Which of the following reactions is the most suitable for the preparation of n-propylbenzene?

Mischmetall consists of a lanthanoid metal (95\(\%\)) and Iron (~5\(\%\)) and traces of S, C, Ca \(\&\) Al. Mischmetall used for producing bullets contains:

Answer the question on the basis of passage given below :
One of the notable features of the transition element is the great variety of oxidation states it may show in its compounds. The elements which give the greatest number of oxidation states occur in or near the middle of the series. Manganese, for example exhibits all the oxidation states from +2 to +7. The lesser number of oxidation states at the extreme ends is either due to losing or sharing of few electrons (Sc, Ti) or too many d electrons of higher valence. Early in the first series scandium (II) is virtually unknown and titanium (IV) which is more stable than Ti (III) or Ti (II). On the other end, the only oxidation state of zinc is \(+ 2\).
For balancing the given reaction, value of \(x\) will be.
\(4 FeCr_2 O_4+Na_2 CO_3+7 O_2 \longrightarrow x Na_2 CrO_4+2 Fe_2 O_3+8 CO_2\)

Read the Passage below and answer the question:
Aldehydes and Ketones, having atleast one methyl group linked to the carbonyl carbon atom (methyl Ketones), are oxidised by sodium hypohalite to sodium salts of corresponding carboxylic acids having one carbon atom less than that of carbonyl compound is converted to haloform. This oxidation does not affect a carbon - carbon double bond, if present in a molecule.
Which of the following statements are true?
A. \(CH_3CHO\) and \(CH_3CH_2CHO\) can be distinguished by Tollen's test.
B. \(CH_3CH_2CHO\) and \(CH_3COCH_3\) can be distinguished by Fehling's test.
C. \(CH_3CHO\) and \(C_6H_5CHO\) can be distinguished by Fehling's test.
D. \(HCHO, CH_3CHO\) can be distinguished by \(NaHCO_3\) test.
E. \(HCOOH, CH_3COOH\) can be distinguished by \(NaHCO_3\) test.
Choose the correct answer from the options given below :

The molality of a solution prepared by dissolving \(4 . 0 ~ g ~ N a O H\) in \(1 0 0 0 ~ m L\) distilled water is _________ (Assume that the density of water is \(1 g mL ^{-1}\) )

Which of the following is true for the given reaction?
\(\text{CH}_3-(\text{CH}_3)_3\text{C-N-CH}_3 + \text{Cl-SO}_2-\text{C}_6\text{H}_5 \rightarrow \text{No Reaction}\)

Read the Passage carefully and answer the Questions
Kinetic studies not only help us to determine the rate of a chemical reaction but also describe the conditions by which the reaction rates can be altered.
The factors such as concentration, temperature, preasure and catalyst affect the rate of a reaction.
The speed of a reaction or the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time.
Rate \(=k|A|^a[B]^y\)
Here \(k\) is the rate constant
\(x+y\) gives the overall order of a reaction, whereas \(x\) and \(y\) represent the order with respect to the reactants \(A\) and \(B\), respectively.
Table: Initial rate of formation of NO₂

S.No.	Initial [NO]/mol L-1	Initial [O2]/mol L-1	Initial rate of formation of [NO2]/mol L-1s-1
1.	0.30	0.30	0.096
2.	0.60	0.30	0.384
3.	0.30	0.60	0.192
4.	0.60	0.60	0.768

Based on the above observations, the rate of formation of NO₂ can be represented as

If \(|\vec{a}|=3\) and \(|\vec{b}|=4\), then a value of \(\lambda\) for which \(\vec{a}+\lambda \vec{b}\) and \(\vec{a}-\lambda \vec{b}\) are perpendicular is :

The composition of Chromate ore is :

The microbe involved in the production of citric acid is -

Match List-I with List-II

List-I (Optical instrument)	List-II (Magnifying power)
(A) Magnifying power m of a simple microscope	(I) \( m = 1 + (D/f) \)
(B) Magnifying power m of a simple microscope if the image is at infinity	(II) \( m = (L/f_0) \times (D/f_e) \)
(C) Magnifying power m of a compound microscope	(III) \( m = f_0 / f_e \)
(D) Magnifying power m of a telescope	(IV) \( m = D/f \)

Choose the correct answer from the options given below:

Match List-l with List-II

LIST-I	LIST-II
A. Planck's constant	(I) \(\left[M L^2 T^{-2}\right]\)
B. Work function	(II) \([L]\)
C. Stopping potential	(III) \(\left[M L^2 T^{-3} A^{-1}\right]\)
D. de Broglie wavelength	(IV) \(\left[M L^2 T^{-1}\right]\)

Choose the correct answer from the options given below :

The function \(f(x)=4-3 x+3 x^2-x^3\) is (Here \(R\) is the set of real numbers)