The half-life of a radioactive nucleus is 5 years. The fraction of the original sample that would decay in 15 years is:
A body is released from a height equal to the radius (r) of the earth. The velocity of the body when it strikes the surface of the earth will be:
If the total charge stored in capacitors is equal to 100μc, then find the value of x. (10V)
Match the list-I with list-II and choose the correct option.
There are 5 black and 3 white balls in the bag. A die is rolled, we need to pick the number of balls appearing on the die. The probability that the balls are white is?
The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded as 50 instead of 40. Then the correct variance is:
\[ f(x) = \log_e \left( 4x^2 + 11x + 6 \right) + \sin^{-1} \left( 4x + 3 \right) + \cos^{-1} \left( \frac{10x + 6}{3} \right) \]then \( 36|\alpha + \beta| \) is equal to:
The total number of three-digit numbers, divisible by 3, which can be formed using the digits 1,3,5,8, if repetition of digits is allowed, is
Let the determinant of a square matrix A of order \( m \) be \( m - n \), where \( m \) and \( n \) satisfy \( 4m + n = 22 \) and \( 17m + 4n = 93 \). If \( \text{det} (n \, \text{adj}(\text{adj}(mA))) = 3^a 5^b 6^c \), then \( a + b + c \) is equal to:
