List of top Questions asked in NIMCET- 2023

Let \( R \) be a reflexive relation on the finite set \( A \) having 10 elements and if \( m \) is the number of ordered pairs in \( R \), then
The coefficient of \( x^{50} \) in the expression of \[ (1 + x)^{1000} + 2x(1 + x)^{999} + 3x^2(1 + x)^{998} + \ldots + 1001x^{1000} \]

Statement: No table is a chair. Not a single chair is a stand. Every stand is a statue. 

Conclusion: 1. Some statues which are stands are tables as well. 2. Some statues are not chairs.

Fill the blanks with the most appropriate combination of options.
Further, to augment bond market liquidity, corporates need to be encouraged to __________ exiting bonds under the same International Securities Identification Number, to duly shore up floating __________.

Find a number from the given options which best completes the series: 39, 416, 525, \(\dots\), 749, 864 
 

Identify the next two numbers in the following sequence: 17, 20, 9, 12, 5, 6, 3, 2, ?, ?
Book : Publisher :: Film : ?
Yamini has at least two sisters younger than her, Rakhi, Pooja, Yamini, and Sweta are four sisters. Pooja is younger than Rakhi who is not oldest. Sweta is older than Pooja but younger than Rakhi, then who is the oldest among them?
Complete the series: 3, 10, 24, 45, 73, ......
Statements:
Statement I: At most teachers are boys.
Statement II: Some boys are students.
Conclusion:
I. Some teachers are students.
II. Some students are boys.
The sum of infinite terms of a decreasing GP is equal to the greatest value of the function \( f(x) = x^3 + 3x - 9 \) in the interval \([-2, 3]\), and the difference between the first two terms is \( f'(0) \). Then the common ratio of the GP is:
If \(a\), \(b\), \(c\), and \(d\) are in HP and the arithmetic mean of \(ab\), \(bc\), and \(cd\) is 9, then which of the following is the value of \(ad\)?
Thirty-six vehicles are parked in a parking lot in a single row. After the first car, there is one scooter. After the second car, there are two scooters. After the third car, there are three scooters and so on. Work out the number of scooters in the second half row.
Pointing towards a person in the photograph, Anjali said, "He is the only son of the father of my sister's brother". How is that person related to Anjali?
Deepa moved a distance of 75 meters towards the north. She then turned left again and walked 80 meters. Finally, she turned to the right at an angle of 45°. In which direction was she moving finally?
Two friends A and B were standing at the diagonally opposite corners of a rectangular plot whose perimeter is 100m. A first walked x meters along the length of the plot towards East and then y meters towards the South. B walked x meters along the breadth towards North and then y meters towards West. At the end of their walks, A and B were standing at the diagonally opposite corners of a smaller rectangular plot whose perimeter is 40m. How much distance did A walk?
If yellow is called white, white is called black, black is called green, green is called pink, pink is called blue, and blue is called water, what is the color of the sky?
For security reasons, a bank manager decided to encrypt the account number in the server. If A/C No. 46873 is coded as 91317157, then 52191 is coded as:
If DENMARK is coded as FCPKCPM, then code SINGAPORE of which option?
If the word IMPACT is coded as RNKZXG, then which of the following represents the code for the word DESCEND?
The perimeter of a triangle \( \triangle ABC \) is 6 times the arithmetic mean of the sines of its angles. If the side \( a \) is 1, then the angle \( A \) is:
For a group of 100 candidates, the mean and standard deviation of scores were found to be 40 and 15 respectively. Later on, it was found that the scores 25 and 35 were misread as 52 and 53 respectively. Then the corrected mean and standard deviation corresponding to the corrected figures are
The equation of the tangent at any point of the curve \[ x = a \cos 2t, \, y = 2 \sqrt{2a} \sin t \, \text{with} \, m \, \text{as its slope is} \]
If \[ \prod_{i=1}^{n} \tan (\alpha_i) = 1 \forall \alpha_i \in \left[0, \frac{\pi}{2}\right] \text{where} i = 1, 2, 3, \dots, n. \] Then the maximum value of \[ \prod_{i=1}^{n} \sin (\alpha_i) \] is

Let \( \mathbf{A} = 2\hat{i} + \hat{j} - 2\hat{k} \) and \( \mathbf{B} = \hat{i} + \hat{j} \). If \( \mathbf{C} \) is a vector such that \( |\mathbf{C} - \mathbf{A}| = 3 \) and the angle between \( \mathbf{A} \times \mathbf{B} \) and \( \mathbf{C} \) is \( 30^\circ \), then \( [(\mathbf{A} \times \mathbf{B}) \times \mathbf{C}] = 3 \), the value of \( \mathbf{A} \cdot \mathbf{C} \) is equal to: