Let $\vec{a},\vec{b},\vec{c}$ be three non-zero vectors, no two collinear. If $\vec{a}+\vec{b}$ is collinear with $\vec{c}$ and $\vec{b}+\vec{c}$ is collinear with $\vec{a}$, then $\vec{a}+\vec{b}+\vec{c}$ is equal to
Previous 10 Questions — NIMCET 2010
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The position vectors of $A,B,C,D$ are
$\hat{i}+\hat{j}+\hat{k}$,
$2\hat{i}+5\hat{j}$,
$3\hat{i}+2\hat{j}-3\hat{k}$,
$\h…
Topic: NIMCET 2010
The vectors $\vec{a},\vec{b},\vec{c}$ are equal in length and taken pairwise make equal angles.
If $\vec{a}=\hat{i}+\ha…
Topic: NIMCET 2010
A vector $\vec{a}$ has components $2p$ and $1$.
After rotation, it becomes $(p+1,\ 1)$.
Find $p$.
Topic: NIMCET 2010
Area between $y = 2 - x^2$ and $y = x^2$
Topic: NIMCET 2010
$I_1 = \int_{0}^{1} 2x^2 dx,\
I_2 = \int_{0}^{1} 2x^3 dx,\
I_3 = \int_{1}^{2} x^2 dx,\
I_4 = \int_{1}^{2} 2x^3 dx$
Topic: NIMCET 2010
$\int \log_{10} x , dx$ is
Topic: NIMCET 2010
If
$
f(x)=
\begin{cases}
x \sin\left(\frac{1}{x}\right), & x \ne 0 \\
0, & x = 0
\end{cases}
$
then
Topic: NIMCET 2010
The value of the integral
$\displaystyle \int_{0}^{\frac{\pi}{4}} \frac{\sin x + \cos x}{3 + \sin 2x}, dx$ is
Topic: NIMCET 2010
The value of the integral
$\displaystyle \int_{3}^{6} \frac{\sqrt{x}}{\sqrt{9-x} + \sqrt{x}}, dx$ is
Topic: NIMCET 2010
If the tangents at the extremities of a focal chord of the parabola $x^2 = 4ay$ meet at a point where the abscissas are…
Topic: NIMCET 2010
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If $C$ is midpoint of $AB$ and $P$ is any point outside $AB$, then
Topic: NIMCET 2010
Value of $\sqrt{3}\cos 20^\circ - 4\cos 20^\circ$ is:
Topic: NIMCET 2010
If $\sin^{-1}\frac{2a}{1+a^2} - \cos^{-1}\frac{1-b^2}{1+b^2} = \tan^{-1}\frac{2x}{1-x^2}$ then $x$ equals:
Topic: NIMCET 2010
In $\triangle ABC$, $R$ is circumradius and $8R^2=a^2+b^2+c^2$.
Then $\triangle ABC$ is:
Topic: NIMCET 2010
The rate of increase of length of the shadow of a man $2$ meters high, due to a lamp at $10$ meters height, when he is …
Topic: NIMCET 2010
A person stands at a point $A$ due south of a tower and observes elevation $60^\circ$.
He walks west to $B$, elevation …
Topic: NIMCET 2010
Distance between the parallel lines
$y = 2x + 4$
and
$6x = 3y + 5$
is
Topic: NIMCET 2010
Which of the following is NOT one of the four major data-processing functions of a computer?
Topic: NIMCET 2010
Simplified form of
$F(X,Y,Z)=\Sigma(0,2,4,5,6)$ is:
Topic: NIMCET 2010
Which gate is equivalent to (NOR) OR (XOR)?
Topic: NIMCET 2010
