List of top Mathematics Questions

If \[ f(x)=|x-2|+|x+1|, \] then the minimum value of \(f(x)\) is:

If the coefficients of the first, second, and third terms in the expansion of \( (1+x)^n \) are in the ratio \(1:20:190\), then \(n\) is equal to:

If the coefficient of \(x^2\) in the expansion of \[ (1+x)^5(1-x)^4 \] is \(k\), then \(k\) is equal to:

If \[ \log_2(x-1)+\log_2(x+1)=3, \] then \(x\) is equal to:

If \(5\) is the remainder when \[ 2x^5+kx^4+5x^3-3x^2+2x-1 \] is divided by \[ x^2+x+1, \] then the quotient is:

The number of integers that satisfy both the inequalities \[ x^2-2x+8>0 \] and \[ x^2-3x+2\le 0 \] is:

The number of arrangements of the letters of the word SEARCH such that no letter remains in its original position is:

2 is a zero of the polynomial function \[ f(x)=x^4+kx^3+22x^2-6x-20. \] If \(-2,\alpha,\beta\) are the roots of the equation \[ x^3+3x^2+2kx-40=0 \] and \(\alpha<\beta\), then \(2\alpha+3\beta=\)

If \[ {}^{n}P_{4}=5040 \] and \[ {}^{15}P_{r}=2730, \] then the value of \(n+r\) is:

If \[ z=\frac{(1-i)^3}{(\sqrt{3}-i)^2}, \] then the complex conjugate of \(z\) is:

Let \(\alpha\) and \(\beta\) be the roots of \[ x^2+bx+c=0. \] If \[ \alpha^2+\beta^2=14 \] and \[ \alpha\beta=3, \] then the value of \(b^2\) is:

Let \(A\) be a \(3\times3\) matrix such that \[ AA^{T}=I_3. \] Then \(A\) is:

If \[ \cos\alpha+\cos\beta+\cos\gamma=0 \] and \[ \sin\alpha+\sin\beta+\sin\gamma=0, \] then which of the following is true?

The locus of the point \(z=x+iy\) satisfying \[ \left|\frac{z-(2+i)}{z+(2-i)}\right|=2 \] is:

If \[ a_n= \sqrt{7+\sqrt{7+\sqrt{7+\cdots}}} \] (\(n\) radicals), then which of the following is true?

Let \(f,g,h\) be differentiable functions such that \[ \begin{vmatrix} f(x) & g(x) & h(x)\\ f'(x) & g'(x) & h'(x)\\ f''(x) & g''(x) & h''(x) \end{vmatrix} =0. \] Then which of the following statements is correct?

Consider the system of linear equations \[ x+y+z=6, \] \[ x+2y+3z=10, \] \[ 3x+2y+\lambda z=\mu. \] If the system has infinitely many solutions, then the value of \(\mu+\lambda\) is:

The function \[ f(x)=\sin\left(\log\left(x+\sqrt{x^2+1}\right)\right) \] is

The domain of the real-valued function \[ f(x)=\cos^{-1}\left(\frac{2-x}{4}\right)+[\log(3-x)]^{-1} \] is:

The mean of 12 observations was calculated as 28. Later, it was found that one observation was wrongly recorded as 46 instead of 26, and another observation was completely omitted. If the correct mean is 27, find the value of the omitted observation.

\(24\left(\sin^2 60^\circ + \cos^2 30^\circ + \cot^2 60^\circ + \csc^2 45^\circ\right) =\)

A bag contains 3 red, 4 blue and 3 green balls. A ball is drawn at random. Event E represents `not drawing a blue ball'. Then find the probability of \(\bar{E}\) (complementary event of E).

Read the following statements and choose the correct option.
Assertion (A): If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Reason (R): In a parallelogram, diagonals bisect each other.

If the centroid of the triangle ABC with vertices A(5,-4), B(7,8) and C(a,b) is G(7,6), then (b-a) is

Find the value of 45^ 30^ + 60^ 45^ - 5 90^2 0^