List of top Questions asked in NIMCET

If \( 8^{x-1} = \left( \frac{1}{4} \right)^x \), then the value of \[ \frac{1}{\log_{x+14} x - \log_{x+15}} \div \frac{1}{\log_{1-x} 4 - \log_{1-x} 5} \] is

The number of accidents per week in a town follows a Poisson distribution with mean 2. If the probability that there are three accidents in two weeks time is \( k e^{-6} \), then the value of \( k \) is:

Ten years ago, Ram was twice as old as Shyam. Ten years from now, the ratio of their ages will be 3:2. What is Ram's present age?

If a number is increased by 30% and then decreased by 20%, what is the net change?

Debugger is a program that

A sum of money was divided into 2 parts in the ratio 2:5. The first part was invested for 2 years at the annual interest rate of 20% compounded annually. At what rate of simple interest per annum the second part must be invested for 2 years so that the interest earned in both cases is the same?

If \( B = \sin^2y + \cos^4y \), then for all real \( y \),

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships as 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is

The value of the integral \[ \int_0^{\frac{\pi}{2}} \frac{1 + 2 \cos x}{(2 + \cos x)^2} \, dx \] lies in the interval:

Statements: 1. All cakes are ice cream 2. No ice cream is chocolate

Conclusions: 1. Some cakes are chocolate 2. No cake is chocolate Choose the correct option:

Let \( A = (1, 2, 3, \dots, 20) \). Let \( R \subseteq A \times A \) such that \( R = \{(x, y) : y = 2x - 7 \} \). Then the number of elements in \( R \) is equal to:

Which of the following is the CORRECT truth table for the XOR gate with two binary inputs A and B?

The slope of the normal line to the curve \( x = t^2 + 3t - 8 \) and \( y = t^2 - 2t - 5 \) at the point \( (2, -1) \) is

Dynamic RAM (DRAM) stores each bit of data in a separate capacitor. Due to leakage, the stored charge tends to dissipate over time and needs to be refreshed periodically. Consider the following statements: \[\begin{array}{rl} \bullet & \text{P: DRAM requires refreshing because it uses capacitors to store bits.} \\ \bullet & \text{Q: SRAM does not require refreshing because it uses flip-flops instead of capacitors.} \\ \bullet & \text{R: DRAM is faster than SRAM because it needs less frequent access.} \\ \bullet & \text{S: DRAM is more suitable for main memory than SRAM due to its density.} \\ \end{array}\]

Consider the sample space \( \Omega = \{(x, y): x, y \in \{1, 2, 3, 4\} \} \) where each outcome is equally likely. Let \( A = \{ x \geq 2 \} \) and \( B = \{ y > x \} \) be two events. Then which of the following is NOT true?

Let \( A \) and \( B \) be two square matrices of the same order satisfying \( A^2 + 5A + 5I = 0 \) and \( B^2 + 3B + I = 0 \) respectively, where \( I \) is the identity matrix. Then the inverse of the matrix \( C = BA + 2B - 2A + 4I \) is:

Let \( g: \mathbb{R} \to \mathbb{R} \) and \( h: \mathbb{R} \to \mathbb{R} \) be two functions such that \( h(x) = s \cdot g \cdot n(g(x)) \), where \( \mathbb{R} \) denotes the set of all real numbers and \( s \) and \( n \) stand for the signum and the sine functions respectively. Then, select which of the following is not true?

Which of the following statements about ASCII and Unicode is correct?

Let \( \mathbf{a} = e\hat{i} + 3\hat{j} + 4\hat{k}, \mathbf{b} = \hat{i} + 2\hat{j} - \hat{k}, \mathbf{c} = 3\hat{i} + \hat{j} + \lambda \hat{k} \) be the co-terminal edges of a parallelepiped whose volume is 5 units. Then the value of \( \lambda \) is:

A remote island has a unique social structure. Individuals are either "Truth-tellers" (who always speak the truth) or "Tricksters" (who always lie). You encounter three inhabitants: X, Y, and Z.

X says: "Y is a Trickster"
Y says: "Exactly one of us is a Truth-teller."
What can you definitively conclude about Z?

In computer architecture, which of the following correctly matches the fundamental unit used in the CPU, cache, and main memory respectively?

What is the equivalent decimal value of the unsigned binary number 10101.10101?

A person walks 8 km north, turns right, walks 4 km, turns right again and walks 6 km. Finally, he turns left and walks 3 km. How far is he from the starting point?

What is the hexadecimal representation of the decimal number 265?

Given the equations \( x + y = 1 \), \( x^2 + y^2 = 2 \), \( x^5 + y^5 = A \). Let N be the number of solution pairs \( (x, y) \) to this system of equations. Then \( N \) is equal to: