List of top Mathematics Questions asked in NIMCET

A computer producing factory has only two plants \(T_1\) and \(T_2\). Plant \(T_1\) produces 20% and plant \(T_2\) produces 80% of total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that \( P(\text{computer turns out to be defective given that it is produced in plant } T_1) = 10P(\text{computer turns out to be defective given that it is produced in plant } T_2)\), where \( P(E) \) denotes the probability of an event \(E\). A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant \(T_2\) is

A real valued function \( f \) is defined as \[ f(x) = \begin{cases} -1 & \text{if} \, -2 \leq x \leq 0 \\ x - 1 & \text{if} \, 0 \leq x \leq 2 \end{cases} \] \(\text{Which of the following statements is FALSE?}\)

If \( f(x) \) is a polynomial of degree 4, \( f(n) = n + 1 \) and \( f(0) = 25 \), then find \( f(5) \)?
If the volume of the parallelepiped whose adjacent edges are \( \vec{a} = 2\hat{i} + 3\hat{j} + 4\hat{k} \), \( \vec{b} = \hat{i} + \alpha\hat{j} + 2\hat{k} \), \( \vec{c} = \hat{i} + 2\hat{j} + \alpha\hat{k} \) is 15, then \( \alpha \) is equal to
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
Coordinate of focus of the parabola \(4y^2 + 12x - 20y + 67 = 0\) is
The eccentricity of an ellipse, with its center at the origin is \( \frac{1}{3} \). If one of the directrices is \( x = 9 \), then the equation of ellipse 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 value of \( 3^{3-\log_3 5} \) is
A four-digit number is formed using the digits 1, 2, 3, 4, 5 without repetition. The probability that is divisible by 3 is
The value of \( \cot(\csc^{-1}\frac{5}{3} + \tan^{-1}\frac{2}{3}) \) is
If the angle of elevation of the top of a hill from each of the vertices A, B and C of a horizontal triangle is \( \alpha \), then the height of the hill is
The function \( f(x) = \log(x + \sqrt{x^2 + 1}) \) is
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

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
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)
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?

The function \( f(x) = \begin{cases} (1+2x)^{1/x}, & x \neq 0 \\ e^2, & x=0 \end{cases} \) is
 

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively is
Area of the parallelogram formed by the lines \( y = 4x, y = 4x + 1, x + y = 0 \) and \( x + y = 1 \) is
The area enclosed within the curve \( |x| + |y| = 2 \) is
If \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) (\( a > b \)) and \( x^2 - y^2 = c^2 \) cut at right angles, then
Angles of elevation of the top of a tower from three points (collinear) A, B and C on a road leading to the foot of the tower are 30\(^{\circ}\), 45\(^{\circ}\) and 60\(^{\circ}\) respectively. The ratio of AB and BC is
Solutions of the equation \( \tan^{-1}\sqrt{x^2+x} + \sin^{-1}\sqrt{x^2+x+1} = \frac{\pi}{2} \) are