List of top Mathematics & Statistics Questions asked in Maharashtra Board Class XII Exam

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.
The amount paid to the holder of the bill after deducting banker's discount is known as ..............
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.
Quantity index number by weighted aggregate method is given by ..............
Find the mean of number of heads in three tosses of a fair coin.
Moving averages are useful in identifying
If \( b_{yx} + b_{xy} = 1.30 \) and \( r = 0.75 \) then the given data is inconsistent.
The objective of an assignment problem is to assign
If \(P_{01}(L)=90\) and \(P_{01}(P)=40\), then \(P_{01}(D-B)\) is ..............
The expected value of the sum of two numbers obtained when two fair dice are rolled is ..............
Cost of living index number is used in calculating purchasing power of money.
Cyclic variation can occur several times in a year.
Divide the number 84 into two parts such that the product of one part and square of the other is maximum.
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 \( \frac{dy}{dx} = -\frac{9x}{4y} \).
Solve the following differential equation \( (x^2 - yx^2)dy + (y^2 + xy^2)dx = 0 \).
An agent who gives guarantee to his principal that the party will pay the sale price of goods is called --
Find the differential equation by eliminating arbitrary constants from the relation \( y = Ae^{3x} + Be^{-3x} \).
In an ordinary annuity, payments or receipts occur at
Find the area of the region bounded by the parabola \( y^2 = 25x \) and the line \( x=5 \).
Write the converse, inverse and contrapositive of the statement "If a triangle is equilateral then it is equiangular".
If \( f'(x) = x^2 + 5 \) and \( f(0) = -1 \) then \( f(x) = ..............\)
Find \( \frac{dy}{dx} \) if \( y = x^x + a^x \).
Solve the following equations by the method of inversion: \( 2x-y+z=1 \), \( x+2y+3z=8 \), \( 3x+y-4z=1 \).
\( \int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx = ............. + c \)