Question 1 :
The normal at the point $(1,1)$ on the curve $2y+{x}^{2}=3$ is
Question 2 :
The equation of normal to the curve $y=\left| { x }^{ 2 }-\left| x \right| \right| $ at $x=-2$ is
Question 3 :
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 4 :
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 5 :
The equation of normal to the curve $\displaystyle y=\tan x $ at the point $(0, 0)$ is -
Question 6 :
Find the tangents and normal to the curve $y(x-2)(x-3)-x+7=0,$ at point (7,0) are
Question 7 :
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 8 :
The slope of tangent to the curve $y=\int_{0}^{x}\displaystyle \frac{dx}{1+x^{3}}$ at the point where $x=1$ is
Question 9 :
What is/are the tangents to $\displaystyle y=(x^{3}-1)(x-2)$ at the points where the curve cuts the x-axis
Question 10 :
At what point the tangent to the curve $\displaystyle \sqrt{x}+\sqrt{y}=\sqrt{a}$ is perpendicular to the $x$ - axis
Question 11 :
If tangent to the curve $\displaystyle x={ at }^{ 2 },y=2at$ is perpendicular to $x$-axis, then its point of contact is:
Question 12 :
The equation of the normal to the curve $\displaystyle 2y=3-x^{2}$ at the point $(1,1)$
Question 13 :
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 14 :
The slope of the tangent to the curve $\displaystyle y=-x^{3}+3x^{2}+9x-27$ is maximum when x equals.
Question 15 :
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 16 :
If tangent to curve at a point is perpendicular to $x$ - axis then at that point -
Question 17 :
If $\displaystyle \frac{x}{a}+\frac{y}{b}=1$ is a tangent to the curve $\displaystyle x=Kt,y=\frac{K}{t},K> 0$ than
Question 18 :
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 19 :
The intercept on x-axis made by tangent to the curve, $\displaystyle y=\int _{ 0 }^{ x }{ \left| t \right| } dt,x\in R$, which are parallel to the line $y=2x$, are equal to
Question 20 :
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 21 :
The slope of the tangent to the curve represented by $x= t^{2}+3t-8$ and $y= 2t^{2}-2t-5$ at the point $M\left ( 2,-1 \right )$ is<br><br>
Question 22 :
The slope of the normal to the curve $\displaystyle x=a\left ( \theta -\sin \theta \right ),\: \: y=a\left ( 1-\cos \theta \right )$ at point $\displaystyle \theta =\dfrac{\pi }2$ is
Question 23 :
The equation of tangent to the curve ${ \left( \cfrac { x }{ a } \right) }^{ n }+{ \left( \cfrac { y }{ b } \right) }^{ n }=2\quad $ at the point $(a,b)$ is
Question 24 :
Let $y=e^{x^2}$ and $y=e^{x^2}\sin\, x$ be two given curves. Then, angle between the tangents to the curves at any point their intersection is
Question 25 :
If $\left | f(x_{1})-f(x_{2}) \right |< (x_{1}-x_{2})^{2}$ for all $x_{1}$ $x_{2}$ $\in $ R. Find the equation of tangent to the curve y = f(x) at the point (1, 2).
Question 26 :
If $m$ is the slope of a tangent to the curve $e^y= 1+x^2$, then
Question 27 :
The slope of the tangent and normal to $y={ x }^{ 2 }-3x+5$ at $(2,3)$ are ______ and _____ respectively.
Question 28 :
Tangent is drawn to ellipse $\displaystyle \frac{x^{2}}{27}+y^{2}=1$ at $\left ( 3\sqrt{3}\cos \theta ,\sin \theta \right )$ (where $\theta \in \left ( 0,\dfrac{\pi}2 \right )).$ Then the value of $\theta$ such that sum of intercepts on axes made by this tangent is least is<br/>
Question 29 :
If the tangent at $(1,\,1)$ on $y^2=x(2-x)^2$ meets the curve again at $P(a,\,b)$ then $a/b$ is equal to
Question 30 :
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 31 :
The angle made by the tangent of the curve $x=a (t+\sin t \cos t)$, $y=a(1+sint)^2$ with the $x- axis$ at any point on it is
Question 32 :
At the point $P(a,a'')$ on the graph of $y=x^n$, $(n \epsilon N)$, in the first quadrant , a normal is drawn. The normal intersects the $y$-axis at the point $(0,b)$. If $\lim_{a\rightarrow 0}b=\displaystyle \frac{1}{2}$, then n equals
Question 33 :
The real number $\displaystyle '\alpha'$ such that the curve $\displaystyle f(x) = e^x$ is tangent to the curve $\displaystyle g(x) = \alpha x^2$.
Question 34 :
If the tangent to the conic, $y - 6 = x^2$ at (2, 10) touches the circle, $x^2 + y^2 + 8x - 2y = k$ (for some fixed k) at a point $(\alpha, \beta)$; then $(\alpha, \beta)$ is;
Question 35 :
The equation of the normal to the curve $y = e^{-2|x|}$ at the point where the curve cuts the line $x=\displaystyle \frac{1}{2}$ is<br>
Question 37 :
If $OT$ and $ON$ are perpendiculars dropped from the origin to the tangent and normal to the curve $x=a\sin^{3}t, y=a\cos^{3}t$ at an arbitrary point, then which of the following is/are correct?<br/>
Question 38 :
The point of intersection of the tangents drawn to the curve $\displaystyle x^{2}y= 1-y$ at the point where it is intersected by the curve xy$=1-y,$ is given by<br>
Question 39 :
The sum of the intercepts on the coordinate axis by any tangent to the curve $\sqrt{x} + \sqrt{y} = 2$ is<br>
Question 40 :
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/>
