If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors, then $|\vec{a}-\vec{b}|^2 + |\vec{b}-\vec{c}|^2 + |\vec{c}-\vec{a}|^2$ does not exceed:
Previous 10 Questions — NIMCET 2009
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A box open at the top is made by cutting squares from the four corners of a $6 \times 6$ m sheet.
The height of the box…
Topic: NIMCET 2009
The probability that a man who is 85 yrs old will die before attaining the age of 90 is $1/3$.
$A_1, A_2, A_3, A_4$ are…
Topic: NIMCET 2009
Water runs into a conical tank of radius $5$ ft and height $10$ ft at a constant rate of
$2\text{ ft}^3/\text{min}$.
Ho…
Topic: NIMCET 2009
The total number of relations that exist from a set $A$ with $m$ elements into the set $A \times A$ is:
Topic: NIMCET 2009
A set contains $(2n+1)$ elements. If the number of subsets that contain at most $n$ elements is $4096$, then the value …
Topic: NIMCET 2009
If $A$ is a $3\times 3$ matrix with $\det(A)=3$, then $\det(\operatorname{adj}A)$ is:
Topic: NIMCET 2009
A and B are independent witnesses.
Probability A speaks the truth = $x$,
Probability B speaks the truth = $y$.
If both…
Topic: NIMCET 2009
If
$\sin^{-1}x + \cos^{-1}(1-x) = \sin^{-1}(1-x)$
then $x$ satisfies the equation:
Topic: NIMCET 2009
If the distance of $(x,y)$ from the origin is defined as
$d(x,y) = \max(|x|,|y|)$,
then the locus of points where $d(x,…
Topic: NIMCET 2009
How many different paths in the $xy$-plane are there from $(1,3)$ to $(5,6)$,
if a path proceeds one step at a time eit…
Topic: NIMCET 2009
Next 10 Questions — NIMCET 2009
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Let $f(x) = \lfloor x^2 - 3 \rfloor$ where $\lfloor \cdot \rfloor$ is the greatest integer function.
Number of points i…
Topic: NIMCET 2009
If $a + b + c \neq 0$, the system of equations:
$(b+c)(y+z) - ax = b - c$
$(c+a)(z+x) - by = c - a$
$(a+b)(x+y) - cz =…
Topic: NIMCET 2009
If $y = f(x)$ is odd and differentiable on $(-\infty,\infty)$ such that
$f'(3) = -2$, then $f'(-3)$ equals:
Topic: NIMCET 2009
The value of
$\displaystyle \int_{0}^{\pi} \frac{x \sin x}{1+\cos^2 x},dx$
is:
Topic: NIMCET 2009
If $\tan^{-1}(2x) + \tan^{-1}(3x) = \dfrac{\pi}{4}$, then $x$ is:
Topic: NIMCET 2009
The equation $\sin^4 x + \cos^4 x + \sin 2x + \alpha = 0$ is solvable for:
Topic: NIMCET 2009
If $x < -1$ and
$2^{|x+1|} - 2^x = |2x - 1| + 1$
then the value of $x$ is:
Topic: NIMCET 2009
The vector $\vec{B} = 3\vec{i} + 4\vec{k}$ is to be written as the sum of a vector $\vec{B_1}$ parallel to
$\vec{A} = \…
Topic: NIMCET 2009
Find $k$ in the equation
$x^3 - 6x^2 + kx + 64 = 0$
if roots are in geometric progression.
Topic: NIMCET 2009
If
$P = {(4^n - 3n - 1) : n \in N}$
and
$Q = {(9n - 9) : n \in N}$,
then $P \cup Q$ equals to:
Topic: NIMCET 2009
