If $f:\mathbb R\to\mathbb R$ and $g:\mathbb R\to\mathbb R$ are continuous functions, then evaluate $\displaystyle \int_{-\pi/2}^{\pi/2}[f(x)+f(-x)][g(x)-g(-x)],dx$
Previous 10 Questions — NIMCET 2008
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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
The function $f(x)=2\sin x+\sin 2x,\ x\in[0,2\pi]$ has absolute maximum and minimum at
Topic: NIMCET 2008
The area of the plane bounded by
$y=\sqrt{x},\ x\in[0,1]$,
$y=x^2,\ x\in[1,2]$,
$y=-x^2+2x+4,\ x\in[0,2]$
Topic: NIMCET 2008
The integer $n$ for which
$\displaystyle \lim_{x\to0}\frac{(\cos x-1)(\cos x-e^x)}{x^n}$
is finite and non-zero
Topic: NIMCET 2008
The value of
$\displaystyle \int_0^{\pi/2} \frac{dx}{1+\tan^3 x}$
is
Topic: NIMCET 2008
The number of functions $f$ from $A={0,1,2}$ into $B={0,1,2,3,4,5,6,7}$ such that
$f(i) \le f(j)$ for $i
Topic: NIMCET 2008
Suppose $P_1,P_2,\dots,P_{30}$ are thirty sets each having $5$ elements and $Q_1,Q_2,\dots,Q_n$ are $n$ sets with $3$ e…
Topic: NIMCET 2008
If $f(x)$ is a polynomial satisfying
$f(x)f\left(\frac{1}{x}\right)=f(x)+f\left(\frac{1}{x}\right)$
and $f(3)=28$, then…
Topic: NIMCET 2008
Next 10 Questions — NIMCET 2008
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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
Let $M$ be a point inside the triangle $ABC$. Then which one of the following is true?
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
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
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
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
Let $\alpha$ and $\beta$ be the roots of $x^2+x+1=0$. The equation whose roots are $\alpha^{19}$ and $\beta^{19}$ is
Topic: NIMCET 2008
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
