If $a,b,c$ are the integers between $1$ and $9$ and $a51,\ b41,\ c31$ are three-digit numbers and the value of determinant $D=\left|\begin{array}{ccc}5&4&3\\a51&b41&c31\\a&b&c\end{array}\right|$ is zero, then $a,b,c$ are

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If $A=\left[\matrix{k&l\cr m&n}\right]$ and $kn\ne lm$, then the value of $A^2-(k+n)A+(kn-lm)I$ equals

Topic: AMU MCA 2018

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If $R$ is the set of real numbers and $f:R\to R$ is a function defined by $f(x)=\sin x$, then $f^{-1}([-1,1])$ is

Topic: AMU MCA 2018

3

Let $\frac{\sin(\theta-\alpha)}{\sin(\theta-\beta)}=\frac{a}{b},\ \frac{\cos(\theta-\alpha)}{\cos(\theta-\beta)}=\frac{…

Topic: AMU MCA 2018

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The equation $|x|+\left|\frac{x}{x-1}\right|=\frac{x^2}{|x-1|}$ will be always true for $x$, belonging to

Topic: AMU MCA 2018

5

Let $0

Topic: AMU MCA 2018

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The distance of point of intersection of the line $\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}$ with the plane $x-y+z=5$…

Topic: AMU MCA 2018

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The area bounded by the curve $y=\begin{cases} x^{1/\ln x}, & x\ne1 \ e, & x=1 \end{cases}$ and $y=|x-e|$ is

Topic: AMU MCA 2018

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If $\cot^{-1}(\sqrt{\cos\alpha})-\tan^{-1}(\sqrt{\cos\alpha})=x$, then $\sin x$ is equal to

Topic: AMU MCA 2018

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If $\lim_{x\to0}|x|^{[\cos x]}=l$, where $[.]$ denotes the greatest integer function, then the value of $l$ is

Topic: AMU MCA 2018

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The unit vector which is orthogonal to the vector $\hat{i}+\hat{j}+\hat{k}$ and is coplanar with vectors $\hat{i}+2\hat…

Topic: AMU MCA 2018

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If $\int_{0}^{\infty}[3e^{-x}],dx=l$, where $[.]$ denotes the greatest integer function, then the value of $l$ is

Topic: AMU MCA 2018

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If $A$ and $B$ are disjoint sets, then $B\cap A'$ where $A'$ is complement of $A$ is equal to

Topic: AMU MCA 2018

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Which of the following is an incorrect statement?

Topic: AMU MCA 2018

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The angle between the line $x-2y+z=0=x+2y-2z$ and the plane $5x-2y-z+17=0$ is

Topic: AMU MCA 2018