List of top Mathematics Questions asked in CBSE CLASS XII

A bag contains 4 red and 4 black balls,another bag contains 2 red and 6 black balls.One of the two bags is selected at random and a ball is drawn from the bag which is found to be red.Find the probability that the ball is drawn from the first bag.

Show that the points (2,3,4),(-1,-2,1),(5,8,7)are collinear.

The probability of obtaining an even prime number on each die when a pair of dice is rolled is:

Find \(\frac {dy}{dx}\): \(ax+by^2=cos\ y\)

If \(A\) and \(B\) are two events such that \(P(A)=\frac{1}{4},P(B)=\frac{1}{2}\) and \(P(A∩B)=\frac{1}{8}\),find \(P\) (not \(A\) and not \(B\)).

Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.

Find the intervals in which the following functions are strictly increasing or decreasing:
\((a) x^2 + 2x − 5 \)
\((b) 10 − 6x − 2x^2 \)
\((c) −2x^3 − 9x^2 − 12x + 1 \)
\((d) 6 − 9x − x^2 \)
\((e) (x + 1)^3 (x − 3)^3\)

A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10cm.

The integrating factor of the differential equation.
\((1-y^{2})\frac{dx}{dy}+yx=ay\)\((-1<y<1)\)\(is\)

Find the integrals of the function: \(sin^3 (2x+1)\)

Find a particular solution satisfying the given condition: \(\frac {dy}{dx}+2y\ tan\ x=sin\ x;\ y=0\ when \ x=\frac \pi3\)

Find general solution: \((x+3y^2) \frac {dy}{dx} = y,\ (y>0)\)

In a culture,the bacteria count is 1,00,000.The number is increased by \(10\%\) in 2 hours. In how many hours will the count reach 2,00,000,if the rate of growth of bacteria is proportional to the number present?

In a bank,principal increases continuously at the rate of \(5\%\) per year. An amount of Rs1000 is deposited with this bank,how much will it worth after 10years\((e^{0.5}=1.648)\).

In a bank principal increases continuously at the rate of \(r\%\) per year.Find the value of \(r\) is Rs100 doubles itself in 10years\((log_e2=0.6931).\)

At any point \((x,y)\) of a curve,the slope of a tangent is twice the slope of the line segment joining the point of contact to the point \((-4,-3)\).Find the equation of the curve given that it passes through \((-2,1)\).

Find the equation of a curve passing through the point \((0,-2)\) given that at any point \((x,y)\) on the curve,the product of the slope of its tangent and y-coordinate of the point is equal to the x-coordinate of the point.

Find the equation of the curve passing through the point \((0,\frac \pi4) \)whose differential equation is, \(sin\ x cos \ y\ dx+cos\ xsin\ y\ dy=0\)

Find the equation of a curve passing through the point \((0,2)\) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.

For the differential equations, find a particular solution satisfying the given condition:\(cos(\frac{dy}{dx})=α(α∈R);y=1\) when x=0

For the differential equations, find the general solution: \(x^5\frac{dy}{dx}=-y^5\)