List of top Questions asked in AP EAPCET

If \[ A= \begin{bmatrix} 1&2\\ 3&4 \end{bmatrix}, \] then \(\det(A)\) is equal to:

If \[ z=\cos\theta+i\sin\theta, \] then \(|z|\) is equal to:

The distance between the points \[ (1,2) \quad \text{and} \quad (4,6) \] is:

If the arithmetic mean of the numbers \[ 2,4,6,\ldots,2n \] is \(\frac{7}{4}\), then \(n\) is equal to:

If \[ x+\frac1x=3, \] then the value of \[ x^2+\frac1{x^2} \] is:

If \[ \sin\theta+\cos\theta=1, \] then the value of \[ \sin\theta\cos\theta \] is:

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

If \[ \log_2(x-1)+\log_2(x+1)=3, \] then \(x\) 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 \(\alpha,\beta\) are the roots of the quadratic equation \[ x^2-3x+1=0, \] then the value of \(\alpha^3+\beta^3\) 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:

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 \(2\alpha+3\beta=\)

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:

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

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:

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:

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

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

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

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

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

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

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?