List of top Mathematics Questions asked in NIMCET

The number of values of \(\theta\) in \([0,2\pi]\) for which the following homogeneous system has a non-trivial solution is: \[ x+(\sin\theta)y+(\cos\theta)z=0 \] \[ x+(\cos\theta)y+(\sin\theta)z=0 \] \[ x-(\sin\theta)y-(\cos\theta)z=0 \]

Let \(f:[0,\infty)\to\mathbb{R}\) be defined by \[ f(x)=\frac{3x^2+4x+1}{x^2+3x+2}. \] Then the value of \((f^{-1})'(2)\) is:

Find the value of \[ \lim_{x\to\infty} \frac{\sqrt{x}} {\sqrt{x+\sqrt{x+\sqrt{x}}}} \]

Number of triplets of sets \((A,B,C)\) with \(A,B,C\subseteq \{1,2,3,\ldots,n\}\) such that \[ (A\cap B)\subseteq C\subseteq (A\cup B) \] is:

Find the value of determinant at \(x=2026\): \[ \begin{vmatrix} x & x+1 & x+3\\ x+1 & x+3 & x+6\\ x+3 & x+6 & x+10 \end{vmatrix} \]

Let \(a, b, c\) be non-zero number such that \(a+b+c\neq 0\) and \(4a-2b+c\neq 0\). If \(\alpha\) and \(\beta\) are the roots of quadratic equation \(ax^2+bx+c=0\), then which of the following equation has roots \(\dfrac{\alpha+2}{\alpha-1}\) and \(\dfrac{\beta+2}{\beta-1}\)?

From top of view point at height of \(80\,\text{m}\), the angles of depression of the top and bottom of a flag standing on the same plane are observed to be \(30^\circ\) and \(45^\circ\). Find the height of the flag.

A triangle has a vertex at \((1,2)\) and the midpoints of two sides through it are \((-1,1)\) and \((2,3)\). Find its area.

The eccentricity of ellipse whose centre at origin is \(\frac{1}{2}\). If one of its directrices is \(x=-4\), then equation of normal to it at \(\left(1,\frac{3}{2}\right)\) is:

If \(x,y\) are real numbers such that \[ 2^{x+\frac12}\times4^{y-\frac56} = 3^{x-\frac12}\times9^{y-\frac13}, \] then which of the following is true?

A die is rolled twice independently. Probability that either first die shows number no less than \(4\) or second die shows at least \(4\)?

Evaluate \[ \int_{0}^{\frac{\pi}{4}}\frac{dx}{\cos^4x}. \]

If \(f:[0,\infty)\to\mathbb R\), \[ f(x)=\frac{x^2-1}{x^2+1}, \] then find \[ \int_{-1}^{1}f^{-1}(y)\,dy. \]

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 \(a+b+c\).

Find the value of \[ \lim_{x\to 0}\frac{x^2+2\cos x-2}{x\sin 3x} \]

Find the area of the triangle in the right half plane formed by the lines \(x-y=0\) and \(x+y=0\), and which is tangent to the hyperbola \[ x^2-y^2=a^2. \]

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:

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?

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 \(x\).

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

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