List of practice Questions

Per one Calvin cycle, the number of CO\(_2\) molecules fixed, ATP utilized, and the number of Glucose, NADPH molecules produced respectively are:
In C\(_4\) plants, the Oxaloacetic acid is formed by this reaction:
Identify the correct sentences regarding the role of physiological responses of phytohormones:
I. Ethylene initiates sprouting of potato tubers
II. Gibberellins promote senescence
III. Auxins promote flowering in pineapple
IV, Abscisic acid inhibits seed germination
Cell organelles included in the endomembrane system are:
Dehydration occurs during the formation of the following types of bonds:
The site of transcription and translation in eukaryotic cells are respectively:
Specialized epidermal cells surrounding the guard cells are:
Ategmic, Unitegmic, and Bitegmic ovules are present serially in:
In one helix of DNA, minimum and maximum number of hydrogen bonds present between nitrogen bases:

. If a random variable X has the following probability distribution, then the mean of X is:

X = xiP(X = xi)
12k²
2k
3k²

 

Define \( f: \mathbb{R} \to \mathbb{R} \) by \[ f(x) = \begin{cases} \frac{1 - \cos 4x}{x^2}, & x < 0 \\ a, & x = 0 \\ \frac{\sqrt{x}}{\sqrt{16 + \sqrt{x}} - 4}, & x > 0 \end{cases} \] Find the value of \( a \) such that \( f \) is continuous at \( x = 0 \).
If \( y (\cos x)^{\sin x} = (\sin x)^{\sin x} \), then the value of \( \frac{dy}{dx} \) at \( x = \frac{\pi}{4} \) is:
The system of equations \( x + 3y + 7 = 0 \), \( 3x + 10y - 3z + 18 = 0 \), and \( 3y - 9z + 2 = 0 \) has:
If \( \mathbf{a} = 2\overline{i} - \overline{j}, \overline{b} = 2\overline{j} - \overline{k}, \overline{c} = 2\overline{k} - \overline{i} \) are three vectors and \( \overline{d} \) is a unit vector perpendicular to \( \overline{c} \), If \( \overline{a}, \overline{b}, \overline{d} \) are coplanar vectors, then \( |\overline{d} \cdot \overline{b}| = \):
If two dice are thrown, then the probability of getting co-prime numbers on the dice is:
The slope of the tangent drawn from the point \( (1,1) \) to the hyperbola \( 2x^2 - y^2 = 4 \) is:
The vertices of triangle \( \Delta ABC \) are \( A(2, 3, k) \), \( B(-1, k, -1) \), and \( C(4, -3, 2) \). If \( AB = AC \) and \( k>0 \), then the triangle \( ABC \) is:
If \( a, b, c \) are the intercepts made on X, Y, Z-axes respectively by the plane passing through the points \( (1, 0, -2) \), \( (3, -1, 2) \), and \( (0, -3, 4) \), then \( 3a + 4b + 7c = \)?
If \( \lim_{x \to 4} \frac{2x^2 + (3+2a)x + 3a{x^3 - 2x^2 - 23x + 60} = \frac{11}{9} \), then find \( \lim_{x \to a} \frac{x^2 + 9x + 20}{x^2 - x - 20} \).}
If \(6x-5y-20=0\) is a normal to the ellipse \(x^2 + 3y^2 = k\), then \(k =\)
The domain of the real valued function: \[ f(x) \;=\; \sqrt[3]{\frac{x \,-\, 2}{2x^2 \,-\, 7x \,+\,5}} \;+\; \log\bigl(x^2 \,-\, x \,-\, 2\bigr). \]
If the number of circular permutations of 9 distinct things taken 5 at a time is \(n_1\), and the number of linear permutations of 8 distinct things taken 4 at a time is \(n_2\), then what is \(\frac{n_1}{n_2}\)?
The number of ways in which 4 different things can be distributed to 6 persons so that no person gets all the things is \;?
If \[ \frac{3x^4 - 2x^2 +1}{(x-2)^4} = A + \frac{B}{x-2} + \frac{C}{(x-2)^2} + \frac{D}{(x-2)^3} + \frac{E}{(x-2)^4}, \] then \(2A + 3B - C - D + E =\;?\)

The maximum value of the function \[ f(x) = 3\sin^{12}x + 4\cos^{16}x \] is ?