$A_1, A_2, A_3, A_4$ are subsets of $U$ (75 elements). Each $A_i$ has 28 elements. Any two intersect in 12 elements. Any three intersect in 5 elements. All four intersect in 1 element. Find the number of elements belonging to none of the four subsets.
Previous 10 Questions — NIMCET 2009
Nearest first
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If $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$, then
$I + A + A^2 + A^3 + \cdots \infty$ equals:
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
Find $k$ in the equation
$x^3 - 6x^2 + kx + 64 = 0$
if roots are in geometric progression.
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
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:
$(b+c)(y+z) - ax = b - c$
$(c+a)(z+x) - by = c - a$
$(a+b)(x+y) - cz =…
Topic: NIMCET 2009
Next 10 Questions — NIMCET 2009
Ascending by ID
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$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
From 50 students:
37 passed Math, 24 Physics, 43 Chemistry.
At most 19 passed Math & Physics,
at most 29 passed Mat…
Topic: NIMCET 2009
Number of solutions for
$\tan^{-1}\sqrt{x(x+1)} + \sin^{-1}\sqrt{x^2 + x + 1} = \dfrac{\pi}{2}$ is:
Topic: NIMCET 2009
If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar unit vectors and
$\vec{a} \times (\vec{b} \times \vec{c}) = \dfrac{\vec…
Topic: NIMCET 2009
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
