List of top Questions asked in CBSE CLASS XII

In an LPP, if the objective function \( Z = ax + by \) has the same maximum value on two corner points of the feasible region, then the number of points at which the maximum value of \( Z \) occurs is:
The graph of the inequation \( 2x + 3y>6 \) is the:
What sum of money should be deposited at the end of every 6 months to accumulate ₹ 50,000 in 8 years, if money is worth 6% p.a. compounded semi-annually?
\[ \text{{Given: }} (1.03)^{16} = 1.6047 \]

Using flat rate method, the EMI to repay a loan of ₹ 20,000 in \( 2 \frac{1}{2} \) years at an interest rate of 8% p.a. is:

For the given values 23, 32, 40, 47, 58, 38, 42; the 5-yearly moving averages are:
What time will it be after 1275 hours, if the present time is 9:00 p.m.?
A fair coin is tossed twice and outcomes are noted. If the random variable \( X \) represents the number of heads that appeared in the experiment, then the mathematical expectation of \( X \) is:
The order and degree of the differential equation \[ y \, dx + x \, \log{\left(\frac{y}{x}\right)} \, dy - 2x \, dy = 0 \] are respectively:
The function \( f(x) = x^2 - x + 1 \) is:
The value of \[ \Delta = \begin{vmatrix} 42 & 2 & 5 \\ 79 & 7 & 9 \\ 29 & 5 & 3 \end{vmatrix} \] is:
Amrita buys a car for which she makes a down payment of ₹ 2,50,000 and the balance is to be paid in 2 years by monthly installments of ₹ 25,448 each. If the financer charges interest at the rate of 20\% p.a., find the actual price of the car.
[Given \( \left(\frac{61}{60}\right)^{-24} = 0.67253 \)]
Give a linear equation that describes the computer system's book value at the end of \( t \)th year, where \( 0 \leq t \leq 3 \).
What is the rate of depreciation?
What will be the computer system's book value at the end of the first year and a half?
Given that the scores of a set of candidates on an IQ test are normally distributed, if the IQ test has a mean of 100 and a standard deviation of 10, determine the probability that a candidate who takes the test will score between 90 and 110.
[Given \( P(Z<1) = 0.8413 \) and \( P(Z<-1) = 0.1587 \)]
A container has 50 litres of juice in it. 5 litres of juice is taken out and is replaced by 5 litres of water. This process is repeated 4 more times. Determine the quantity of juice in the container after final replacement.
[Use \( (0.9)^5 = 0.59049 \)]
Assume an investment’s starting value is ₹ 20,000 and it grows to ₹ 50,000 in 3 years. Calculate CAGR (Compounded Annual Growth Rate).
[Use: \( (2.5)^{1/3} = 1.355 \)]
For testing the significance of the difference between the means of two independent samples, the degree of freedom (\( v \)) is taken as:
A mobile phone costs ₹ 12,000 and its scrap value after a useful life of 3 years is ₹ 3,000. Then, the book value of the mobile phone at the end of 2 years is:
If for a Poisson variate \( X \), \( P(X = k) = P(X = k + 1) \), then the variance of \( X \) is:
If the calculated value of \( |t|<t_v(\alpha) \) (critical value of \( t \)), then the null hypothesis:
If \( y = e^{-2x} \), then \( \frac{d^3y}{dx^3} \) is equal to:
If \( AB = A \) and \( BA = B \), then \( (B^2 + B) \) equals:
If \( x>y \) and \( z<0 \), then:
In a 1 km race, player P beats player Q by 18 metres or 9 seconds. What is P's time to complete the race?