The value of $\lambda$ for which the volume of the parallelepiped formed by the vectors $\vec i+\lambda\vec j+\vec k,\ \vec j+\lambda\vec k,\ \lambda\vec i+\vec k$ is minimum is
Previous 10 Questions — NIMCET 2008
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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…
Topic: NIMCET 2008
A pair of unbiased dice is rolled together till a sum of either $5$ or $7$ is obtained.
The probability that $5$ comes …
Topic: NIMCET 2008
The number of roots of the equation
$|x^2-x-6|=x+2$ is
Topic: NIMCET 2008
Equation of the common tangent touching the circle
$(x-3)^2+y^2=9$
and the parabola
$y^2=4x$
above the $x$-axis is
Topic: NIMCET 2008
If $a,b,c$ are the roots of the equation
$x^3-3px^2+3qx-1=0$,
then the centroid of the triangle with vertices
$\left(a,…
Topic: NIMCET 2008
The number of ordered pairs $(m,n)$, $m,n\in{1,2,\ldots,100}$ such that
$7^m+7^n$ is divisible by $5$ is
Topic: NIMCET 2008
An eight digit number divisible by $9$ is to be formed by using $8$ digits out of the digits $0,1,\ldots,9$ without rep…
Topic: NIMCET 2008
For $a>0,\ a\ne1$, the number of values of $x$ satisfying
$2\log_x a+\log_{ax} a+3\log_{a^2x} a=0$
is
Topic: NIMCET 2008
If $H_1,H_2,\ldots,H_n$ are $n$ harmonic means between $a$ and $b$, $a\ne b$, then the value of
$\dfrac{H_1+a}{H_1-a}+\…
Topic: NIMCET 2008
Next 10 Questions — NIMCET 2008
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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…
Topic: NIMCET 2008
A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope, just two consecutive letters, TA, ar…
Topic: NIMCET 2008
If $\cos\alpha+\cos\beta=a$, $\sin\alpha+\sin\beta=b$ and $\theta$ is the arithmetic mean between $\alpha$ and $\beta$,…
Topic: NIMCET 2008
If
$(1+\tan1^\circ)(1+\tan2^\circ)\cdots(1+\tan45^\circ)=2^n$,
then the value of $n$ is
Topic: NIMCET 2008
The value of $\sin12^\circ\sin48^\circ\sin54^\circ$ is
Topic: NIMCET 2008
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
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=|\…
Topic: NIMCET 2008
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 $\vec B$…
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
