List of top Questions asked in Bihar Board XII

Evaluate: \(\displaystyle \int_0^4 \sqrt{x} \, dx = \)
Evaluate: \(\displaystyle \cos^{-1}\left(-\frac{1}{2}\right) = \)
If \( x \in [-1,1] \), then \(\displaystyle \cos^{-1} x = \)
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:
What is circulating capital ?
What are the two functions of middle-level management ?
What is the difference between average cost and marginal cost?
What is the importance of financial planning ?