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Let $A$ and $B$ be non singular square matrices of order $3$ satisfying $A+adjA=B$ and $|A|=3,$ then $|\left(adjA\right)B-3I|$ is equal to:

The set of values of x satisfying $\left[ta{n}^{-1}x\right]+\left[co{t}^{-1}x\right]=2$ where [.] is greatest integer function is

Let $a_1,a_2,.....,a_n$ be fixed real numbers such that $f\left(x\right)=(x-a_1)(x-a_2)....(x-a_n)$ What is $li{m}_{x\to a_1}$ f(x)? For $a\ne a_1,a_2,....,a_n$ compute $li{m}_{x\to a}f\left(x\right).$

Let each of the equations $x^2+2xy+a{y}^2=0$ & $a{x}^2+2xy+y^2=0$ represent two straight lines passing through the origin. If they have a common line, then the other two lines are given by

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

$\int \frac{5x}{(x+1)(x^2+9)}dx$

Equation of the chord of contact, drawn to the ellipse $4x^2+9y^2=36$ from the point $(m,n)$ where $m\cdot n=m+n$ and $m,n\in I^{+}$ is

Let $a,s,t$ be nonzero real numbers. Let $P(a{t}^2,2at),\text{and}S(a{s}^2,2as)$ be distinct points on the parabola $y^2=4ax$. If $st=1$, then the tangent at $P$ and the normal at $S$ to the parabola meet at a point whose ordinate is

Maximum number of points of intersection of $n$ straight lines if $n$ satisfies ${}^{n+5}{P}_{n+1}=\frac{11(n-1)}{2}\times {}^{n+3}{P}_n$ is

$\int \frac{e^{6logx}-e^{5logx}}{e^{4logx}-e^{3logx}}dx$

The set of values of $\alpha$ for which the point $P(\alpha ,{\alpha }^2-2)$ lies inside the triangle formed by the lines $x+y=1,$ $y=x+1$ and $y=-1,$ is

Find the equation of the plane through the line of intersection of the planes x + y +z =1 and 2x + 3y + 4z =5 which is perpendicular to the plane x - y + z = 0. Also find the distance of the plane obtained above, from the origin.

OR

Find the distance of the point (2, 12, 5) from the point of intersection of the line $\overrightarrow{r}=2\hat{i}-4\hat{j}+2\hat{k}+\lambda (3\hat{i}+4\hat{j}+2\hat{k})$ and the plane $\overrightarrow{r}.(\hat{i}-2\hat{j}+\hat{k})=0$.

If the points A(3, 2, -4), B (9, 8, -10) and C(5, 4, -6) are collinear, find the ratio in which C divides AB.

$ta{n}^{-1}\left(\frac{3a^{2}x-x^3}{a^3-3a{x}^2}\right),a>0;\frac{-a}{\sqrt{3}}\le x\le \frac{a}{\sqrt{3}}$

If the abscissas and ordinates of two points $P$ and $Q$ are the roots of the equations $x^2-7x+10=0$ and $x^2+7x+12=0$ respectively, then the equation of the circle with $PQ$ as diameter is

A series of concentric ellipses $E_1,E_2,\dots ,E_n$ are drawn such that $E_n$ touches the extremities of the major axis of $E_{n-1}$ and the foci of $E_n$ coincide with the extemities of minor axis of $E_{n-1}.$ If the eccentricites of the ellipse are independent of $n,$ then the value of the eccentricity, is

Which of the following sets are convex ?

In which quadrant does the point whose abscissa and ordinate have different signs lie?

The sum of the coefficients of even power of $x$ in the expansion of ${(1+x+x^2+x^3)}^5$ is

The roots of the equation $x^4-4x^3+6x^2-4x+1=0$ are

If 0 < x < $\frac{\pi }{2}$ and $si{n}^{n}x+co{s}^{n}x\ge 1$ then $nϵ$

Which are the most important days to remember during NEET preperation

Find the roots of the $3x^2-5x+2=0$ quadratic equation, using the quadratic formula.

The inverse of the function $f\left(x\right)=\frac{e^x-e^{-x}}{e^x+e^{-x}}+2$ is given by

The locus point of intersection of tangents to the parabola $y^2=4ax$, the angle between them being always ${45}^{\circ }$
is

Evaluate ${\int }_0^2{e}^x$as the limit of a sum.

The set $A$ has 4 elements and set $B$ has 5 elements then number of injective mappings that can be defines from $A$ to $B$ is

In any discrete series, the relationship between mean deviation from mean (M.D) and standard deviation (S.D) is

If one root of the equation $(a^2-5a+3)x^2+(3a-1)x+2=0$ be double the other, then $a=$

Three lines $L_1:\overrightarrow{r}=\lambda \hat{i},\lambda \in R,$$L_2:\overrightarrow{r}=\hat{k}+\mu \hat{j},\mu \in R,$ and $L_3:\overrightarrow{r}=\hat{i}+\hat{j}+\nu \hat{k},\nu \in R$ are given.
For which point(s) $Q$ on $L_2$ can we find a point $P$ on $L_1$ and a point $R$ on $L_3$ so that $P,Q$ and $R$ are collinear ?

Let X be a universal set such that n(X) = k. the probability of selecting two subset A and B such that B = A’, A’ is complement of the set A, is

The ratio in which the line joining$(2,-4,3)and(-4,5,-6)$ is divided by the plane $3x+2y+z-4=0$ is

The locus of a point, from where pair of tangents to the rectangular hyperbola $x^2-y^2=a^2$ contain an angle of ${45}^{\circ }$, is :

Area bounded by the curves $x=\sqrt{2-y^2}$ and $|x|\ge |y|$ is

If $ta{n}^{-1}\left(x\right)+ta{n}^{-1}\left(y\right)+ta{n}^{-1}\left(z\right)=\pi$, then $\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx}=$

Let $k$ be an integer such that the triangle with vertices $(k,–3k),(5,k)\text{and}(–k,2)$ has area $28$ sq. units. Then the orthocentre of this triangle is at the point:

Solve

$2x^2+x+1=0$

Given that ${\sin }^{10}x+{\cos }^{10}x=\frac{29}{64},$ if ${\sin }^{12}x+{\cos }^{12}x=\frac{a}{b}$, $a$ and $b$ are coprime, then the value of $b-a$ is

Find the distance of the point (4, 5) from the straight line $3x-5y+7=0$

For any two complex numbers $z_1,z_2$ we have $|z_1+z_2{|}^2=|z_1{|}^2+|z_2{|}^2.$ Then