If $ f(x)= \begin{cases} x \sin\left(\frac{1}{x}\right), & x \ne 0 \\ 0, & x = 0 \end{cases} $ then
Previous 10 Questions — NIMCET 2010
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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
The value of the integral
$\displaystyle \int_{3}^{6} \frac{\sqrt{x}}{\sqrt{9-x} + \sqrt{x}}, dx$ is
Topic: NIMCET 2010
If the tangents at the extremities of a focal chord of the parabola $x^2 = 4ay$ meet at a point where the abscissas are…
Topic: NIMCET 2010
The angle of intersection of the cardioids $r = a(1 + \cos\theta)$ and $r = a(1 - \cos\theta)$ is
Topic: NIMCET 2010
The angle between the asymptotes of the hyperbola $27x^2 - 9y^2 = 24$ is
Topic: NIMCET 2010
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…
Topic: NIMCET 2010
The circle $x^2 + y^2 = 9$ is contained in the circle $x^2 + y^2 - 6x - 8y + 25 = c^2$ if
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…
Topic: NIMCET 2010
The point $(4,1)$ undergoes the following transformations successively:
(i) Reflection about the line $y=x$
(ii) Transl…
Topic: NIMCET 2010
If $\omega \ne 1$ is a cube root of unity and $i = \sqrt{-1}$, the value of the determinant
$\left|\begin{matrix}
1 …
Topic: NIMCET 2010
Next 10 Questions — NIMCET 2010
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$\int \log_{10} x , dx$ is
Topic: NIMCET 2010
$I_1 = \int_{0}^{1} 2x^2 dx,\
I_2 = \int_{0}^{1} 2x^3 dx,\
I_3 = \int_{1}^{2} x^2 dx,\
I_4 = \int_{1}^{2} 2x^3 dx$
Topic: NIMCET 2010
Area between $y = 2 - x^2$ and $y = x^2$
Topic: NIMCET 2010
A vector $\vec{a}$ has components $2p$ and $1$.
After rotation, it becomes $(p+1,\ 1)$.
Find $p$.
Topic: NIMCET 2010
The vectors $\vec{a},\vec{b},\vec{c}$ are equal in length and taken pairwise make equal angles.
If $\vec{a}=\hat{i}+\ha…
Topic: NIMCET 2010
The position vectors of $A,B,C,D$ are
$\hat{i}+\hat{j}+\hat{k}$,
$2\hat{i}+5\hat{j}$,
$3\hat{i}+2\hat{j}-3\hat{k}$,
$\h…
Topic: NIMCET 2010
Let $\vec{a},\vec{b},\vec{c}$ be three non-zero vectors, no two collinear.
If $\vec{a}+\vec{b}$ is collinear with $\vec…
Topic: NIMCET 2010
If $C$ is midpoint of $AB$ and $P$ is any point outside $AB$, then
Topic: NIMCET 2010
Value of $\sqrt{3}\cos 20^\circ - 4\cos 20^\circ$ is:
Topic: NIMCET 2010
If $\sin^{-1}\frac{2a}{1+a^2} - \cos^{-1}\frac{1-b^2}{1+b^2} = \tan^{-1}\frac{2x}{1-x^2}$ then $x$ equals:
Topic: NIMCET 2010
