List of top Questions asked in AP EAPCET- 2022

In a set of \(30\) game cards, \(17\) are white and the rest are green. Out of \(30\), \(4\) white and \(5\) green are marked IMPORTANT. If a card is chosen randomly from this set, the possibility of choosing a green card or an IMPORTANT card is:

Suppose that a book of 600 pages contains 40 print mistakes. Assume that these errors are randomly distributed throughout the book and the number of errors per page follows a Poisson distribution. The probability that all the 10 pages selected at random will have no print mistakes is:

If \(A\) and \(B\) are two independent events such that \(P(A)=0.3\), \(P(B)=x\), and \(P(A\cup B)=0.44\), then \(x=\)

The maximum value of the variance of Binomial distribution with parameters \(n\) and \(p\) is:

In a toy factory, the machines \(A\), \(B\), and \(C\) are used to manufacture \(30\%\), \(40\%\), and \(30\%\) of the output, respectively. The probabilities of toys made by machines \(A\), \(B\), and \(C\) to be defective are respectively \(2\%\), \(3\%\), and \(1\%\). A toy is taken from the factory and is found to be defective. The probability that it was manufactured by machine \(B\) is

If a number is chosen at random from the set \[ \{1,2,3,\ldots,100\}, \] then the probability that the chosen number is a perfect cube is:

Two vertices of a triangle are at \(-\hat{i}+3\hat{j}\) and \(2\hat{i}+5\hat{j}\), and its orthocenter is at \(\hat{i}+2\hat{j}\). If the position vector of the \(3^{rd}\) vertex is \(a\hat{i}+b\hat{j}\), then \((a,b)=\)

If \(3\) vectors \(\overline{a},\overline{b},\overline{c}\) are such that \(\overline{a}\neq \overline{0}\) and \(\overline{a}\times \overline{b}=2(\overline{a}\times \overline{c})\), \(|\overline{a}|=1\), \(|\overline{c}|=1\), \(|\overline{b}|=4\), and angle between \(\overline{b}\) and \(\overline{c}\) is \(\cos^{-1}\left(\dfrac{1}{4}\right)\) and \(\overline{b}-2\overline{c}=\lambda \overline{a}\), then \(\lambda=\)

\(\overline{a}\), \(\overline{b}\) are non-collinear vectors, \(|\overline{a}|=2\sqrt{2}\), \(|\overline{b}|=3\), and the angle between \(\overline{a}\) and \(\overline{b}\) is \(45^\circ\). Then the lengths of the diagonals of the parallelogram whose adjacent sides are represented by the vectors \(5\overline{a}+2\overline{b}\) and \(\overline{a}-3\overline{b}\) are

PQRS is a quadrilateral and \(\overrightarrow{PQ}=\vec a\), \(\overrightarrow{QR}=\vec b\), \(\overrightarrow{SP}=\vec a-\vec b\). M is the midpoint of \(QR\) and X is a point on \(SM\) such that \[ \overrightarrow{SX}=\frac{4}{5}\overrightarrow{SM} \] If \[ \overrightarrow{SM}=m(4\vec a-\vec b) \] and \[ \overrightarrow{SX}=n(4\vec a-\vec b), \] then \(m+n=\)

If \(C\) is the midpoint of the line segment \(AB\) and \(P\) is any point outside the line \(AB\), then:

The range of the data \(35, 12, 21, 24, 15, 7, 16, 12, 30, 32, 13, 17\) is:

In a triangle \(ABC\), if \(a=2\), \(b=3\), and \(\sin A=\dfrac{2}{3}\), then \(\angle B=\)

In a \(\triangle ABC\), \(a:b:c=4:5:6\). The ratio of the radius of the circumcircle to that of the incircle is:

The value of \[ \sin(x+y)\sec x\sec y \] is

If \[ \sin\left(x+\frac{\pi}{3}\right)+\sin\left(x-\frac{\pi}{3}\right)=1, \] then the value of \(x\) in the interval \([0,\pi]\) is

The sides of a triangle \(ABC\) are given by \(a=3\), \(b=5\), and \(c=3\). Then \(\cos A=\)

If \(\cosh(x-\log 3)=\sinh x\), then \(x=\)

In \(\triangle ABC\), if \[ 3\sin A+4\cos B=6 \] and \[ 4\sin B+3\cos A=1, \] then the angle \(C\) is

Let \(P_1,P_2,\ldots,P_{15}\) be \(15\) points on a circle. The number of distinct triangles formed by points \(P_i,P_j,P_k\) such that \(i+j+k\neq 15\), is

If \[ \frac{4x^3+16x+7}{(x^2+4)^2} = \frac{Ax+B}{x^2+4} + \frac{Cx+D}{(x^2+4)^2}, \] then the number of non-zero values in \(A,B,C,D\) is

The value of \[ 1+\cot^2 30^\circ-\sec^2 45^\circ \] is

The smallest integer \(n\) such that \[ \frac{1}{\sin45^\circ\sin46^\circ} + \frac{1}{\sin47^\circ\sin48^\circ} +\cdots+ \frac{1}{\sin133^\circ\sin134^\circ} = \frac{1}{\sin(n^\circ)} \] is

What is the sum of the first \(n\)-terms of the series, whose \(k\)-term is \(k!\times k\)?

If \[ {}^nC_{r-1}=36,\qquad {}^nC_r=84,\qquad {}^nC_{r+1}=126, \] then the value of \(nr^2\) is