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Find the equation of tangent to parabola $y^2=4axat(a{t}^2,2at)$

Which of the following relations is incorrect?

Find the
equation of the curve passing through the point
whose
differential equation is,

The graph of the function $y=2\cos x+1$ is

If $z$ be a complex number satisfying $|Re\left(z\right)|+|Im\left(z\right)|=4$, then $|z|$ cannot be:

The volume of tetrahedron included between the plane $3x+4y–5z–60=0$ and co-ordinate planes is

Find
f(x)
andf(x),
where f(x) =

For natural number $m,n$, if $(1-y{)}^m(1+y{)}^n=1+a_{1}y+a_2{y}^2+...,$ and $a_1=a_2=10$, then

The number of ordered pairs $(x,y)$ satisfying the equation $x^2+2x\sin \left(xy\right)+1=0$ is

$(\text{where}y\in [0,2\pi \left]\right)$

Write the values of the square root of i.

The sum of the solutions of the equation $|\sqrt{x}-2|+\sqrt{x}(\sqrt{x}-4)+2=0,(x>0)$ is equal to:

The number of permutations of the word BIOLOGY is

The value(s) of $\underset{0}{\overset{1}{\int }}\frac{x^4(1-x{)}^4}{1+x^2}dx$ is/are

Let $f:[0,\infty )\to [2,\infty )$ be a differentiable increasing and onto function satisfying $f^2\left(x\right)-2f\left(x\right)-\sqrt{x}=f^2\left(y\right)-2f\left(y\right)-\sqrt{y}$
If $g\left(x\right)$ be the inverse of $f\left(x\right)$, then $g^{\prime }\left(4\right)$ is

The corner
points of the feasible region determined by the following system of
linear inequalities:

Let Z = px + qy, where p, q > 0.
Condition on p and q so that the maximum of Z occurs at
both (3, 4) and (0, 5) is

(A) p
= q (B) p = 2q (C) p = 3q (D) q
= 3p

Find the equation of all lines having
slope −1 that are tangents to the curve
.

Find the area of the region bounded by the curve $y^2=4x$ and the line x = 3.

The direction cosines of the line x = y = z are
[MP PET 1989]

Two numbers $a$ and $b$ are selected at random from the set of first $10$ natural numbers. Then the probability that $f\left(x\right)=x^3-15x^2+72x+8$ monotonically increases in the interval $[a,b],$ is equal to

Let P be the point on the parabola, $y^2=8x$, which is at a minimum distance from the centre C of the circle,$x^2+(y+6{)}^2=1$. Then, the equation of the circle, passing through C and having its centre at P is

If $A$ and $B$ are two matrices such that $A$ has identical rows and $AB$ is defined, then $AB$ has

Choose the correct answer.
If $f\left(x\right)={\int }_x^0$ t sin t dt, then f'(x)is
(a)cos x+x sin x
(b)x sin x
(c)x cos x
(d)sin x +x cos x