List of practice Questions

Evaluate \[ (4 \cos^2 \frac{\pi}{20} - 1)(4 \cos^2 \frac{3\pi}{20} - 1)(4 \cos^2 \frac{5\pi}{20} - 1)(4 \cos^2 \frac{7\pi}{20} - 1)(4 \cos^2 \frac{9\pi}{20} - 1). \]
If $\cos 80^\circ + \cos 40^\circ - \cos 20^\circ = k$, then $\frac{4k}{3} =$
The number of integers greater than 6000 that can be formed by using the digits 0, 5, 6, 7, 8 and 9 without repetition is
Evaluate \[ \frac{1}{3 . 5} + \frac{1}{5 . 7} + \frac{1}{7 . 9} + .s \text{ up to } 24 \text{ terms}. \]
If B is the inverse of a third order matrix A and det B = k, then $(\text{adj}(\text{adj} A))^{-1}=$
If $A = \begin{bmatrix} 2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2 \end{bmatrix}$ and $\alpha, \beta, \gamma$ are the roots of the equation represented by $|A - xI| = 0$, then $\alpha^2 + \beta^2 + \gamma^2 =$
The product of the four values of the complex number $(1+i)^{3/4}$ is
Which of the following is NOT a characteristic of cloud computing?
In a turning operation, the cutting speed is 120 m/min, and the diameter of the workpiece is 50 mm. What is the spindle speed in RPM?
Which of the following materials is most suitable for high-temperature applications in gas turbines?
A 3-phase, 400 V, 50 Hz induction motor runs at 1440 RPM. If the synchronous speed is 1500 RPM, what is the slip?
In a series RLC circuit, R = 10 $\Omega$, L = 0.1 H, and C = 100 $\mu$F. What is the resonance frequency (in Hz)?
Which of the following is a key advantage of a PID controller in control systems?
Which of the following sorting algorithms has the best average-case time complexity?
In a relational database, a table has 5 attributes and 1000 records. If a query returns 200 records after applying a condition, what is the selectivity of the query?
If the efficiency of a machine is 80% and it consumes 500 W of power, what is the useful output power?
Which of the following methods is most suitable for the design of flexible pavements in high-traffic areas?
A Carnot engine operates between a hot reservoir at 800 K and a cold reservoir at 300 K. What is its maximum theoretical efficiency?
The Supreme Court’s judgment in the case of Kesavananda Bharati v. State of Kerala (1973) is associated with which doctrine?
Under which article of the Indian Constitution can the President of India impose President’s Rule in a state?
If the day after tomorrow is Wednesday, and today is Monday, what day will it be three days from now?
The river Godavari, significant for Telangana, originates in which state?
Which of the following is NOT a source of law in India?
Consider the following statements:
1. The power of Judicial Review is vested in the Supreme Court under Article 13 of the Indian Constitution.
2. The President of India can dissolve the Rajya Sabha under Article 108 of the Indian Constitution.
Which of the above statements is/are correct?
In 2024, the Supreme Court of India upheld the constitutional validity of which law related to personal laws, sparking widespread debate?