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A tangent is drawn to the curve $y=x^3+3x^2+1$ at $(h,k);h>0$. If the equation of tangent is $y=9x-4$ then the value of $h+k$ is

Equation of the plane containing the line $x+2y+3z-5=0=3x+2y+z-5$ which is parallel to the line $x-1=2-y=z-3$, is-

The value of definite integral ${\int }_{-1}^2\left(x^3-x\right|\mathrm{dx}$ is

Find the degree measure corresponding to the following radian measures (Use $\pi =\frac{22}{7}$):

(i) $\frac{9\pi }{5}$

(ii) $\frac{-5\pi }{6}$

(iii) ${\left(\frac{180\pi }{5}\right)}^c$

(iv) $(-3{)}^c$

(v) ${11}^c$

(vi) $1^c$

The value
of
is

(A) 0 (B) –1 (C) 1 (D) 3

Find the graph of the function $f\left(x\right)=a^x$ where $0<a<1.$

For any two non-empty sets $A$ and $B$, $(A\cup B{)}^C\cap (A^C\cap B)$ is equal to

Find the equation of the circle whose centre is (1, 2) and which passes through the point (4, 6).

Let $f:N\to R$ be such that $f\left(1\right)=1$ and $f\left(1\right)+2f\left(2\right)+3f\left(3\right)+...+nf\left(n\right)=n(n+1)f\left(n\right)$, for all $n\in N,n\ge 2,$ where $N$ is the set of natural numbers and $R$ is the set of real numbers. Then the value of $f\left(500\right)$ is

Let $A=\{1,2,3\},B=\{1,3,5\}.$ A relation $R$ is defined from $A$ to $B$ as $R=\left\{\right(1,3),(1,5),(2,1\left)\right\}.$ Then $R^{-1}=$

The value of $\underset{0}{\overset{\pi /2}{\int }}{\cos }^{2}xdx$ is

$a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ represents a pair of distinct non parallel line. If constant c is changed as new constant k then new equation represents.

Find $x$, when $\frac{x}{10}=\frac{2}{60}$

The equation of the ellipse, whose axes are of lengths $6$ and $2\sqrt{6}$ and their equations are $x-3y+3=0$ and $3x+y-1=0$ respectively, is

Let $S_n=\frac{1}{n}\sum _{r=0}^{n-1}f\left(\frac{r}{n}\right),T_n=\frac{1}{n}\sum _{r=1}^{n}f\left(\frac{r}{n}\right)$ and $f$ is strictly increasing function, then which of the following option(s) is/are correct?

If $\overrightarrow{a}=x\hat{i}+\hat{j}+2\hat{k}$ and $\overrightarrow{b}=\hat{i}+y\hat{j}+5\hat{k}$ such that $\overrightarrow{a}\cdot \overrightarrow{b}=8,$ then the value of $x+y$ is

A dice is rolled, the probability to get the number greater than $4$ is

Is the
function defined by
continuous
at x
=
p?

Let us consider a curve, $y=f\left(x\right)$ passing through the point $(-2,2)$ and slope of the tangent to the curve at any point $(x,f(x\left)\right)$ is given by $f\left(x\right)+x{f}^{\prime }\left(x\right)=x^2$. Then

A conic section is defined by the equations x = - 1 + sect y = 2 + z tant. The coordinates of the foci are,

What is the minimum number of elements an equivalence relation defined on the set A {1,2,3} would have?

If $\overrightarrow{x}$ is a vector whose initial point divides the line joining $5\hat{i}$ and $5\hat{j}$ in the ratio $\lambda :1$ and the terminal point is the origin. Also $|\overrightarrow{x}|\le \sqrt{37},$ then $\lambda$ belongs to

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$Letf:[0,\sqrt{3}]\to [0,\frac{\pi }{3}+lo{g}_{e}2]definedf\left(x\right)=lo{g}_e\sqrt{x^2+1}+ta{n}^{-1}xthenf\left(x\right)is$

If $x^2$ - x + a - 3 < 0 for at least one negative value of x, then complete set of values of a

Simplify:

1. (2x-5y)cube -(2x+5y)cube

Find the equation of
the plane through the intersection of the planes

and

and the point (2, 2, 1)

The average of $m\sin \left(m^{\circ }\right)$ where $m=2,4,6,\cdots ,180$ is equal to
(correct answer + 1, wrong answer - 0.25)