Let $\vec A=2\vec i+\vec j-2\vec k$ and $\vec B=\vec i+\vec j$. If $\vec C$ is a vector such that $\vec A\cdot\vec C=|\vec C|$, $|\vec C-\vec A|=2\sqrt2$ and the angle between $\vec A\times\vec B$ and $\vec C$ is $30^\circ$, then $|(\vec A\times\vec B)\times\vec C|$ is equal to
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The value of $\lambda$ such that the four points whose position vectors are
$3\vec i-2\vec j+\lambda\vec k,\ 6\vec i+3\…
Topic: NIMCET 2008
The value of $\sin12^\circ\sin48^\circ\sin54^\circ$ is
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If
$(1+\tan1^\circ)(1+\tan2^\circ)\cdots(1+\tan45^\circ)=2^n$,
then the value of $n$ is
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If $\cos\alpha+\cos\beta=a$, $\sin\alpha+\sin\beta=b$ and $\theta$ is the arithmetic mean between $\alpha$ and $\beta$,…
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A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope, just two consecutive letters, TA, ar…
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A six-faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thro…
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The value of $\lambda$ for which the volume of the parallelepiped formed by the vectors
$\vec i+\lambda\vec j+\vec k,\ …
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A bag contains $6$ red and $4$ green balls.
A fair die is rolled and a number of balls equal to that appearing on the d…
Topic: NIMCET 2008
A letter is taken at random from the letters of the word STATISTICS and another letter is taken at random from the lett…
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A pair of unbiased dice is rolled together till a sum of either $5$ or $7$ is obtained.
The probability that $5$ comes …
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Next 10 Questions — NIMCET 2008
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A rigid body is rotating at the rate of $3$ radians per second about an axis $AB$, where
$A(1,-2,1)$ and $B(3,-4,2)$.
T…
Topic: NIMCET 2008
If $\vec A+\vec B+\vec C=\vec0$, $|\vec A|=3$, $|\vec B|=5$, $|\vec C|=7$,
then the angle between $\vec A$ and $\vec B$…
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(i) P ψ Q means P is mother of Q(ii) P ∈ Q means P is sister of Q(iii) P $ Q means P is father of Q(iv) P # Q means P i…
Topic: NIMCET 2008
(i) P ψ Q means P is mother of Q(ii) P ∈ Q means P is sister of Q(iii) P $ Q means P is father of Q(iv) P # Q means P i…
Topic: NIMCET 2008
(i) P ψ Q means P is mother of Q(ii) P ∈ Q means P is sister of Q(iii) P $ Q means P is father of Q(iv) P # Q means P i…
Topic: NIMCET 2008
(i) P ψ Q means P is mother of Q(ii) P ∈ Q means P is sister of Q(iii) P $ Q means P is father of Q(iv) P # Q means P i…
Topic: NIMCET 2008
(i) P ψ Q means P is mother of Q(ii) P ∈ Q means P is sister of Q(iii) P $ Q means P is father of Q(iv) P # Q means P i…
Topic: NIMCET 2008
There are six houses in a row. Mr. Lal has Mr. Babu and Mr. Anil as neighbours.
Mr. Bhatia has Mr. Gupta and Mr. Sharma…
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A watch which gains 10 seconds in 5 minutes was set correct at 9 a.m.
When the watch indicated 20 minutes past 7 o’cloc…
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A boy observes the reflection of a clock in a mirror.
The time observed by the boy in the mirror is 8 hours 45 minutes.…
Topic: NIMCET 2008
