Consider \(f(x)=\sin (3 x)+4, \forall x \in \mathbb{R}\)
(A) Maximum value of f(x) is 5
(B) Maximum value of f(x) is 3
(C) Maximum value of f(x) is attained at \(x=\frac{\pi}{3}\)
(D) Minimum value of f(x) is attained at x = 0
Choose the correct answer from the options given below:

If for the following data :

YEAR (X)	2000	2001	2002	2003	2004	2005	2006
PRODUCTION (iN TONNES) (Y)	40	45	46	42	47	50	46

the equation of the straight line trend is \(y=45.143+1.036(x-2003)\), then the trend value for the year 2004 is

\(\int_{-1}^1 \frac{x^3+|x|+1}{x^2+2|x|+1} d x\) is equal to

Given differential equation,
\(\left(1+y^2\right) d x=\left(\tan ^{-1} y-x\right) d y\)
then which of the following is/are true?
(A) Integrating factor \(=\tan ^{-1} x\)
(B) Integrating factor \(=\tan ^{-1} y\)
(C) Integrating factor \(=e^{\tan ^{-1} y}\)
(D) Degree \(=1\)
Choose the correct answer from the options given below :

If the lines \(\frac{1-x}{3}=\frac{y-2}{2 \lambda}=\frac{z-3}{2}\) and \(\frac{x-1}{3 \lambda}=\frac{y-1}{1}=\frac{6-z}{5}\) are perpendicular, then \(\lambda\) is equal to

Data available for profit (₹ Thousands) of a company as

Year	2004	2005	2006	2007	2008	2009	2010
Profit(000)	114	130	126	144	138	156	164

Based on the above data using least square method the trend value for the year ‘2007’ is

The area bounded by the curve y = sin x and x-axis between \(x=-\pi\) and \(x=\pi\) is:

Bacillus thuringiensis is widely used these days as:

Match List I with List - II.

List - I	List - II
(A) Mature mRNA	(I) Adenylation
(B) Heterogeneous nuclear RNA	(II) Exons
(C) Tailing	(III) Methyl guanosine triphosphate
(D) Capping	(IV) RNA polymerase II

Choose the correct answer from the options given below :

A pair of dice is thrown 5 times. If getting a total of 7 is considered a success, then the probability of at least 3 successes is :

Two parallel plate capacitors of capacitances \(2 \, \mu\text{F}\) and \(3 \, \mu\text{F}\) are joined in series and connected to a battery of V volts. The values of potential across the two capacitors \(V_1\) and \(V_2\) and energy stored in them \(U_1\) and \(U_2\) are related as :

Which of the following statements is incorrect with respect to the use of a catalyst in the reversible reaction?

Read the passage carefully and answer the Questions
In the formation of coordination complexes, if the inner \(d\) orbital \((n - 1)d\) is used in hybridisation, the complex, is called an inner orbital or low spin or spin paired complex. And if it uses outer \(d\) orbital \((nd)\) in hybridisation (like \(sp^3d^2\)), it is called outer orbital or high spin or spin free complex. The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the complex. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting. For coordination complexes, the magnetic moment is determined by the number of unpaired electrons and is calculated by using the 'spin-only' formula, \(\mu = \sqrt{n(n+2)}\) where \(n\) is the number of unpaired electrons and \(\mu\) is the magnetic moment in units of Bohr magneton \((BM)\). The coordination compounds are of great importance. These compounds are widely present in the mineral, plant and animal worlds and are known to play many important functions in the area of analytical chemistry, metallurgy, biological systems, industry and medicine.
Which of the following metals belongs to Wilkinson catalyst?