List of practice Questions

If \( x \in [-1,1] \), then \(\displaystyle \sin^{-1}(-x) = \)
Evaluate: \(\displaystyle \int (x + \cos 2x) \, dx = \)
Evaluate: \(\displaystyle \int e^x \left( \sin^{-1} x + \frac{1}{\sqrt{1 - x^2}} \right) dx = \)
Evaluate: \(\displaystyle \int \frac{dx}{x(x+2)} = \)
Evaluate: \(\displaystyle \int \sqrt{a^2 - x^2} \, dx = \)
Evaluate: \(\displaystyle \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin^7 x \, dx = \)
Evaluate: \(\displaystyle \int_0^a \left( \sqrt{x} + \sqrt{a - x} \right) \sqrt{x} \, dx = \)
Evaluate: \(\displaystyle \int_0^{\frac{\pi}{2}} \cos 2x \, dx = \)
If \( P(A) = \frac{1}{3} \), \( P(B) = \frac{1}{4} \), and \( P(A \cap B) = \frac{1}{5} \), then \( P(B|A) \) is:
A coin is tossed 10 times. The probability of getting exactly six heads is:
If \( P(A) = \frac{6}{11} \), \( P(B) = \frac{5}{11} \), and \( P(A \cup B) = \frac{7}{11} \), then \( P(A \cap B) \) is:
The equation of the \( xy \)-plane is:
The direction cosines of the \( z \)-axis are:
The distance between the points \( (4, 3, 7) \) and \( (1, -1, -5) \) is:
The slope of the tangent to the curve \( y = 2x^P + 3\sin x \) at \( x = 0 \) is:
The rate of change of the area of a circle with respect to its radius \( r \) (in cm\(^2\)/cm) at \( r = 6 \) cm is:
If events \( A \) and \( B \) are independent, then:
The probability of drawing a king from a pack of 52 cards is:
$\text{Molality of 0.8 M H}_2\text{SO}_4 \text{ solution (density 1.06 g cm}^{-3}\text{) is \_\_\_\_\_\_} \times 10^{-3} \, \text{m}.$
10 g of a metal (M) reacts with oxygen to form 11.6 g of oxide. What is the equivalent weight of \( M \)?

A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of 60° by a force of 10 N parallel to the inclined surface as shown in the figure. When the block is pushed up by 10 m along the inclined surface, the work done against frictional force is:

A block of mass 1 kg
\(^{n-1}C_r = (k^2 - 8)  ^{n}C_{r+1}\) if and only if:
Suggest any two measures to solve the problem of ‘land degradation’.
Stephen Spender’s visit to the Gemini Studios was viewed as an unexplained mystery by the Gemini family. How did Asokamitran solve this mystery years later? (Poets and Pancakes)
Which of the following rational number has terminating decimal?