List of practice Questions

The coefficient of \( x^3 \) in the power series expansion of \( \frac{1+4x-3x^2}{(1+3x)^3 \) is}
The terms containing \( x^r y^s \) (for certain r and s) are present in both the expansions of \( (x+y^2)^{13 \) and \( (x^2+y)^{14} \). If \( \alpha \) is the number of such terms, then the sum \( \sum_{r,s} \alpha (r+s) = \) (Note: The sum is over the common terms)}
If four letters are chosen from the letters of the word ASSIGNMENT and are arranged in all possible ways to form 4 letter words (with or without meaning), then total number of such words that can be formed is
Let 'a' be a non-zero real number. If the equation whose roots are the squares of the roots of the cubic equation \( x^3 - ax^2 + ax - 1 = 0 \) is identical with this cubic equation, then 'a' =
When the roots of \( x^3 + \alpha x^2 + \beta x + 6 = 0 \) are increased by 1, if one of the resultant values is the least root of \( x^4 - 6x^3 + 11x^2 - 6x = 0 \), then
If \( {}^{27}P_{r+7} = 7722 \cdot {}^{25}P_{r+4} \), then r =
If \( x^6 = (\sqrt{3}-i)^5 \), then the product of all of its roots is
The points in the Argand plane represented by the complex numbers \(4\hat{i}+3\hat{j}\), \(6\hat{i}-2\hat{j}-3\hat{k}\) and \(\hat{i}-\hat{j}-3\hat{k}\) form
If \( \alpha \neq 0 \) and zero are the roots of the equation \( x^2 - 5kx + (6k^2-2k) = 0 \), then \( \alpha = \)
If \( z = x+iy \) and \(x^2+y^2=1\), then \( \frac{1+x+iy}{1+x-iy} = \)
The number of solutions of the system of equations \(2x+y-z=7\), \(x-3y+2z=1\), \(x+4y-3z=5\) is
The set of all real values of x satisfying the inequation \( \frac{8x^2-14x-9}{3x^2-7x-6}>2 \) is
If \( A = \begin{pmatrix} 1 & 2 & 3 \\ 1 & 3 & 5 \\ 2 & 1 & 6 \end{pmatrix} \) and \( |adj(adj(A))|(adj A)^{-1} = kA \), then k =
If the values \( x = \alpha, y = \beta, z = \gamma \) satisfy all the 3 equations \(x+2y+3z=4\), \(3x+y+z=3\) and \(x+3y+3z=2\), then \(3\alpha + \gamma = \)
\( \sum_{k=1}^{n} k(k+1)(k+2)...(k+r-1) = \)
\(f(x)\) is a quadratic polynomial satisfying the condition \( f(x) + f\left(\frac{1}{x}\right) = f(x)f\left(\frac{1}{x}\right) \). If \(f(-1)=0\), then the range of \(f\) is
The set of all real values of \(x\) for which \(f(x) = \sqrt{\frac{|x|-2}{|x|-3}}\) is a well defined function is

What is the angle between the hour and minute hands at 4:30?

आप नव्या / भव्य हैं। आपने पुस्तकालय विज्ञान में स्नातक डिग्री (बी.लिब.) प्राप्त की है। आपके क्षेत्र के सार्वजनिक पुस्तकालय में पुस्तकालय अध्यक्ष का पद रिक्त है। उक्त पद के लिए आवेदन हेतु लगभग 80 शब्दों में अपना एक स्ववृत्त तैयार कीजिए।

Who is the current Chief Justice of India in 2025?
Which global event in 2024 significantly impacted international climate policies?

Which Indian state launched the ‘Mukhyamantri Majhi Ladki Bahin Yojana’ in 2024 to empower women?

A contract is voidable if it is entered into under:

Principle: A person is liable for the tort of negligence if they fail to exercise reasonable care, causing harm to another. 
Facts: Ram, a driver, was driving at 80 km/h in a residential area with a speed limit of 40 km/h. He hits a pedestrian, Shyam, causing injury. Is Ram liable?

A Hydrocarbon which does not belong to the same homologous series of carbon compounds is: