List of top Mathematics Questions asked in AP EAMCET

Statement (S1): $ \sin 55^\circ + \sin 53^\circ - \sin 19^\circ - \sin 17^\circ = \cos 2^\circ $
Statement (S2): The range of $ \frac{1}{3 - \cos 2x} $ is $ \left[ \frac{1}{4}, \frac{1}{2} \right] $ Which one of the following is correct?

In $\Delta ABC$ if $B = 90^\circ$ then $2(r + R) = $

In a triangle ABC, if $ (a-b)(s-c) = (b-c)(s-a) $, then $ r_1 + r_3 = $:

Let ABC be an equilateral triangle of side $a$. M and N are two points on the sides AB and AC respectively such that $AN = K \cdot AC$ and $AB = 3 \cdot AM$. If the vectors $BN$ and $CM$ are perpendicular, then $K = $ ?

Let a and b be two non-collinear vectors of unit modulus. If u = a − (a · b)b and v = a × b, then ∥v∥ = ?

Find the shortest distance between the skew lines $\vec{r} = (-\hat{i} - 2\hat{j} - 3\hat{k}) + t(3\hat{i} - 2\hat{j} - 2\hat{k})$ and $\vec{r} = (7\hat{i} + 4\hat{k}) + s(\hat{i} - 2\hat{j} + 2\hat{k})$.

If 7 different balls are distributed among 4 different boxes, then the probability that the first box contains 3 balls is:

Out of the first 5 consecutive natural numbers, if two different numbers x and y are chosen at random, then the probability that x⁴- y⁴is divisible by 5 is:

If two cards are drawn randomly from a pack of 52 playing cards, then the mean of the probability distribution of number of kings is:

In a consignment of 15 articles, it is found that 3 are defective. If a sample of 5 articles is chosen at random from it, then the probability of having 2 defective articles is:

The area (in square units) of the triangle formed by the lines 6x² + 13xy + 6y² = 0 and x + 2y + 3 = 0 is:

If the area of the circum-circle of the triangle formed by the line 2x + 5y + a = 0 and the positive coordinate axes is $\frac{29\pi}{4}$ sq. units, then |a| =

If a tangent of slope 2 to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ touches the circle $x^2 + y^2 = 4$, then the maximum value of ab is:

A line $ L $ passes through $ (1,2,-3) $ and $ (3,3,-1) $, and a plane $ \pi $ passes through $ (2,1,-2), (-2,-3,6), (0,2,-1) $. If $ \theta $ is the angle between $ L $ and $ \pi $, then $ 27 \cos^2 \theta = $ ?

$ \lim_{x \to 3} \frac{x^3 - 27}{x^2 - 9}. $

If $ f(x) $ is given as: $ f(x) = \begin{cases} 3ax - 2b, & x<1 ax + b + 1, & x<1 \end{cases} $ and $ \lim_{x \to 1} f(x) $ exists, then the relation between $ a $ and $ b $ is:

.The function $ f(x) $ is given by: \[ f(x) = \begin{cases} \frac{2}{5 - x}, & x<3 \\ 5 - x, & x \geq 3 \end{cases} \] Which of the following is true

If \[ f(x) = \begin{cases} x^\alpha \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x = 0 \end{cases} \] Which of the following is true?

If the equation of the tangent at (2, 3) on y² = ax³ + b is y = 4x - 5, then the value of a² + b² is:

If Rolle's theorem is applicable for the function $f(x) = x(x+3)e^{-x/2}$ on $[-3, 0]$, then the value of $c$ is:

For all x ∈ [0, 2024] assume that f (x) is differentiable. f (0) = −2 and f ′(x) ≥ 5. Then the least possible value of f (2024) is:

Let f(x) = $\int \frac{x}{(x^2+1)(x^2+3)} dx$. If f(3) = $\frac{1}{4} \log(\frac{5}{6})$, then f(0) =

$\int\frac{2\cos 2x}{(1+\sin 2x)(1+\cos 2x)}dx=$

$\int\left(\frac{x}{x\cos x - \sin x}\right)^2 dx = $

If $\lim_{n\rightarrow\infty}[(1+\frac{1}{n^{2}})(1+\frac{4}{n^{2}})(1+\frac{9}{n^{2}})\cdots(1+\frac{n^{2}}{n^{2}})]^{\frac{1}{n}}=ae^{b}$, then a+b=