Let $\alpha$ and $\beta$ be the roots of $x^2+x+1=0$. The equation whose roots are $\alpha^{19}$ and $\beta^{19}$ is
Previous 10 Questions — NIMCET 2008
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Suppose $a,b,c$ are in A.P. with common difference $d$. Then $e^{1/c},e^{1/b},e^{1/a}$ are
Topic: NIMCET 2008
If $f(x)+f(1-x)=2$, then the value of
$f\left(\dfrac{1}{2001}\right)+f\left(\dfrac{2}{2001}\right)+\cdots+f\left(\dfrac…
Topic: NIMCET 2008
If $a,b$ are the roots of $x^2+px+1=0$ and $c,d$ are the roots of $x^2+qx+1=0$, the value of
$E=(a-c)(b-c)(a+d)(b+d)$ is
Topic: NIMCET 2008
A line $L$ has intercepts $a$ and $b$ on the coordinate axes. When the axes are rotated through a given angle, keeping …
Topic: NIMCET 2008
Let $M$ be a point inside the triangle $ABC$. Then which one of the following is true?
Topic: NIMCET 2008
The maximum value of
$(\cos\alpha_1)(\cos\alpha_2)\cdots(\cos\alpha_n)$
where $0\le \alpha_1,\alpha_2,\ldots,\alpha_n\l…
Topic: NIMCET 2008
If $f:\mathbb R\to\mathbb R$ and $g:\mathbb R\to\mathbb R$ are continuous functions, then evaluate
$\displaystyle \int_…
Topic: NIMCET 2008
If $y=mx$ bisects the angle between the lines
$x^2(\tan^2\theta+\cos^2\theta)+2xy\tan\theta-y^2\sin\theta=0$
when $\the…
Topic: NIMCET 2008
If two events $A$ and $B$ such that
$P(A')=0.3,\ P(B)=0.5$ and $P(A\cap B)=0.3$, then $P(B\mid A\cup B')$ is
Topic: NIMCET 2008
If
$y=\sec^{-1}\left(\frac{x+1}{x-1}\right)+\sin^{-1}\left(\frac{x-1}{x+1}\right)$,
$x\in[0,\infty)$ and $x\ne1$, then …
Topic: NIMCET 2008
Next 10 Questions — NIMCET 2008
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In the expression
$(x+1)(x+4)(x+9)(x+16)\cdots(x+400)$
the coefficient of $x^{19}$ is
Topic: NIMCET 2008
The value of
$y=0.36\log_{0.25}\left(\dfrac13+\dfrac1{3^2}+\cdots\right)$
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
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
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
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
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
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
The number of roots of the equation
$|x^2-x-6|=x+2$ is
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
