List of practice Questions

Evaluate the integral: \[ \int \frac{\sin x + \cos x}{\sin x - \cos x} \, dx =\ ? \]
Evaluate the integral: \[ \int_0^{\pi} \frac{x \sin x}{\sin^2 x + 2\cos^2 x} \, dx \]
Evaluate the limit: \[ \lim_{n \to \infty} \left( \frac{1}{1^2 + n^2} + \frac{2}{2^2 + n^2} + \frac{3}{3^2 + n^2} + \cdots + \frac{n}{n^2 + n^2} \right) \]
If \[ \int \frac{1}{\cot \frac{x}{2} \cot \frac{x}{3} \cot \frac{x}{6}} \, dx = A \log \left| \cos \frac{x}{2} \right| + B \log \left| \cos \frac{x}{3} \right| + C \log \left| \cos \frac{x}{6} \right| + k, \] then \(A + B + C =\)
If \( \cosh 2x = 199 \), then \( \cot hx = \)
In a \( \triangle ABC \), \( A - B = 120^\circ \), \( R = 8r \), then \[ \frac{1 + \cos C}{1 - \cos C} =\ ? \]
The minimum value of \( |z - 1| + |z - 5| \) is:
If \( z = x + iy \) and if the point \( P \) in the Argand diagram represents \( z \), then the locus of the point \( P \) satisfying the equation \( 2|z - 2 - 3i| = 3|z + i - 2| \) is a circle with centre:

Which of the following represents Gattermann reaction?

The incorrect statement about the product ‘Z’ in the given reaction sequence is

What is the end product 'R' in the reaction sequence?

What is the major product Y in the following reaction sequence?

A halide with formula C6H13Br gave two isomeric alkenes A and B on dehydrobromination. On ozonolysis of mixture of A and B the following compounds were obtained: CH3COCH3, CH3CHO, CH3CH2CHO and (CH3)2CHCHO. The halide is:

The correct statement regarding the mechanism involved in the above reactions is

Match the following:

List-I (reaction)List-II (catalyst)
A) SO2(g) + Cl2(g) → SO2Cl2(l)I) Pt / Rh gauge
B) 2SO2(g) + O2(g) → 2SO3(g)IV) V2O5
C) 4HCl + O2 → 2Cl2 + 2H2OII) CuCl2
D) 4NH3(g) + 5O2(g) → 4NO(g) + 6H2O(g)III) Charcoal
Identify the correct statements from the following:
I) In adsorption process, both enthalpy and entropy decrease.
II) In general, physisorption is an irreversible process.
III) The catalyst used in the decomposition of potassium chlorate is manganese dioxide.
When 3 amp current was passed through an aqueous solution of salt of a metal M (atomic weight 106.4 u) for 1 hour, 2.977 g of Mn+ was deposited at cathode. The value of n is (1 F = 96500 C mol-1)
What are X and Y respectively in the following set of reactions?
2-Bromobutane $\xrightarrow{{alc. KOH}}$ C$_4$H$_8$ (major)
C$_4$H$_8$ $\xrightarrow{{KMnO}_4/{H}^+}$ X
C$_4$H$_8$ $\xrightarrow{{Baeyer's reagent}}$ Y
Which of the following metals is used for measuring high temperatures?

Match the following:

List - I (Metal) List - II (Flame colour) 
A)LiI)Crimson red
B)NaII)Yellow
C)CaIII)Brick red
D)BaIV)Apple green
Match the following:
Hormones Chemical Nature
A) InsulinIV) Protein
B) EstrogenI) Steroid
C) OxytocinII) Peptide
D) ThyroxineIII) Amine

Identify the correct match:
Identify the incorrect statement regarding artificial sweeteners.
What are X and Y in the following set of reactions?
(dry acetone)
Y’ in the following reaction sequence
The SN$_2$ reactivity of the following compounds will be in the order:
I) C$_6$H$_5$CH(CH$_3$)Br
II) (C$_6$H$_5$)$_2$CHBr
III) (C$_6$H$_5$)$_2$C(CH$_3$)Br
IV) C$_6$H$_5$CH$_2$Br
What is ‘Y’ in the following reaction sequence?
Y’ in the following reaction sequence