The straight line $x + y = \sqrt{2},p$ will touch the hyperbola $4x^2 - 9y^2 = 36$ if
Previous 10 Questions — AMU MCA 2019
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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
The normal to the parabola $y^2 = 8x$ at the point $(2,4)$ meets the parabola again at the point
Topic: AMU MCA 2019
The length of the chord joining the points in which the straight line $\dfrac{x}{3} + \dfrac{y}{4} = 1$ cuts the circle…
Topic: AMU MCA 2019
The equation $4x^2 - 24xy + 11y^2 = 0$ represents
Topic: AMU MCA 2019
A ray of light passing through the point $(1,2)$ is reflected on the $x$-axis at a point $P$ and passes through the poi…
Topic: AMU MCA 2019
If $\alpha, \beta; (\alpha \ne \beta)$ satisfies the equation $a\cos\theta + b\sin\theta = c$, then the value of $\tan\…
Topic: AMU MCA 2019
Let $A, B$ and $C$ are the angles of a plain triangle and $\tan\left(\dfrac{A}{2}\right)=\dfrac{1}{3},; \tan\left(\dfra…
Topic: AMU MCA 2019
If $\theta = \sin^{-1} x + \cos^{-1} x - \tan^{-1} x, x \ge 0$ then the smallest interval in which $\theta$ lies is
Topic: AMU MCA 2019
The equation $\sin x + \sin y + \sin z = -3$ for $0 \le x \le 2\pi,; 0 \le y \le 2\pi,; 0 \le z \le 2\pi$ has
Topic: AMU MCA 2019
The value of $\cot 70^\circ + 4\cos 70^\circ$ is
Topic: AMU MCA 2019
Next 10 Questions — AMU MCA 2019
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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
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
Area of the figure bounded by the curves $y=|x-1|$ and $y=3-|x|$ is
Topic: AMU MCA 2019
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
$\int_{0}^{1} \tan^{-1}\left(\dfrac{1}{x^2 - x + 1}\right),dx$ is
Topic: AMU MCA 2019
The curves $x=\log(y+e)$ and $y=\log\left(\dfrac{1}{x}\right)$
Topic: AMU MCA 2019
$\lim_{x \to 0} \dfrac{\cos(\sin x) - 1}{x^2}$ equals
Topic: AMU MCA 2019
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
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 va…
Topic: AMU MCA 2019
The value of \( \int_{a}^{b} \frac{x}{\left|x\right|} dx,\ a<b<0 \) is
Topic: AMU MCA 2019
