List of top Questions asked in NIMCET- 2026

Given \[ \cos6x=(a)\cos^6x+(b)\cos^4x+(c)\cos^2x+(d) \] for any real number \(x\), where \(a,b,c,d\) are constants. Find the value of \(a+b+c\).

Let \(A_k\) be the arithmetic mean of the squares of \(k\) natural numbers. \[ \sum_{k=1}^{n}(6A_k-3k)=31 \] Find the value of \(n\):

The value of \(\cos^{-1}\left(\cos\left(-\frac{\pi}{6}\right)\right)+\sin^{-1}\left(\sin\left(\frac{5\pi}{6}\right)\right)\) is:

Arithmetic mean of two numbers \(a\) and \(b\) is \(5\) and the harmonic mean is \(3.2\). Find the numbers \(a\) and \(b\)?

A person who opposes established beliefs and traditions.

One who collects and studies coins.

A person who believes that pleasure is the highest good.

A jar contains a mixture of two liquids A and B in the ratio \(4:1\). When \(10\) liters of the mixture is taken out and \(10\) liters of liquid B is poured into the jar, the ratio becomes \(2:3\). How many liters of liquid A was contained in the jar initially?

A person who deliberately sets fire to buildings or property.

One who studies ancient inscriptions and writings.

The difference between Compound Interest (compounded annually) and Simple Interest on a certain sum of money at \(10\%\) per annum for \(3\) years is ₹155. Find the principal sum.

A dishonest dealer claims to sell his goods at a loss of \(10\%\) on cost price but uses a false weight of \(800\) g instead of \(1\) kg. Find his actual profit or loss percentage.

The average weight of 24 students in a class is 52 kg. If the weight of the teacher is added, the average increases by 1 kg. Find the weight of the teacher.

The price of a laptop is first increased by \(x\%\), then decreased by \(x\%\). The new price becomes \(\frac{7}{16}\) of the original price. Find the value of \(x\).

Floating-point representation is mainly used for:

IEEE 754 single precision uses:

What is the decimal equivalent of binary number \(101101\)?

Convert decimal number \(25\) into binary.

Overflow occurs when:

The maximum value of \(\sin x+\sin(x+1)\) is \(k\cos\frac12\). Find \(k\).

If the equation \(\cos^4\theta+\sin^4\theta+\lambda=0\) has real solutions, then \(\lambda\) lies in which interval?

There are two sets \(A\) and \(B\) with \(|A|=m\) and \(|B|=n\). If \(|P(A)|-|P(B)|=112\), choose the wrong option.

A survey is done among 200 people. 60% like tea and 72% like coffee. Let \(x\) be the number who like both. Let \(m\le x\le n\). Find the correct option.

If \(A \subseteq B\) and \(B \subseteq C\), then cardinality of \(A \cup B \cup C\) is equal to: