List of practice Questions

Which one of the following techniques/tools is NOT used for inserting a foreign gene into a cell?

Under standard temperature (T) and pressure (P) conditions, 128 g of an ideal gas molecule A occupies a volume of 1 L. The gas molecule A obeys the relationship $RT = 0.25PV$. R and V are universal gas constant and ideal gas volume, respectively. The molecule A is:

CRISPR-Cas system is associated with:

The process by which intracellular macromolecules are supplied for lysosomal degradation during nutrient starvation is:

The enzyme that transcribes the eukaryotic genes encoding precursor ribosomal RNAs (pre-rRNAs) of 28S, 18S and 5.8S rRNAs is

Number of unrooted trees in a phylogeny of five sequences is

Which one of the following methods is used to test the significance of a predicted phylogeny?

The Cartesian coordinates $(x,y)$ of a point $A$ with polar coordinates $(4,\pi/4)$ is

Which one of the following statements is INCORRECT about hybridoma production?

Coronavirus genome consists of

The boxes of masses 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (use g = 10 m/s$^2$):

Match List - I with List - II.

Choose the most appropriate answer from the options given below :

If $ \int \frac{2e^x + 3e^{-x}}{4e^x + 7e^{-x}} dx = \frac{1}{14}(ux + v \log_e(4e^x + 7e^{-x})) + C $, where C is a constant of integration, then u + v is equal to _________.

Let S be the mirror image of the point Q(1, 3, 4) with respect to the plane 2x - y + z + 3 = 0 and let R(3, 5, $\gamma$) be a point of this plane. Then the square of the length of the line segment SR is _________.

Let S be the sum of all solutions (in radians) of the equation $\sin^4\theta + \cos^4\theta - \sin\theta \cos\theta = 0$ in [0, 4$\pi$]. Then $\frac{8S}{\pi}$ is equal to _________.

An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The variance of marks obtained by 30 girls is also 2. The average marks of all 50 candidates is 15. If $\mu$ is the average marks of girls and $\sigma^2$ is the variance of marks of 50 candidates, then $\mu + \sigma^2$ is equal to _________.

The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m - n = 0 and mn + nl + lm = 0, is :

The equation of the plane passing through the line of intersection of the planes $ \vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 1 $ and $ \vec{r} \cdot (2\hat{i} + 3\hat{j} - \hat{k}) + 4 = 0 $ and parallel to the x-axis is :

The Boolean expression $(p \land q) \Rightarrow ((r \land q) \land p)$ is equivalent to :

The area of the region bounded by the parabola $(y-2)^2 = (x-1)$, the tangent to it at the point whose ordinate is 3 and the x-axis is :

If 0 $<$ x $<$ 1 and y = $\frac{1}{2}x^2 + \frac{2}{3}x^3 + \frac{3}{4}x^4 + ...$, then the value of e$^{1+y}$ at x = $\frac{1}{2}$ is :

If $ \lim_{x \to \infty} (\sqrt{x^2 - x + 1} - ax) = b $, then the ordered pair (a, b) is :

A box open from top is made from a rectangular sheet of dimension a $\times$ b by cutting squares each of side x from each of the four corners and folding up the flaps. If the volume of the box is maximum, then x is equal to:

The set of all values of k $>$ -1, for which the equation
(3x$^2$+4x+3)$^2$ - (k+1)(3x$^2$+4x+3)(3x$^2$+4x+2) + k(3x$^2$+4x+2)$^2$ = 0 has real roots, is :

Let [$\lambda$] be the greatest integer less than or equal to $\lambda$. The set of all values of $\lambda$ for which the system of linear equations x+y+z=4, 3x+2y+5z=3, 9x + 4y + (28 + [$\lambda$])z = [$\lambda$] has a solution is :