NIMCET 2027 2014 Previous Year Questions (PYQs) – Page 9 of 12
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If $\vec{A}=4\hat{i}+3\hat{j}+\hat{k}$ and $\vec{B}=2\hat{i}-\hat{j}+2\hat{k}$ , then the unit vector $\hat{N}$ perpendicular to the vectors $\vec{A}$ and $\vec{B}$ ,such that $\vec{A}, \vec{B}$ , and $\hat{N}$ form a right handed system, is:
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The value of $\int \frac{(x+1)}{x(xe^{x}+1)} dx$ is equal to
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The sum of two vectors $\vec{a}$ and $\vec{b}$ is a vector $\vec{c}$ such that $|\vec{a}|=|\vec{b}|=|\vec{c}|=2$. Then, the magnitude of $\vec{a}-\vec{b}$ is equal to:
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If x and y are positive real numbers satisfying the system of equations $x^{2}+y\sqrt{xy}=336$ and $y^{2}+x\sqrt{xy}=112$, then x + y is:
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$x^2+y\sqrt{xy}=336 \quad ...(1)$
$y^2+x\sqrt{xy}=112 \quad ...(2)$
Dividing (1) by $\sqrt{x}$,
$x\sqrt{x}+y\sqrt{y}=\frac{336}{\sqrt{x}}$
Dividing (2) by $\sqrt{y}$,
$y\sqrt{y}+x\sqrt{x}=\frac{112}{\sqrt{y}}$
Since LHS are equal,
$\frac{336}{\sqrt{x}}=\frac{112}{\sqrt{y}}$
$\frac{\sqrt{x}}{\sqrt{y}}=3$
$\sqrt{x}=3\sqrt{y}$
$\therefore x=9y$
Substituting in (2),
$y^2+9y\sqrt{9y^2}=112$
$y^2+27y^2=112$
$28y^2=112$
$y^2=4$
$\therefore y=2$
$x=9(2)=18$
$\therefore \boxed{x+y=20}$
From three collinear points A, B and C on a level ground, which are on the same side of a tower, the angles of elevation of the top of the tower are 30°, 45° and 60° respectively. If BC = 60 m, then AB is:
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If $x = 1$ is the directrix of the parabola $y^{2} = kx - 8$, then k is:
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A condition that $x^{3} + ax^{2} + bx + c$ may have no extremum is
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If n and r are integers such that 1 ≤ r ≤ n, then the value of n n-1Cr-1is
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If the foci of the ellipse $b^{2}x^{2}+16y^{2}=16b^{2}$ and the hyperbola $81x^{2}-144y^{2}=\frac{81 \times 144}{25}$ coincide, then the value of $b$, is
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NIMCET 2027
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NIMCET 2027
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and More.
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