If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar unit vectors and $\vec{a} \times (\vec{b} \times \vec{c}) = \dfrac{\vec{b} + \vec{c}}{\sqrt{2}}$, then the angle between $\vec{a}$ and $\vec{b}$ is:
Previous 10 Questions — NIMCET 2009
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Number of solutions for
$\tan^{-1}\sqrt{x(x+1)} + \sin^{-1}\sqrt{x^2 + x + 1} = \dfrac{\pi}{2}$ is:
Topic: NIMCET 2009
From 50 students:
37 passed Math, 24 Physics, 43 Chemistry.
At most 19 passed Math & Physics,
at most 29 passed Mat…
Topic: NIMCET 2009
If $A = \cos^2\theta + \sin^4\theta$, then for all values of $\theta$:
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
Number of distinct integer values of $a$ satisfying
$2^{2a} - 3(2^{a+2}) + 25 = 0$ is:
Topic: NIMCET 2009
There are 10 points, out of which 6 are collinear.
Number of triangles formed:
Topic: NIMCET 2009
The smaller area bounded by
$y = 2 - x$
and
$x^2 + y^2 = 4$
is:
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
$A_1, A_2, A_3, A_4$ are subsets of $U$ (75 elements).
Each $A_i$ has 28 elements.
Any two intersect in 12 elements.
An…
Topic: NIMCET 2009
If $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$, then
$I + A + A^2 + A^3 + \cdots \infty$ equals:
Topic: NIMCET 2009
Next 10 Questions — NIMCET 2009
Ascending by ID
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The straight lines
$\dfrac{x}{a} + \dfrac{y}{b} = k$
and
$\dfrac{x}{a} + \dfrac{y}{b} = \dfrac{1}{k}$ (with $k\neq0$)
m…
Topic: NIMCET 2009
Events $A$ and $B$ satisfy:
$P(A \cup B) = \dfrac{1}{6}$,
$P(A \cap B) = \dfrac{1}{4}$,
$P(A) = \dfrac{1}{4}$
Then eve…
Topic: NIMCET 2009
An anti-aircraft gun fires a maximum of four shots.
Probabilities of hitting in the 1st, 2nd, 3rd, and 4th shot are
0.4…
Topic: NIMCET 2009
If
$2x^4 + x^3 - 11x^2 + x + 2 = 0$
then the values of
$x + \dfrac{1}{x}$
are:
Topic: NIMCET 2009
If all digits 6 in the numbers from 1 to 100 are replaced by 9,
by how much does the algebraic sum change?
Topic: NIMCET 2009
Pick 1st, 2nd, 4th, 5th, 6th letters from REASONING,
form another word,
then write the first and last letters of the ne…
Topic: NIMCET 2009
The sum of the numbers from 1 to 100 which are not divisible by 3 and 5 is:
Topic: NIMCET 2009
Three shopkeepers each make one true statement and one false statement.Shopkeeper 1:• Dog had black hair• Dog had a lon…
Topic: NIMCET 2009
A train travels 60 km, then due to an accident runs at $\dfrac{3}{4}$ of its former speed and reaches 40 minutes late.
…
Topic: NIMCET 2009
Find the remainder when
$X = 1! + 2! + 3! + \cdots + 100!$
is divided by $240$.
Topic: NIMCET 2009
