List of practice Questions

What is the total heat needed to change 1g of water from -10°C to 110°C at 1 atm? \[ \Delta H_{fusion} = 80 \, \text{cal/g}, \Delta H_{vaporisation} = 540 \, \text{cal/g}, \text{specific heat of ice and steam are 0.5 cal/g°C} \]
Calcium chloride is sometimes sprinkled on winter sidewalks to melt snow and ice. If 333g of calcium chloride is dissolved completely in 1.00 kg of water, what will be the freezing point of the solution? (The molal freezing point depression constant for water is 1.86°C kg/mol)
Which of the following is true for an electrolytic cell?
What type of intermolecular bonding occurs in gaseous CH$_4$?
Which of the following demonstrates non-ideal behaviour of a gas?
Given the following notation for an electrochemical cell,
Pt(s) $|$ H$_2$(g)$|$ H$^+$(aq) $//$ Ag$^+$(aq)$|$Ag(s)
Which of the following represents the overall balanced (net) cell reaction?
Which of the following periodic properties increases with increasing atomic number within a family in the periodic table?
Name the given compound : Cu(ClO$_4$)$_2$
A 13 g gaseous sample of an unknown hydrocarbon occupies a volume of 11.2 L at STP. What is the hydrocarbon?
Immediately, upon bringing a hot piece of metal into a room, the heat is felt from 5 m away. The type of heat transfer is probably
In aqueous solution Cu(+1) salts are unstable because
Which of the following statements is most likely true concerning the given reaction?
2A(g) + B(g) → 2C(g) + D(s)
Choose the most appropriate options.
The period of the function \(f(x) = |\sin x| - |\cos x|\) is
\[ \int_{-\pi/2}^{\pi/2} |\sin x| dx \text{ equals to} \]
If \(P(x)\) is a polynomial such that \[ P(x^2 + 1) = \{P(x)\}^2 + 1 \] then \(P'(0)\) is equal to
\[ \int \frac{x^2}{(x \sin x + \cos x)^2} dx \text{ is equal to} \]
A real solution of the equation \[ \cosh x - 5 \sinh x - 5 = 0 \text{ is} \]
Find the derivative of \[ y = (1 - x)^m (1 + x)^n \text{ at } x = 0, \text{ where } m, n>0 \]
The straight line \( r = (i - j + k) + \lambda (2i + j - k) \) and the plane \( r \cdot (2i + j - k) = 4 \) are
\[ \frac{1}{2 \sin 10^\circ} - 2 \sin 70^\circ \text{ is equal to} \]

$ (1 + 2i)^6 $ is equal to:

What is the number of ordered pairs of real numbers (a, b) such that \[ (a + bi)^{2002} = a - bi \]
Given \(\varepsilon = \cos\left(\frac{2\pi k}{n}\right) + i \sin\left(\frac{2\pi k}{n}\right)\), find the value of \[ \prod_{k=0}^{n-1} \left( \varepsilon^2k - 2\varepsilon k \cos \theta + 1 \right) \]

$ \lim_{x \to 0} \frac{a^x - 1}{x} $ is equal to

$\lim_{x \to 0} \frac{\tan^{-1} \left( \frac{-x}{\sqrt{1 - x^2}} \right)}{\ln(1 - x)} =\ ?$