining the points $(5,-1,4)$ and $(4,-1,3)$ on the plane $x+y+z=7$ is:

Find the value of $\underset{x\to \infty }{lim}\frac{8-\frac{3}{x}+\frac{5}{x^2}}{4+\frac{2}{x}+\frac{12}{x^2}}$

In a multiple choice question there are four alternative answers of which one or more than one is or are correct. A candidate will get marks on the question only if he ticks all correct answers. The candidate decides to tick answers at random. If he is allowed up to three chances to answer the question, the probability that he will get marks on it is given by

The domain of the function $f\left(x\right)=\frac{1}{{\log }_{10}(1-x)}+\sqrt{x+2}$ is

In how many ways can five keys be put in a ring?

A line
passes through.
If slope of the line is m, show that.

Assuming that the petrol burnt in a motor boat varies as the cube of its velocity, the most economical speed, when going against a current of c km/h is

In a first-order reaction of the type: $A\left(g\right)\to 2B\left(g\right)$, the initial and pressures at time $t$ are $p_1$ and $p$, respectively. The rate constant can be expressed by:

How many four -digit numbers can be formed with the digit 3,5,7,8,9 which are greater than 7000, if repetition of digits is not allowed ?

If $\sin \theta =\frac{3}{5},\cos \varphi =\frac{12}{13}$ (where $\theta$ and $\varphi$ both belongs to $1^{\text{st}}$ quadrant), then which of the following is/are true?

The function $f\left(x\right)=2|x|+|x+2|-||x+2|-2|x||$ has a local minimum or a local maximum at $x=$

If F is the set of all onto functions from a set of vowels to set having 3 elements and $f\in F$ is chosen randomly ,then the probability that $f^{-1}\left(x\right)$ is a singleton is

Let $A$ be a $3\times 3$ matrix and $A^T$ be transpose matrix of $A.$ If $A=3A^T-4I,$ where $I$ is identity matrix of order $3,$ then $det\left(A\right)$ is equal to

Accordin to the Mean value theorem, for a continuous function $f\left(x\right)$ in the interval [a,b], there exists a vlue $\xi$ in thiis interval such that${\int }_a^{b}f\left(x\right)dx=$

The shaded region shown in the figure is given by the inequation

Find the equation of the circle passing the point (1, 2) and touching the line 2x + y - 1 = 0 at the point (1, -1).

In the game odd man out, each of $m\ge 2$ person tosses a coin to determine who will buy refreshments for the entire group. The odd man out is the one with a different outcomes from the rest. The probability that there is a loser in any game is:

The number of integers λ for which the equation x³ - 3x + λ = 0 has integer roots is

A number is chosen at random from the numbers 10 to 99. By seeing the number a man will laugh if product of the digits is 12. If he choose three numbers with replacement, then the probability that he will laugh atleast once is

Let ${(-2-\frac{1}{3}i)}^3=\frac{x+iy}{27}(i=\sqrt{-1})$, where $x$ and $y$ are real numbers, then $y-x$ equals :

If foot of the perpendicular of P(2,-3,1) on the line $\frac{x+1}{2}=\frac{y-3}{3}=\frac{z+2}{-1}$ is Q(a,b,c) then find the value of 14(a+b+c)