A company has been producing steel tubes of mean inner diameter 2 cm.
A sample of 10 tubes gives a mean inner diameter of 2.01 cm and a variance of \(0.0004 cm^2\).
The value of the test statistic is :

The probability distribution function of a normal variate with mean \(\mu\) and variance \(\sigma^2\) is given by :
\(f(x)=\frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2},-\infty< x< \infty,-\infty < \mu < \infty, \sigma>0\)
If \(y=f(x)\) be the normal probability curve, then which of the following is correct?
(A) The normal curve is symmetrical about the line \(x=\mu\).
(B) Mean, median and mode of the distribution coincide.
(C) \(Y\)-axis is an asymptote to the normal curve.
(D) If \(x\) increases numerically, \(f(x)\) decreases rapidly.
Choose the correct answer from the options given below :

Two persons A and B throw a die alternately till one of them gets a 'three' and wins the game. The probability of A's winning if A starts first is :

Derivative of \(\cos \left(\sin \left(x^2\right)\right)\) with respect to x is:

Function \(f(x)=x^x, x>0\) decreases on the interval

With reference to square matrices, which one of the following statement is NOT correct ?

If \(y=38.85+7.64(x-2020)\) is the equation of the straight line trend for the following data:

Year(x)	2017	2018	2019	2020	2021	2022	2023
Profit( Rs. '000) (y)	14	30	26	44	38	56	64

The trend value for the year 2021 by least square method is :

Out of following plants, which one is not browsed by cattle :

Antibiotic, which is bacteriostatic among the following is:

What is the product of the following reaction?

Mr. X wishes to purchase a flat for Rs. \(44,65,000\) with a down payment of Rs. 10,00,000 and balance in equated monthly installments (EMI) for 25 years.
If the bank charges \(6 \%\) per annum compounded monthly, the EMI is :
[Given: \((1.005)^{300}=4.465\)]

The variance of number of heads in three tosses of a coin is:

If \(\int_0^a 3 x^2 d x=27\), then value of \(a\) is :