If the area above the $X$-axis bounded by the curves $y=2^{kx}$ and $x=0$ and $x=2$ is $\dfrac{3}{\log 2}$, then the value of $k$ is

1

Let $\vec{a}, \vec{b}, \vec{c}$ be three vectors, then $\vec{a} \times (\vec{b} \times \vec{c}) = (\vec{a} \times \vec{…

Topic: AMU MCA 2019

2

$\lim_{x \to 0} \dfrac{\cos(\sin x) - 1}{x^2}$ equals

Topic: AMU MCA 2019

3

The curves $x=\log(y+e)$ and $y=\log\left(\dfrac{1}{x}\right)$

Topic: AMU MCA 2019

4

$\int_{0}^{1} \tan^{-1}\left(\dfrac{1}{x^2 - x + 1}\right),dx$ is

Topic: AMU MCA 2019

5

Let $x=\left[\dfrac{a+2b}{a+b}\right]$ and $y=\dfrac{a}{b}$, where $a$ and $b$ are positive integers. If $y^2>2$, then

Topic: AMU MCA 2019

6

Area of the figure bounded by the curves $y=|x-1|$ and $y=3-|x|$ is

Topic: AMU MCA 2019

7

If $f(x)=\sin^2 x$ and the composite function $g(f(x))=|\sin x|$, then the function $g(x)$ is equal to

Topic: AMU MCA 2019

8

The function $f(x)=\dfrac{1 - \sin x + \cos x}{1 + \sin x + \cos x}$ is not defined at $x=\pi$. The value of $f(\pi)$, …

Topic: AMU MCA 2019

9

The straight line $x + y = \sqrt{2},p$ will touch the hyperbola $4x^2 - 9y^2 = 36$ if

Topic: AMU MCA 2019

10

If a bar of given length moves with its extremities on two fixed straight lines at right angles, then the locus of any …

Topic: AMU MCA 2019

1

The value of \( \int_{a}^{b} \frac{x}{\left|x\right|} dx,\ a<b<0 \) is

Topic: AMU MCA 2019

2

The value of $\int_{-2}^{2}\left[p\log\left(\dfrac{1+x}{1-x}\right) + q\log\left(\dfrac{1-x}{1+x}\right)^{-2} + r\right…

Topic: AMU MCA 2019

3

A curve having the condition that the slope of tangent at some point is two times the slope of the straight line joinin…

Topic: AMU MCA 2019

4

If $a$ is an arbitrary constant, then solution of the differential equation $\dfrac{dy}{dx} + \sqrt{\dfrac{1-y^2}{1-x^2…

Topic: AMU MCA 2019

5

A particle is moving along the curve $x = at^2 + bt + c$. If $ac = b^2$, then the particle would be moving with uniform

Topic: AMU MCA 2019

6

If $ \hat{i}, \hat{j}, \hat{k} $ are unit vectors and $ |\vec{a}| = a $, then the value of $ |\hat{i} \times \vec{a}|^2…

Topic: AMU MCA 2019

7

The solution of the equation $ x^2 \dfrac{d^2 y}{dx^2} = \log x $ when $ x = 1,; y = 0 $ and $ \dfrac{dy}{dx} = -1 $ is

Topic: AMU MCA 2019

8

Let the unit vectors $ \vec{a} $ and $ \vec{b} $ be perpendicular to each other and the unit vector $ \vec{c} $ be incl…

Topic: AMU MCA 2019

9

If $ y = \dfrac{1}{\sqrt{a^2 - b^2}} \cos^{-1}\left[\dfrac{a\cos(x-a) + b}{\theta}\right] $ where $ \theta = a + b\cos(…

Topic: AMU MCA 2019

10

Let $K$ be a set of real number and $f:K \to R$ such that for all $x$ and $y$, $ |f(x) - f(y)| \le |x - y|^5 $. If $f(3…

Topic: AMU MCA 2019