If $\omega \ne 1$ is a cube root of unity and $i = \sqrt{-1}$, the value of the determinant $\left|\begin{matrix} 1 & 1+i+\omega^2 & \omega \\ 1-i & -1 & \omega^2 - 1 \\ -i & -i+\omega-1 & -\omega^3 \end{matrix}\right|$ is
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If $a \ne p$, $b \ne q$, $c \ne r$ and
$\left|\begin{matrix}
p & b & c \\
a & q & c \\
a & b & r
\end{matrix}\right| =…
Topic: NIMCET 2010
If $a, b, c$ are in A.P., $p, q, r$ are in H.P. and $ap, bq, cr$ in G.P.$,$ then $\frac{p}{r} + \frac{r}{p}$ is equal to
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If $y = a \log x + b x^2 + x$ has its extremum value at $x = -1$ and $x = 2$, then
Topic: NIMCET 2010
The value of $X^4 + 9X^3 + 35X^2 - X + 4$ for $X = -5 + 2\sqrt{-4}$ is
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The value of ‘a’ for which the system of equations
$a^3 x + (a+1)^3 y + (a+2)^3 z = 0$
$ax + (a+1) y + (a+2) z = 0$
$x…
Topic: NIMCET 2010
The average marks per student in a class of 30 students were 45. On rechecking it was found that marks had been entered…
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n a Poisson distribution if $P[X=3] = \frac{1}{4} P[X=4]$ then $P[X=5] = k P[X=7]$ where $k$ equals to
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One hundred identical coins, each with probability $p$ of showing up a head, are tossed. If $0
Topic: NIMCET 2010
A coin is tossed three times. Probability of getting heads and tails alternately is:
Topic: NIMCET 2010
India plays 4 matches. Probabilities of scoring $0,1,2$ points: $0.45,\ 0.05,\ 0.50$. Find probability of at least $7$ …
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The point $(4,1)$ undergoes the following transformations successively:
(i) Reflection about the line $y=x$
(ii) Transl…
Topic: NIMCET 2010
If the two pair of lines $X^2 - 2mXY - Y^2 = 0$ and $X^2 - 2nXY - Y^2 = 0$ are such that one represents the bisector of…
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The circle $x^2 + y^2 = 9$ is contained in the circle $x^2 + y^2 - 6x - 8y + 25 = c^2$ if
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If any tangent to the ellipse $\frac{X^2}{a^2} + \frac{Y^2}{b^2} = 1$ intercepts equal length $l$ on both axes, then $l…
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The angle between the asymptotes of the hyperbola $27x^2 - 9y^2 = 24$ is
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The angle of intersection of the cardioids $r = a(1 + \cos\theta)$ and $r = a(1 - \cos\theta)$ is
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If the tangents at the extremities of a focal chord of the parabola $x^2 = 4ay$ meet at a point where the abscissas are…
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The value of the integral
$\displaystyle \int_{3}^{6} \frac{\sqrt{x}}{\sqrt{9-x} + \sqrt{x}}, dx$ is
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The value of the integral
$\displaystyle \int_{0}^{\frac{\pi}{4}} \frac{\sin x + \cos x}{3 + \sin 2x}, dx$ 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
