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 thrown twice. The probability that the sum of the numbers in the two throws is even is
Previous 10 Questions — NIMCET 2008
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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,\ …
Topic: NIMCET 2008
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
Next 10 Questions — NIMCET 2008
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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…
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
(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
