If there are $5$ sets represented via a Venn diagram, the number of regions that arise in the Venn diagram equals:
Previous 10 Questions — NIMCET 2026
Nearest first
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Let $n$ be the number of injective functions $f:{1,2,3,4}\to {1,2,3,4,5,6,7,8}$ sending an even number to an even numbe…
Topic: NIMCET 2026
Define a relation $\sim$ on the set $\{1,2,3,4,5,6,7,8,9,10\}$ by $a \sim b$ if $a - 2b$ is divisible by $3$. Then:
Topic: NIMCET 2026
The set $ (A \Delta B) \cap C $ is not equal to:
Topic: NIMCET 2026
From the top of a viewpoint at a height of 80 m, the angles of depression of the top and bottom of a flag standing on t…
Topic: NIMCET 2026
If $x,y$ are real numbers such that
$2^{x+\frac{1}{2}}\times 4^{y-\frac{5}{6}}=3^{x-\frac{1}{2}}\times 9^{y-\frac{1}{3}…
Topic: NIMCET 2026
The eccentricity of an ellipse whose center is at the origin is $\frac{1}{2}$. If one of its directrices is $x=-4$, fin…
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A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (-1, 1) and (2, 3). Then the area …
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If $f:[0,\infty)\to R$ is defined by
$f(x)=\frac{x^2-1}{x^2+1}$,
find the value of:
$\int_{-1}^{1} f^{-1}(y)dy$
Topic: NIMCET 2026
A die is rolled twice independently. What is the probability that either the first die shows a number no less than 4 or…
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Evaluate the following definite integral:$\int_{0}^{\frac{\pi}{4}} \frac{dx}{\cos^4 x}$
Topic: NIMCET 2026
Next 10 Questions — NIMCET 2026
Ascending by ID
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Let $R\subset \mathbb{N}\times \mathbb{N}$. Which of the following statement is necessarily true?
Topic: NIMCET 2026
The number of triples of sets $(A,B,C)$ with $A,B,C\subseteq \{1,\ldots,n\}$ such that
$(A\cap B)\subseteq C\subseteq (…
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The number of ordered tuples $(p,q,r)$ in the truth table for which the statement
$(\neg p\vee q)\Rightarrow r$ is true…
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In a tuition batch of two students, the probability that $X$ will pass the exam is $\frac{2}{5}$ and that of $Y$ is $\f…
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Let $A_1,A_2,A_3$ are three events in a sample space with the condition $A_1\cap A_2\neq \phi$, then always:
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The distances in meters for seven throws of a shotputter are: $14.5,15.2,16.8,17.1,15.9,16.3,14.7$. Calculate the sampl…
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consider the following grouped data: Class IntervalNumber of students 20-258 25-30 14 30…
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An investigator has missed a value while collecting data in an experiment. Denoting the missing value by $x$, the obser…
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Let $X$ and $Y$ be two independent identically distributed Bernoulli random variables with common probability mass func…
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For a given sample, the computed values of the variance and fourth central moment are $3$ and $63$ respectively. Then t…
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