Question 1 :
At what point the tangent to the curve $\displaystyle \sqrt{x}+\sqrt{y}=\sqrt{a}$ is perpendicular to the $x$ - axis
Question 2 :
The normal drawn at the point $\displaystyle P\left ( at_{1}^{2},2at_{1} \right )$ on the parabola meets the curve again at$\displaystyle Q\left ( at_{2}^{2},2at_{2} \right ).$ then $\displaystyle t_{2} =?$
Question 3 :
Which one of the following be the gradient of the hyperbola $xy=1$ at the point $\left(t,\dfrac{1}{t}\right)$
Question 4 :
The equation of normal to the curve $y=\left| { x }^{ 2 }-\left| x \right| \right| $ at $x=-2$ is
Question 5 :
The equation of the normal to the curve $\displaystyle 2y=3-x^{2}$ at the point $(1,1)$
Question 6 :
The normal at the point $(1,1)$ on the curve $2y+{x}^{2}=3$ is
Question 7 :
The gradient of the tangent line at the point $(a cos \alpha, a sin \alpha)$ to the circle $x^2 + y^2 = a^2$, is
Question 8 :
The equation of normal to the curve $\displaystyle y=\tan x $ at the point $(0, 0)$ is -
Question 9 :
If tangent at a point of the curve $y = f(x)$ is perpendicular to $2x - 3y = 5$ then at that point $\displaystyle \dfrac{dy}{dx}$ equals
Question 10 :
The slope of the tangent to the curve $\displaystyle y=-x^{3}+3x^{2}+9x-27$ is maximum when x equals.
Question 11 :
Normal to the parabola $\displaystyle y^{2}=4ax$ where $m$ is the slope of the normal is
Question 12 :
The equation of the normal to the curve $\displaystyle 2y=3-x^{2}$ at $(1, 1)$ is -
Question 13 :
Find the tangents and normal to the curve $y(x-2)(x-3)-x+7=0,$ at point (7,0) are
Question 14 :
If a tangent to the curve $\displaystyle y=6x-{ x }^{ 2 }$ is parallel to the line $\displaystyle 4x-2y-1=0$, then the point of tangency on the curve is:
Question 15 :
What is/are the tangents to $\displaystyle y=(x^{3}-1)(x-2)$ at the points where the curve cuts the x-axis
Question 16 :
The chord of the curve $y = x^{2} + 2ax + b$, joining the points where $x = \alpha$ and $x = \beta$, is parallel to the tangent to the curve at abscissa $x =$
Question 17 :
If tangent to the curve $\displaystyle x={ at }^{ 2 },y=2at$ is perpendicular to $x$-axis, then its point of contact is:
Question 18 :
The values of $x$ for which the tangents to the curves $y=x\cos{x},y=\cfrac{\sin{x}}{x}$ are parallel to the axis of $x$ are roots of (respectively)
Question 19 :
Find the equation of the tangent to the curve $\displaystyle y=x^{2}+1$ at the point $(1,2).$
Question 20 :
The slope of the tangent to the curve $y = \int_{0}^{x} \dfrac {dt}{1 + t^{3}}$ at the point where $x = 1$ is
Question 21 :
The slope of normal to the curve y= log (logx) at x = e is
Question 22 :
The equation of tangent to the curve $y = 3x^{2} - x + 1$ at $P(1, 3)$ is ____
Question 23 :
Find the co-ordinates of the points on the curve $\displaystyle y= x/\left ( 1+x^{2} \right )$ where the tangent to the curve has greatest slope.
Question 24 :
Consider the equation $x^y=e^{x-y}$<br>What is $\dfrac{dy}{dx}$ at $x=1$ equal to ?
Question 25 :
The sum of the intercepts of a tangent to $\displaystyle \sqrt{x}+\sqrt{y}=\sqrt{a}, a> 0$ upon the coordinate axes is<br>
Question 26 :
I. lf the curve $y=x^{2}+ bx +c$ touches the straight line $y=x$ at the point $(1, 1)$ then $b$ and $c$ are given by $1, 1.$<br>II. lf the line $Px+ my +n=0$ is a normal to the curve $xy=1$, then $P> 0,\ m <0$.<br>Which of the above statements is correct<br>
Question 27 :
The curve $\displaystyle \frac{x^{n}}{a^{n}}+\frac{y^{n}}{b^{n}}=2$ touches the line $\displaystyle \frac{x}{a}+\frac{y}{b}=2$ at the point
Question 28 :
The normal to the curve $x=a\left ( \cos \theta +\theta \sin \theta \right )$, $y=a\left ( \sin \theta -\theta \cos \theta \right )$ at any point $\theta $ is such that<br>
Question 30 :
If the normal to the curve $y=f(x)$ at the point $(3,4) $ makes an angle $3\pi /4 $ with the positive x-axis, then $f'(3)=$
Question 31 :
The tangent to the curve $2a^2y=x^3-3ax^2$ is parallel to the x-axis at the points
Question 32 :
Find the slope of tangent of the curve$x = a\,{\sin ^3}t,y = b\,\,{\cos ^3}t$ at $t = \frac{\pi }{2}$
Question 33 :
The equation of the common tangent to the curves $\displaystyle y^{2}= 8x$ and $ \displaystyle xy= -1$ is<br/>
Question 34 :
The perpendicular distance between the point (1, 1) and the tangent to the curve y $=e^{2x}+x^2$ drawn at the point x $=$ 0 is<br/>
