\(g(x)=\left\{\begin{array}{ll}\frac{\alpha x}{|x|}, & x<0 \\ 5, & x \geq 0\end{array}\right.\) is continuous at \(x=0\), then the value of \(\alpha\) is

Sum of the minor and the cofactor of the element 6 in the determinant \(\left|\begin{array}{lll}2 & 3 & 1 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right|\) is :

The remainder when \(2^{340}\) is divided by 341 is :

In a binomial distribution, the probability of getting a success is \(\frac{1}{3}\) and the standard deviation is 2 . Then its mean is :

A 95% confidence interval states that the population mean is greater than 152 and less than 160.
If \(\sigma=15\) and \(Z_{0.025}=1.96\), then what sample size was used in the study?

The first \(m\)-year moving average of the data \(10,20,30,40,50\) is 30 . The value of \(m\) is :

Which of the following statements are correct ?
(A) Determinant is a square matrix
(B) Determinant of a matrix of order \(3 \times 3\) is \(a_{11} c_{11}+a_{12} c_{21}+a_{13} c_{31}\left(a_{i j}=\right.\) element, \(c_{i j}=\) cofactor \()\)
(C) Determinant is a number associated with a matrix
(D) Determinant is a number associated with a square matrix
(E) Determinant of a matrix of order \(3 \times 3\) is \(a_{11} c_{11}+a_{12} c_{12}+a_{13} c_{13}\), where \(a_{i j}\) is the element, while \(c_{i j}\) is its corresponding cofactor
Choose the correct answer from the options given below :

The complex \(\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4\left(\mathrm{NO}_2\right)_2\right] \mathrm{Cl}\) will show.......
(A) Linkage isomerism.
(B) Ionization isomerism
(C) Coordination isomerism
(D) Geometrical isomerism
Choose the correct answer from the options given below:

Which of the following statements are correct?
A. The various lines in the atomic spectra are produced when electrons jump from higher energy state to a lower energy state.
B. An accelerated atomic electron must spiral into the nucleus as it losses energy.
C. Rutherford scattering determines an upper limit to the size of the nucleus.
D. Angular momentum of the electron orbiting around the nucleus is not quantised.

Conductors develop electric currents in them

If \(x, y\) and \(z\) are non-zero distinct numbers, then \(\left|\begin{array}{ccc}x+y & y+z & z+x \\ z & x & y \\ 1 & 1 & 1\end{array}\right|\) is equal to

Read the passage carefully and answer the questions based on the passage:
Species diversity on earth is not uniformly distributed. It is generally highest in the tropics and decreases towards the poles. Earth's fossil history reveals the incidences of mass extinctions in the past. Earth's rich biodiversity is vital for the very survival of mankind. It is believed that communities with high diversity tend to be less variable and more productive. The reasons of conserving biodiversity are narrowly utilitarian, broadly utilitarian and ethical. Biodiversity conservation may be in-situ as well as ex-situ.
Which of the following might not account for the greater biological diversity in the tropic region?

Arrange the following steps of PCR in correct sequence.
(A) Temperature induced denaturation of double stranded DNA.
(B) Isolation of gene of interest
(C) Amplification of gene by using Taq polymerase
(D) Primer annealing on the separated templates
Choose the correct answer from the options given below: