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 $\vec{A} = \vec{i} + \vec{j}$ and a vector $\vec{B_2}$ perpendicular to $\vec{A}$. Then $\vec{B_1}$ is:
Previous 10 Questions — NIMCET 2009
Nearest first
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If $x < -1$ and
$2^{|x+1|} - 2^x = |2x - 1| + 1$
then the value of $x$ is:
Topic: NIMCET 2009
The equation $\sin^4 x + \cos^4 x + \sin 2x + \alpha = 0$ is solvable for:
Topic: NIMCET 2009
If $\tan^{-1}(2x) + \tan^{-1}(3x) = \dfrac{\pi}{4}$, then $x$ is:
Topic: NIMCET 2009
The value of
$\displaystyle \int_{0}^{\pi} \frac{x \sin x}{1+\cos^2 x},dx$
is:
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
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
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 $\vec{a}, \vec{b}, \vec{c}$ are unit vectors, then
$|\vec{a}-\vec{b}|^2 + |\vec{b}-\vec{c}|^2 + |\vec{c}-\vec{a}|^2$…
Topic: NIMCET 2009
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
Next 10 Questions — NIMCET 2009
Ascending by ID
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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
If $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$, then
$I + A + A^2 + A^3 + \cdots \infty$ equals:
Topic: NIMCET 2009
$A_1, A_2, A_3, A_4$ are subsets of $U$ (75 elements).
Each $A_i$ has 28 elements.
Any two intersect in 12 elements.
An…
Topic: NIMCET 2009
$ABC$ is isosceles with $AB = AC$.
$BC$ is parallel to x-axis.
$m_1, m_2$ are slopes of the medians from $B$ and $C$.
T…
Topic: NIMCET 2009
The smaller area bounded by
$y = 2 - x$
and
$x^2 + y^2 = 4$
is:
Topic: NIMCET 2009
There are 10 points, out of which 6 are collinear.
Number of triangles formed:
Topic: NIMCET 2009
Number of distinct integer values of $a$ satisfying
$2^{2a} - 3(2^{a+2}) + 25 = 0$ is:
Topic: NIMCET 2009
A man has 5 coins:
2 double-headed
1 double-tailed
2 normal
He randomly picks a coin and tosses it.
Probability tha…
Topic: NIMCET 2009
If $A = \cos^2\theta + \sin^4\theta$, then for all values of $\theta$:
Topic: NIMCET 2009
