If A is a square matrix of order 3 such that A(adj A) = \(\left[\begin{array}{ccc}-2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2\end{array}\right]\), then \(|A|\) is equal to

Given two independent events A and B such that P(A) = 0.3 and P(B) = 0.6,
Match the following:

List - I	List - II
(A) P(A and B)	(I) 0.28
(B) P(A and not B)	(II) 0.72
(C) P(A or B)	(III) 0.12
(D) P(neither A nor B)	(Iv) 0.18

Mameesh took a loan of Rs 9,00,800 from bank at an interest rate of \(6 \%\) per annum for 10 years. If she has to pay the loan back with the help of equal monthly installments (EMI). Then, the EMI using reduced balance method is (approx) :
(Given: \((1.005)^{-120}=0.5496\))

match List - I with List - II

List - I	List - II
(A) \(\tan ^{-1}\left(\frac{2}{11}\right)+\tan ^{-1}\left(\frac{7}{24}\right)\)	(I) \(\frac{3 \pi}{4}\)
(B) \(\tan ^{-1} 2+\tan ^{-1} 3\)	(II) \(\pi\)
(C) \(\tan ^{-1} 1+\tan ^{-1} 2+\tan ^{-1} 3\)	(III) \(\tan ^{-1}\left(\frac{1}{2}\right)\)
(D) \(\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{13}\right)\)	(IV) \(\tan ^{-1}\left(\frac{2}{9}\right)\)

Choose the correct answer from the options given below:

Let two independent random samples of sizes \(n_1\) and \(n_2\) respectively have been drawn from the same normal population. Let \(\overline{X_1}\) and \(\overline{X_2}\) be the means and let \(s_1\) and \(s_2\) be their standard deviations. In order to test whether the the two sample means \(\overline{X_1}\) and \(\overline{X_2}\) differ significantly or not, the \(t\)-test statistic is given by

The following data shows the percentage of rural and urban Indian households who have a high speed internet connection.

Year(x)	Rural Household \((y \%)\)	Urban Household\((y \%)\)
2020	2	6
2021	3	7
2022	3	9
2023	4	15
2024	5	20

Based on the above data, which of the following statements are correct?
(A) A straight line trend by the method of least squares for rural Indians \(y_t=3.4+0.7(x-2022)\)
(B) A straight line trend by the method of least squares for urban Indians is \(y_t=11.4+4.3(x-2022)\)
(C) The forecast for the year 2025 for urban group using the trend equation is \(22.2 \%\)
(D) The forecast for the year 2025 for rural group using the trend equation is \(5.5 \%\)
Choose the correct answer from the options given below :

Let A and B be two events. Then which of the following statements are TRUE?
(A) \(P(B \mid A)=\frac{P(A \cap B)}{P(A)}\), provided \(P(A) \neq 0\)
(B) \(P\left(B^{\prime}\right)=1+P(B)\)
(C) \(P(A \cup B)=P(A)+P(B)+P(A \cap B)\)
(D) \(P(A \cap B)=P(A) \cdot P(B)\) if A and B are independent events
Choose the correct answer from the options given below:

When a p-n junction is forward biased, the width of depletion region

Let \(f(x)=x^2+\frac{250}{x}\) be any function defined on \(R -\{0\}\), where \(R\) is the set of real numbers. Then which of the following are FALSE?

A parallel plate air capacitor is charged, and then the battery is disconnected. Now on inserting a dielectric between the plates of the capacitor, which of the following change:
1. potential difference between the plates
2. charge on the plates
3. electric field between the plates
4. energy stored in the capacitor
Choose the correct answer from the options given below:

In a moving coil galvanometer, the coil is wound over a metallic frame in order to

The rate of a chemical reaction doubled for every \(10^{\circ} C\) rise in temperature. If the temperature is raised by \(50^{\circ} C\), the rate of reactions will be

If the lines \(\frac{x-1}{-3} = \frac{y-2}{2\lambda} = \frac{z-3}{2}\) and \(\frac{x-1}{3\lambda} = \frac{y-1}{2} = \frac{z-6}{-5}\) are perpendicular. Then the value of \(\lambda\) is: