List of top Mathematics Questions asked in AP EAPCET

If \( 0<x<1 \), then first negative term in the expansion of \( (1+x)^{\frac{47}{5}} \) is

Assertion (A): \( cos^{2}5^{\circ}+cos^{2}10^{\circ}+cos^{2}15^{\circ}+...+cos^{2}85^{\circ}=\frac{17}{2} \)
Reason (R): If \( A+B=90^{\circ} \), then \( cos^{2}A+cos^{2}B=1 \)
Then, which one of the following is True?

If \( sin~A=\frac{3}{5} \) and A lies in the second quadrant, then \( \frac{tan~A-sec~A}{cot~A+cosec~A}= \)

If \( C_{o},C_{1},C_{2},...,C_{n} \) represent the coefficients in the binomial expansion of \( (1+x)^{n} \), then \( C_{o}+\frac{c_{2}}{3}+\frac{c_{4}}{5}+\cdot\cdot\cdot+\frac{c_{16}}{17}= \)

If \( \cos x+\cos^{2}x=1 \) , then \( \sin^{6}x+3 \sin^{8}x+3 \sin^{10}x+\sin^{12}x= \)

If a and b are the greatest values of \( {}^{2n}C_{r} \) and \( {}^{(2n-1)}C_{r} \) respectively, then

If \( x^{5}+ax^{4}+b death^{3}+cx^{2}+5x+e=0 \) is a reciprocal equation of second kind such that \( a+b=4 \) then the number of complex roots of this equation is

A student has to answer 10 out of 13 questions in an examination choosing atleast 3 from the 5 particular questions. The number of choices available to the student is

If all the letters of the word MESSI are permuted in all possible ways and the words [with or without meaning] thus formed are arranged in dictionary order, then the rank of the word MESSI is

The equation formed with the roots obtained by diminishing the roots of the equation \( x^{4}+3x^{3}-7x^{2}+4x+1=0 \) by 'h', does not contain the \( x^{2} \) term. If the possible values of such 'h' are \( h_{1}<0 \) and \( h_{2}>0, \) then which one of the following is true?

If \( z_{1}=x+iy \), \( z_{2}=a+ib \) and \( x^{2}+y^{2}=a^{2}+b^{2} \), then \( z_{2} = \)

If \( a, b, c \in \mathbb{R} \) and \( -a^{2}x^{2}+bx+c>0 \quad \forall x \in \left(\frac{3-\sqrt{14}}{2},\frac{3+\sqrt{14}}{2}\right) \), then \( c^{2}-\left(\frac{b}{4}\right)^{2} = \)

For a quadratic expression \( ax^{2}+bx+c \), if the minimum value \( \frac{49}{12} \) exists at \( x=\frac{-5}{6} \), then \( 12c-5b = \)

If \( z=(1+\sqrt{3}i)^{4/3} \), then the product of all the values of \( z \) is

The locus of \( |z-2i|+|z+4i|=10 \) is

Let \( A, B \) be \( 3^{\text{rd}} \) order non-singular square matrices and \( K \) is a real number. Which of the following is true?

The expression \( \frac{n(n + 1)^2(n+2)}{12} \) for all \( n \in \mathbb{N} \) is always:

If \( A=\begin{bmatrix}1&-2&2\\ 2&1&-2\\ 2&K&4\end{bmatrix} \), \( B=\begin{bmatrix}2&4&3\\ 3&4&5\\ 1&2&2\end{bmatrix} \) and \( \text{Rank}(A)=2 \), then \( K + \text{Rank}(B) = \)

The augmented matrix of a non-homogeneous system of equations \( AX = B \) is reduced to the following form after applying a series of elementary row transformations: \[ \begin{bmatrix}1&1&1&5\\ 0&0&-3&4\\ 0&0&\mu+1&\lambda^{2}-2\lambda+1\end{bmatrix} \] Then, which of the following is correct?

The domain of the real valued function \( f(x)=\log_{x-1}(3x+1) \) is

If \( f:A\rightarrow B \), \( g:B\rightarrow C \) are two functions such that \( gof: A\rightarrow C \) is an onto function, then it is necessary that

At a point $P(x,y)$ on a curve $x=f(y)$, the x-intercept of the tangent is always equal to the y-coordinate of the point of contact, then $f(y)=$

If $f(x)=\left|\frac{x}{3}-3^{-x}\right|$ and $\int_{0}^{5}f(x)dx=K+\frac{3^{n}+1}{3^{5}\log 3}$, then $nK=$

_n=1^_0^1x^3(1-x^2)^ndx=

If $y=f(x)$ is a solution of $\frac{dy}{dx}=(y-kx)^{2}+K$ when $x=0$ and $y=1$, then $f(2)=$