List of top Questions asked in Maharashtra Board Class XII Exam

Find x, y, z if
\[ \begin{bmatrix} 5 & 1 & 0 \\ 1 & 1 & 1 \end{bmatrix} \begin{bmatrix} 0 & 1 & -2 \\ 1 & -2 & 3 \\ -1 & 1 & 1 \end{bmatrix} \begin{bmatrix} x-1 \\ y+1 \\ 2z \end{bmatrix} = \begin{bmatrix} 2 \\ 1 \end{bmatrix}. \]

A house valued at INR 8,00,000 is insured at 75% of its value. If the rate of premium is 0.80%, find the premium paid by the owner of the house. If agent's commission is 9% of the premium, find agent's commission.

Solve the following L.P.P. by graphical method. Maximize : \(z = 4x + 6y\) Subject to : \(3x + 2y \leq 12\), \(x + y \geq 4\), \(x, y \geq 0\)

Defects on plywood sheet occur at random with the average of one defect per 50 sq.ft. Find the probability that such a sheet has : (a) no defect (b) at least one defect (use \(e^{-1} = 0.3678\))

The equations of two regression lines are \(10x-4y=80\) and \(10y-9x=-40\). Find (a) \(\bar{x}\) and \(\bar{y}\) (b) \(b_{yx}\) and \(b_{xy}\) (c) \(r\) (d) If Var(Y) = 36, obtain var (X).

The amount paid to the holder of the bill after deducting banker's discount is known as ..............

The simplest method of measuring trend of time series is ..............

Quantity index number by weighted aggregate method is given by ..............

A company makes concrete bricks made up of cement and sand. The weight of a concrete brick has to be at least 5 kg. Cement costs INR 20 per kg and sand costs INR 6 per kg. Strength consideration dictate that a concrete brick should contain minimum 4 kg of cement and not more than 2 kg of sand. Formulate the L.P.P. for the cost to be minimum.

Find the mean of number of heads in three tosses of a fair coin.

Five cards are drawn successively with replacement from a well shuffled deck of 52 cards. Find the probability that : (a) all the five cards are spades (b) only 3 cards are spades.

If \( b_{yx} + b_{xy} = 1.30 \) and \( r = 0.75 \) then the given data is inconsistent.

Cyclic variation can occur several times in a year.

Cost of living index number is used in calculating purchasing power of money.

Find the area of the region bounded by the parabola \( y^2 = 25x \) and the line \( x=5 \).

Find the differential equation by eliminating arbitrary constants from the relation \( y = Ae^{3x} + Be^{-3x} \).

Using the truth table, verify \( p \lor (q \land r) \equiv (p \lor q) \land (p \lor r) \).

If \( x = \frac{4t}{1+t^2} \), \( y = 3\left(\frac{1-t^2}{1+t^2}\right) \), then show that \( \frac{dy}{dx} = -\frac{9x}{4y} \).

Divide the number 84 into two parts such that the product of one part and square of the other is maximum.

Solve the following differential equation \( (x^2 - yx^2)dy + (y^2 + xy^2)dx = 0 \).