CBSE(NCERT) GRADE 12 MATHS 2022 SET1

Find the probability that the sum of numbers appearing on both dice is an even number. Find the probability that the number appearing on at least one die is 3.

Probabilities of A and B solving a specific problem are $\frac{3}{2}$ and $\frac{5}{3}$, respectively. If both of them try independently to solve the problem, then find the probability that the problem is solved.

Write the cartesian equation of the line PQ passing through points $P(2, 2, 1)$ and $Q(5, 1, 2)$. Hence, find the $y$-coordinate of the point on the line PQ whose $z$-coordinate is 2.

ABCD is a parallelogram such that $\overrightarrow{AC}=\hat i+\hat j$ and $\overrightarrow{BD}=2\hat i+\hat j+\hat k$. Find $\overrightarrow{AB}$ and $\overrightarrow{AD}$. Also, find the area of the parallelogram ABCD.

(a) Evaluate: $\int_0^1 x \tan^{-1}(x)\,dx$

(b) Find: $\int \frac{dx}{2x^3+3x^2}$

Find the particular solution of the differential equation $(y+3x^2)\frac{dy}{dx}=x$, given that $y=1$ when $x=1$.

(a) Find the equation of the plane passing through points $(2,1,0)$, $(3,2,2)$ and $(1,1,7)$. Also, obtain its distance from the origin.

(b) Find the distance between the lines $\frac{x}{1}=\frac{y}{2}=\frac{z}{3}$ and $\frac{x-1}{1}=\frac{y}{2}=\frac{z}{3}$.

At the start of a cricket match, a coin is tossed and the team winning the toss has the opportunity to choose to bat or bowl. Such a coin is unbiased with equal probabilities of getting head and tail. Based on the above information, answer the following questions: (a) If such a coin is tossed 2 times, then find the probability distribution of number of tails.

Find the probability of getting at least one head in three tosses of such a coin.