List of top Mathematics Questions asked in AP EAPCET

A basket contains 5 apples and 7 oranges, and another basket contains 4 apples and 8 oranges. If one fruit is picked out at random from each basket, then the probability of getting one apple and one orange is
In a school there are 3 sections A, B, and C. Section A contains 20 girls and 30 boys, section B contains 40 girls and 20 boys, and section C contains 10 girls and 30 boys. The probabilities of selecting section A, B, and C are 0.2, 0.3, and 0.5, respectively. If a student selected at random from the school is a girl, then the probability that she belongs to section A is
Two cards are drawn from a pack of 52 playing cards one after the other without replacement. If the first card drawn is a queen, then the probability of getting a face card from a black suit in the second draw is
In a right-angled triangle, if the position vector of the vertex having the right angle is $-3\mathbf{i} + 5\mathbf{j} + 2\mathbf{k}$ and the position vector of the midpoint of its hypotenuse is $6\mathbf{i} + 2\mathbf{j} + 5\mathbf{k}$, then the position vector of its centroid is
If the position vectors of the vertices A, B, C of a triangle are $3\mathbf{i} + 4\mathbf{j} - \mathbf{k}$, $\mathbf{i} + 3\mathbf{j} + \mathbf{k}$, and $5(\mathbf{i} + \mathbf{j} + \mathbf{k})$ respectively, then the magnitude of the altitude drawn from A onto the side BC is
If the vectors $2\mathbf{i} + 4\mathbf{j} - 3\mathbf{k}$, $-\mathbf{i} + 2\mathbf{j} + 3\mathbf{k}$, and $p\mathbf{i} - 2\mathbf{j} + \mathbf{k}$ are coplanar, then the unit vector in the direction of the vector $9p\mathbf{i} - 4\mathbf{j} + 4\mathbf{k}$ is
Assertion (A): For the lines $\mathbf{r} = \mathbf{a} + t \mathbf{b}$ and $\mathbf{r} = \mathbf{p} + s \mathbf{q}$, if $(\mathbf{a} - \mathbf{p}) \cdot (\mathbf{b} \times \mathbf{q}) \neq 0$, then the two lines are coplanar. Reason (R): $|(\mathbf{a} - \mathbf{p}) \cdot (\mathbf{b} \times \mathbf{q})|$ is $|\mathbf{b} \times \mathbf{q}|$ times the shortest distance between the lines $\mathbf{r} = \mathbf{a} + t \mathbf{b}$ and $\mathbf{r} = \mathbf{p} + s \mathbf{q}$.
In a triangle ABC, if $a, b, c$ are in arithmetic progression and the angle $A$ is twice the angle $C$, then $\cos A : \cos B : \cos C =$
In a triangle ABC, if A, B, and C are in arithmetic progression, $r_3 = r_1 r_2$, and $c = 10$, then $a^2 + b^2 + c^2 =$
In a $\triangle ABC$, $\frac{2(r_1 + r_3)}{a c (1 + \cos B)} =$
If $\frac{3x^2 - 7x + 1}{(x - 2)^3} = \frac{A}{x - 2} + \frac{B}{(x - 2)^2} + \frac{C}{(x - 2)^3}$, then $A(B + C + D + E) =$
If $\cot(\cos^{-1} x) = \sec\left(\tan^{-1}\left(\frac{a}{\sqrt{b^2 - a^2}}\right)\right)$, $b>a$, then $x =$
$\cos(13^\circ)\sin(17^\circ)\sin(21^\circ)\cos(47^\circ) =$
$\sin\left(\frac{\pi}{5}\right) + \sin\left(\frac{2\pi}{5}\right) + \sin\left(\frac{3\pi}{5}\right) + \sin\left(\frac{4\pi}{5}\right) =$
The sum of the solutions of $\cos x \sqrt{16 \sin^2 x} = 1$ in $(0, 2\pi)$ is
The number of integers between 10 and 10,000 such that in every integer every digit is greater than its immediate preceding digit, is
If $y = \frac{3}{4} + \frac{3 \cdot 5}{4 \cdot 8} + \frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12} + ... \infty$, then
Sum of the coefficients of $x^4$ and $x^6$ in the expansion of $(1 + x - x^2)^6$ is
The number of ways in which a cricket team of 11 members can be formed out of 6 batsmen, 6 bowlers, 4 all-rounders, and 4 wicket-keepers by selecting at least 4 batsmen, at least 3 bowlers, at least 2 all-rounders, and only one wicket-keeper is
All letters of the word `AGAIN' are permuted in all possible ways, and the words so formed (with or without meaning) are written as in a dictionary. Then the $50^{th}$ word is
If $\alpha$, $\beta$, and $\gamma$ are the roots of the equation $2x^3 + 3x^2 - 5x - 7 = 0$, then $\frac{1}{\alpha^2} + \frac{1}{\beta^2} + \frac{1}{\gamma^2} =$
The set of all real values of $x$ for which $\frac{x^2-1}{(x-4)(x-3)} \ge 1$ is
If the order and degree of the differential equation \(x \frac{d^2 y}{dx^2} = \left(1 + \left(\frac{d^2 y}{dx^2}\right)^2\right)^{-1/2}\) are \(k\) and \(l\) respectively, then \(k, l\) are the roots of
The general solution of the differential equation \( \left(x - (x + y)\log(x + y)\right) dx + x\,dy = 0 \) is:
The equation of the curve passing through the point \( (0, \pi) \) and satisfying the differential equation \( ydx = (x + y^3 \cos y)dy \) is