List of practice Questions

Among the following, the compound(s) which produce the same osazone as that obtained from D-glucose, when reacted with phenylhydrazine, is/are

A four-band multispectral image with pixel size of 50 m x 50 m covers a ground area of 20 km × 20 km. If the radiometric resolution of the satellite data is 8 bits, then the uncompressed satellite image contains _______ kilobytes (kB) of data (in integer).

If \(\lim\limits_{x \to1}(\frac {x^2-2ax+b}{x-1})=8\)
then \((a-b)\) is _____ . (Answer in integer)

A plane electromagnetic wave propagating in x-direction is described by \( E_y = (200 \, \text{V/m}) \sin(1.5 \times 10^7 t - 0.05 x) \). The intensity of the wave is:

In the given TLC, the distance of spot \( A \) and \( B \) are 5 cm and 7 cm, from the bottom of the TLC plate, respectively. The \( R_f \) value of \( B \) is \( x \times 10^{-1} \) times more than \( A \). The value of \( x \) is _________ .

Which one or more of the following statements is/are correct in the processing of pre-mRNA in eukaryotes?

Match List-l with List-ll

List I		List II
A.	\(\sqrt{\frac{0.81\times0.484}{0.064\times6.25}}\)	I.	0.024
B.	\(\sqrt{\frac{0.204\times42}{0.07\times3.4}}\)	II.	0.99
C.	\(\sqrt{\frac{0.081\times0.324\times4.624}{1.5625\times0.0289\times72.9\times64}}\)	III.	50
D.	\(\sqrt{\frac{9.5\times0.085}{0.0017\times0.19}}\)	IV.	6

Choose the correct answer from the options given below:

If \( \triangle ABC \) is an isosceles triangle and the coordinates of the base points are \( B(1, 3) \) and \( C(-2, 7) \), the coordinates of \( A \) can be:

The points of extremum of \[ \int_{0}^{x^2} \frac{t^2 - 5t + 4}{2 + e^t} \, dt \] are:

Choose the correct statement:

If \( n \) is a positive integer, the value of:
\[ (2n + 1) \binom{n}{0} + (2n - 1) \binom{n}{1} + (2n - 3) \binom{n}{2} + \dots + 1 \cdot \binom{n}{n} \] is:

If the quadratic equation \( ax^2 + bx + c = 0 \) (\( a > 0 \)) has two roots \( \alpha \) and \( \beta \) such that \( \alpha < -2 \) and \( \beta > 2 \), then:

A square with each side equal to \( a \) lies above the \( x \)-axis and has one vertex at the origin. One of the sides passing through the origin makes an angle \( \alpha \) (\( 0 < \alpha < \frac{\pi}{4} \)) with the positive direction of the \( x \)-axis. The equation of the diagonals of the square is:

The angle between two diagonals of a cube will be:

Let \( \Gamma \) be the curve \( y = b e^{-x/a} \) and \( L \) be the straight line:
\[ \frac{x}{a} + \frac{y}{b} = 1, \quad a, b \in \mathbb{R}. \]
Then:

For the real numbers \( x \) and \( y \), we write \( x \, P \, y \) iff \( x - y + \sqrt{2} \) is an irrational number.
Then the relation \( P \) is:

Let
\[ A = \begin{bmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{bmatrix}. \]
Which of the following is true?

If \( A \) and \( B \) are acute angles such that \( \sin A = \sin^2 B \) and \( 2\cos^2 A = 3\cos^2 B \), then \( (A, B) \) is:

If two circles which pass through the points \( (0, a) \) and \( (0, -a) \) and touch the line \( y = mx + c \) cut orthogonally, then:

Five balls of different colors are to be placed in three boxes of different sizes. The number of ways in which we can place the balls in the boxes so that no box remains empty is:

Let
\[ A = \begin{bmatrix} 1 & -1 & 0 \\ 0 & 1 & -1 \\ 1 & 1 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} 2 \\ 1 \\ 7 \end{bmatrix}. \]
For the validity of the result \(AX = B\), \(X\) is:

If \( a_1, a_2, \dots, a_n \) are in A.P. with common difference \( \theta \), then the sum of the series:
\[ \sec a_1 \sec a_2 + \sec a_2 \sec a_3 + \dots + \sec a_{n-1} \sec a_n = k (\tan a_n - \tan a_1), \]
where \( k = ? \)

Consider the function f(x) = (x−2)logx. Then the equation xlogx = 2−x has:

If \(\alpha, \beta\) are the roots of the equation \(ax^2 + bx + c = 0\), then:
\[ \lim_{x \to \beta} \frac{1 - \cos(ax^2 + bx + c)}{(x - \beta)^2} \]

If \(f(x) = \frac{e^x}{1+e^x}, I_1 = \int_{-a}^a xg(x(1-x)) \, dx\) and \(I_2 = \int_{-a}^a g(x(1-x)) \, dx\), then the value of \(\frac{I_2}{I_1}\) is: