List of top Questions asked in AP EAPCET- 2023

The structure of Gly-Ala (Glycylalanine) is:
The optically inactive compound from the following is:

What are 'X' and 'Y' respectively in the following reactions? \[ \text{C}_6\text{H}_5\text{CHO} + \text{C}_6\text{H}_5\text{COCH}_3 \xrightarrow{\text{OH}^-,\ 293\text{K}} \text{X} \xrightarrow{\text{NaBH}_4} \text{Y} \]

Arrange the following in increasing order of their boiling points:

If \( f(a) = \log \left| \frac{1 - a}{1 + a} \right| \) for \( a \neq \{-1, 1\} \), then the set of values of all \( a \), for which \( f\left( \frac{2a}{1 + a^2} \right)>0 \) is:
If \( \det(AB) = \det(A)\det(B) \) and \( A \) is a non-singular matrix of order \( 3 \times 3 \), then \( \det(\text{adj}(A)) \) is:
One of the 15th roots of \( -1 \) is:
The product of the four values of \( \left( 1 + i\sqrt{3} \right)^{3/4} \) is:
If one root of the equation \( ax^2 + bx + c = 0 \) is twice another root, then the equation \( ax^2 + bx + c = 0 \) is:
If \( -1 \) is a twice repeated root of the equation \( ax^3 + bx^2 + cx + 1 = 0 \), then \( ax^3 + bx^2 + cx + 1 = 0 \) represents:
If \( C_j = \binom{n}{j} \), then \( C_0 C_t + C_1 C_{t+1} + C_2 C_{t+2} + \dots + C_n = \)
The coefficient of the highest power of \( x \) in the expansion of \[ \left( x + \sqrt{x^2 - 1} \right)^3 + \left( x - \sqrt{x^2 - 1} \right)^8 \text{ is:} \]
The number of non-negative integral solutions of \( x_1 + x_2 + x_3 + x_4 = 10 \) is:
If \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), where \( a, b, c, d \in \{-1, 1\} \), then the number of singular matrices in \( A \) is:
If \( \cot x \cot y = a \) and \( x + y = \frac{\pi}{6} \), then the quadratic equation satisfying \( \cot x \) and \( \cot y \) is:
If \( \tan A + \tan B = x \) and \( \cot A + \cot B = y \), then \( \tan(A + B) = \)
If \( \triangle ABC \) is a right-angled isosceles triangle and \( \angle C = 90^\circ \), then \( r = \frac{1}{5} \) is:
If \( 7i - 4j - 5k \) is the position vector of vertex A of a tetrahedron ABCD and \( -i + 4j - 3k \) is the position vector of the centroid of the triangle BCD, then the position vector of the centroid of the tetrahedron ABCD is:
Let \( \mathbf{OA = i + 2j - 2k} \) and \( \mathbf{OB = -2i - 3j + 6k} \) be the position vectors of two points A and B. If C is a point on the bisector of \( \angle AOB \) and \( OC = \frac{\sqrt{42}}{2} \), then \( OC = \)
The distance of a point \( \vec{a} \) from the plane \( r \cdot m = q \) is given by \( \frac{| \vec{a} \cdot m - q |}{|m|} \). If the distance of the point \( i + 2j + 3k \) from the plane \( \vec{r} \cdot (2i + 6j - 9k) = -1 \) is \( p \) and the distance of the origin from this plane is \( q \), then \( p - q = \dots \)
Three screws are drawn at random from a lot of 50 screws containing 5 defective ones. Then the probability of the event that all 3 screws drawn are non-defective, assuming that the drawing is (a) with replacement (b) without replacement respectively is:
A coin is tossed three times. Let A be the event of "getting three heads" and B be the event of "getting a head on the first toss". Then A and B are:
The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least 0.96 is:
If \( P(X = x) = k \left( \frac{3}{8} \right)^x \), where \( x = 1, 2, 3, \dots \) is the probability distribution function of a discrete random variable X, then \( k = \)
If \( A(4, 0) \) and \( B(-4, 0) \) are two points, then the locus of a point \( P \) such that \( PA - PB = 4 \) is: