Calculus PYQ — Page 29

The solution of differential equation $\sqrt{x+1} - \sqrt{x-1}\frac{dy}{dx} = 0$ is

The smaller of the areas enclosed by the circle $x^2 + y^2 = 4$ and the line $x + y = 2$ is

The smaller area enclosed by the curve $y = |x|$ and the circle $(x-a)^2 + y^2 = a^2$ is:

The slope of the tangent to the curve $y = 3x^2 + 2kx - 5$ at $x=1$ is $9$. The value of $k$ is :

The slope of the tangent drawn at the point whose x coordinates is 2 on the curve $y = x|x|$.

The slope of normal to the curve $y = 3x^2 + 3 \sin 3x$, at $x = 0$ is:

The slope of normal to the curve $y = kx^2 - 3x + 2$ at $x = \frac{1}{2}$ is 5. The value of 'k' is

The region bounded by curve $y = x|x|$, x-axis and lines $x = \pm 1$ is best represented graphically by :

The position of Sumit when Amit will hit the paper ball is :

The portion of the area enclosed by the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, that lies in the first quadrant is

The point(s) on the curve $\frac{x^2}{9} + \frac{y^2}{64} = 1$, at which the tangents are parallel to x-axis are

The order and the degree of the differential equation $\frac{d^2y}{dx^2} + x\left(\frac{dy}{dx}\right)^2 = 2x^2 \log\left(\frac{d^2y}{dx^2}\right)$ are respectively:

The order and degree of the differential equation $\left[\left(\frac{d^2y}{dx^2}\right)^2 - 3\right]^{\frac{1}{3}} = 2\left(\frac{dy}{dx}\right)^{\frac{1}{4}}$ are

The number of arbitrary constants in the general solution of a differential equation of fourth order is:

The minimum value of $x^2 - 8x + 17$ on the set $\mathbb{R}$ of all real numbers is:

The maximum value of $x^{-x}$ is

The maximum slope of the tangents to the curve $y(x) = -x^3 + 3x^2 + 9x - 30$ is

The maximum height (in meters) achieved in the first jump is

The line $y = mx$ ($m > 0$) partitions the area of the circle $x^2 + y^2 = a^2$ ($a > 0$) in the ratio:

The line $y = x$, partition the area of the circle $(x-1)^2 + y^2 = 1$, into two segments. The area of the major segment is

The line $ax + by = 7$ is a tangent to the curve $y = \frac{x-7}{(x-2)(x-3)}$ at the point where it cuts the x-axis A. The y-intercept of the line is $-0.7$ B. $b = -7$ C. $a = 1$ D. the line passes through the point $(-13, -1)$ E. $b = -20$ Choose the correct answer from the options given below:

The interval in which the function, $f(x) = 7 - 4x - x^2$ is strictly increasing is

The interval in which the function $f(x) = 2x^3 + 3x^2 - 12x + 1$ is strictly increasing is -

The interval in which the function given by $f(x) = x^2 e^{-x}$ is strictly increasing is: