MAH-MHT CET (PCM/PCB) entrance exam Question Bank Solutions for Mathematics

`"d"/"dx"`[cos (3x + 2)] = ?

The means of two samples of sizes 60 and 120 respectively are 35.4 and 30.9 and the standard deviations are 4 and 5. Obtain the standard deviation of the sample of size 180 obtained by combining the two samples.

Area bounded by the curve y = x⁴, X - axis and ordinates x = 1 and x = 3 is ______.

The derivative of `sqrt(x^2 + 1)` is

If |z₁| = 1, |z₂| = 2, |z₃| = 3 and |9z₁z₂ + 4z₁z₃ + z₂z₃| = 12, then the value of |z₁ + z₂ + z₃| is

If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are ______.

`lim_(x->3) (x^5 - 243)/(x^3 - 27)` = ?

Given 'p' and 'q' as true and 'r' as false, the truth values of p v (q ∧ ~r) and (p → r) ∧ q are respectively

The differential equation whose solution is y = Ae^x + Be^-x, is

The solution of the differential equation `1 + "dy"/"dx" = (sin^2(x + y))/(cos (x + y))` is

The area included between the parabolas y² = 5x and x² = 5y is ______.

If sin(x + y) + cos(x + y) = sin`[cos^-1 (1/3)],` then `"dy"/"dx"` = ?

The particular solution of the differential equation `"y"("dx"/"dy")` = x log x at x = e and y = 1 is ______.

If p, q are true statement and r is false statement, then which of the following statements is a true statement.

`int sin^-1 x`dx = ?

The integrating factor of the differential equation x`"dy"/"dx"` + y log x = x² is ______.

If the sum of the mean and the variance of a binomial distribution for 5 trials Is 1.8, then p = ______.

A line makes angles α, β, γ with the co-ordinate axes and α + β = 90°, then γ = ______.

The area of the region bounded by the curve y = sin x between x = - π and x = `(3pi)/2` is ______.

The general solution of the differential equation (1 + y²) + `(x - e^(tan^-1 y)) "dy"/"dx"` = 0 is.