List of top Mathematics Questions asked in NIMCET

The maximum value of \( f(x) = (x - 1)^2 (x + 1)^3 \) is equal to \[ \frac{2^p 3^q}{3125} \,\, \text{then the ordered pair of} (p, q) \text{ will be} \]

If A and B are square matrices such that \( B = -A^{-1}BA \), \(\text{ then }\) \( (A + B)^2 \) is

If \( f(x) \) is a polynomial of degree 4, \( f(n) = n + 1 \) and \( f(0) = 25 \), then find \( f(5) \)?
A survey is done among a population of 200 people who like either tea or coffee. It is found that 60% of the population like tea and 72% of the population like coffee. Let x be the number of people who like both tea & coffee. Let \( m \leq x \leq n \), then choose the correct option.
There are two sets A and B with \( |A| = m \) and \( |B| = n \). If \( |P(A)| - |P(B)| = 112 \) then choose the wrong option (where \( |A| \) denotes the cardinality of A, and P(A) denotes the power set of A)
If \( a_1, a_2, \ldots, a_n \) are in Arithmetic Progression with common difference d, then the sum \( (\sin d) (\csc a_1 \csc a_2 + \csc a_2 \csc a_3 + \dots + \csc a_{n-1} \csc a_n) \) is equal to
Which term of the series \( \frac{\sqrt{3}}{9}, \frac{1}{3\sqrt{3}}, \frac{1}{9}, \ldots \) is \( \frac{1}{2187} \)?
In a Harmonic Progression, pth term is q and the qth term is p. Then pqth term is
The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively is
The 10th and 50th percentiles of the observation 32, 49, 23, 29, 118 respectively are
The first three moments of a distribution about 2 are 1, 16, -40 respectively. The mean and variance of the distribution are
If \( \alpha, \beta \) are the roots of \( x^2 - x - 1 = 0 \), and \( A_n = \alpha^n + \beta^n \), then Arithmetic mean of \( A_{n-1} \) and \( A_n \) is
The value of \( 3^{3-\log_3 5} \) is

If \( (\vec{a} \times \vec{b}) \times \vec{c} = \vec{a} \times (\vec{b} \times \vec{c}) \), then
 

If \( \csc\theta - \cot\theta = 2 \), then the value of \( \csc\theta \) is
Let a, b, c be distinct non-negative numbers. If the vectors \( a\hat{i} + a\hat{j} + c\hat{k} \), \( \hat{i} + \hat{k} \) and \( c\hat{i} + c\hat{j} + b\hat{k} \) lie in a plane, then c is
Suppose that the temperature at a point (x, y) on a metal plate is \( T(x, y) = 4x^2 - 4xy + y^2 \). An ant, walking on the plate, traverses a circle of radius 5 centered at the origin. What is the highest temperature encountered by the ant?

If \( x^m y^n = (x+y)^{m+n} \), then \( \frac{dy}{dx} \) is
 

The domain of the function \( f(x) = \frac{\cos^{-1}x}{[x]} \) is
 

The mean of 25 observations was found to be 38. It was later discovered that 23 and 38 were misread as 25 and 36, then the mean is
If the foci of the ellipse \( \frac{x^2}{25} + \frac{y^2}{b^2} = 1 \) and the hyperbola \( \frac{x^2}{144} - \frac{y^2}{81} = \frac{1}{25} \) are coincide, then the value of \( b^2 \) is
Let a be the distance between the lines \( -2x + y = 2 \) and \( 2x - y = 2 \), and b be the distance between the lines \( 4x - 3y = 5 \) and \( 6y - 8x = 1 \), then
Coordinate of focus of the parabola \(4y^2 + 12x - 20y + 67 = 0\) is
If the roots of the quadratic equation \( x^2 + px + q = 0 \) are tan 30\(^{\circ}\) and tan 15\(^{\circ}\) respectively, then the value of \( 2 + p - q \) is
The correct expression for \( \cos^{-1}(-x) \) is