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The point on the x-axis which is equidistant from (2, –5) and (–2, 9) is

The distance between the parallel lines $\overrightarrow{r}=2\hat{i}+3\hat{j}-\hat{k}+\lambda (\hat{i}-\hat{j}+2\hat{k})$ and $\overrightarrow{r}=-3\hat{i}+4\hat{j}+\hat{k}+\mu (\hat{i}-\hat{j}+2\hat{k})$ is

If the 7th term of a H.P is $\frac{1}{10}$ and the 12th term is $\frac{1}{25}$, then the 20th term is

If $\int \frac{cos8x+1}{tan2x-cot2x}dx=acos8x+C$, then

The horizontal asymptotes of the curve $y=\frac{e^x-e^{-x}}{e^x+e^{-x}}$ are

The last digit of $(2137{)}^{754}$ is

The parabola $y^2=x$ is symmetric about

If point $(\alpha ,\beta )$ lies on the curve $y=\ln x$, is at the shortest distance from point $(2,3),$ then which of the following is true

If a, b, c are in A.P., prove that:
(i) $(a-c{)}^2=4(a-b\left)\right(b-c)$
(ii) $a^2+c^2+4ac=2(ab+bc+ca)$
(iii) $a^3+c^3+6abc=8b^3$

The locus of the centre of a circle, which touches externally the circle $x^2+y^2-6x-6y+14=0$ and also touches the y-axis, is given by the equation

Which option is true about the following sentence?

Seema is liked by all her family members.

Any chord $ABofy62=4ax$ cuts the axis of the parabola at $P$, so that $AP:AB=1:3whereA(a{t}_1^2,2a{t}_1),B(a{t}_2^2,2a{t}_2)$, then

Let $f:R\to R$ be a function such that $f\left(x\right)=x^3+x^2{f}^{\prime }\left(1\right)+x{f}^{\prime \prime }\left(2\right)+f^{\prime \prime \prime }\left(3\right),x\in R$. Then $f\left(2\right)$ equals :

If ${\theta }_1$ and ${\theta }_2$ be respectively the smallest and the largest values of $\theta$ in $(0,2\pi )-\left\{\pi \right\}$ which satisfy the equation, $2{\cot }^2\theta -\frac{5}{\sin \theta }+4=0$, then which of the following statements is/are correct $?$

If one metre of cloth costs $Rs.10,$ then the cost of $10.75$ metres of cloth is

Let M be the set of all possible $2\times 2$ matrix A of integer entries such that $A{A}^T=I$ where $I=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],$ then

$\text{If cos}\left(\frac{x}{2}\right)cos\left(\frac{x}{2^2}\right)cos\left(\frac{x}{2^3}\right)...............to\infty =\frac{sinx}{x}then\frac{1}{2^2}se{c}^2\left(\frac{x}{2}\right)\frac{1}{2^4}se{c}^2\left(\frac{x}{2^2}\right)+.......=$

If x satisfies $\left(x-1\right|+\left(x-2\right|+\left(x-3\right|\ge 6$, then the values of x lie in the range

Find the multiplicative inverse of the complex number –i

Which of the following transformation reduces the differential equation $\frac{dz}{dx}+\frac{z}{x}logz=\frac{z}{x^2}(logz{)}^2$ to the form P(x)u = Q(x)

The domain of $f\left(x\right)=\sqrt{x-4-2\sqrt{x-5}}-\sqrt{x-4+2\sqrt{x-5}}$ is

The length of a second hand in a watch is $1\text{cm}$. The magnitude of change in velocity of its tip in $15$ seconds is

If the curve $y=a{x}^2+bx+c,x\in R,$ passes through the point $(1,2)$ and the tangent line to this curve at origin is $y=x,$ then the possible values of $a,b,c$ are

The maximum value of $f\left(x\right)=x^3-9x^2+24x+5$ in the interval $[1,6]$

Let $(x,y,z)$ be points with integer coordinates satisfying the system of homogeneous equations:
$3x-y-z=0-3x+z=0-3x+2y+z=0$
Then the number of such points for which
$x^2+y^2+z^2\le 100$ is ___