List of practice Questions

Energy flow is always unidirectional in an ecosystem because?
Energy flow in an ecosystem is based on which laws?
Which component of an ecosystem is responsible for the cycling of nutrients such as carbon, nitrogen and phosphorus?
The residue of \( f(z) = \frac{z^2}{(z-1)^3(z-2)(z-3)} \) at the pole \(z=1\) is
Mean of a binomial distribution 12 and variance is 8. The probability of having at least one success is?

In large sample, the critical value for the single tailed test at 5% level of significance is?

For a bivariate data $(x_i, y_i)$ ($i=1,2,3,\dots,10$), $\sum x_i y_i = 6200$, $\sum x_i = 400$, $\sum y_i = 1220$, $\sum x_i^2 = 1800$, then equation of line of best fit is?
Let $X$ be a discrete random variable with probability mass function $P(X=x_i)$ where $x \in \{x_1, x_2, \dots, x_n\}$. If $\sum_{i=1}^{n} (x_i-2)^2 P(X=x_i) = 28$ and $\sum_{i=1}^{n} (x_i+2)^2 P(X=x_i) = 12$. Then variance of $X$ is?
If the probability density function of a continuous random variable X is $f(X=x) = Ke^{-3x}$, $0<x<\infty$, then a solution of $\frac{P^2+1}{P} = \frac{K}{\sqrt{2}}$ is?
If for a progression, sum of the first $n$ terms is $2n^2+5n+6$ and $T_n$ is the $n^{th}$ term of the progression, then $\sum_{k=1}^{10} T_{3k} = $?
The complete solution of \( (mz-ny)\frac{\partial z}{\partial x} + (nx-lz)\frac{\partial z}{\partial y} = ly-mx \) is
Which of the following pair of functions are linearly dependent
The number of positive integral solutions of $x+y+z = 12$, $x \le y \le z$ is?
If $l>0, K<0$ are roots of $x^2 + x - 20 = 0$, the system of linear equations $3x - y + 4z = 3$, $x + 2y - 3z = -2$ and $6x + 5y + Pz = -3$ has?
Let \( \vec{F} \) be a vector point function defined inside and on the surface (S) of the sphere \( x^2+y^2+z^2=1 \). Then \( \oint_S (\text{Curl} \vec{F}) \cdot \hat{n} ds = \)
\( \int_{0}^{2} \int_{0}^{\sqrt{y}} e^{y/x} dx dy = \)
The system of equations \( \begin{bmatrix} -2 & 1 & 1 \\ 1 & -2 & 1 \\ 1 & 1 & -2 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} a \\ b \\ c \end{bmatrix} \) has
If \( \begin{bmatrix} \frac{1}{\sqrt{3}} & \frac{1+i}{\sqrt{3}} \\ \frac{1-i}{\sqrt{3}} & \frac{K}{\sqrt{3}} \end{bmatrix} \) is a unitary matrix, then the sum of all possible values of K is
Two statements are given. Choose the correct option based on the statements
Statements:
1. Civil cases are filed in courts due to conflicts involving mostly money between people or institutions like businesses
2. Criminal Cases are filed in Courts for offences committed by a group of people.
The term conciliation means
A deponent is a person
The term interrogatories refer to
Two statements are given. Choose the correct option based on the statements
Statements:
1. Lok Sabha of Indian Parliament divides its work into Three Sessions in a year
2. G.V. Mavlankar was the first speaker of the Indian Lok Sabha
Two statements are given. Choose the correct option based on the statements
Statements:
1. A member of the Lok Sabha should be mentally sound
2. A member of the Lok Sabha should not be a bankrupt
Two statements are given. Choose the correct option based on the statements
Statements:
1. The Election Commission of India is an autonomous Constitutional Authority
2. The Election Commission of India administers elections to the Lok Sabha, Rajya Sabha, State Legislative Assemblies and offices of the President and Vice-President in the country.