NCERT Solutions for Class 12 Maths Exercise 9.3

Class XII Mathematics Ex. 9.3 solutions are free to download updated for new academic session 2025-26 for those students who are following NCERT Books. Download NCERT Solutions for other subjects or NCERT Solutions Apps for offline use, which work without internet. All the solutions are applicable for UP board and other state board’s students also.

NCERT Solutions for Class 12 Maths Exercise 9.3 of Differential Equations is given below based on latest NCERT Books 2025-26. For other exercises, please visit to 12 Maths Chapter 9 solutions page. Join the discussion forum to ask your doubts in NIOS or CBSE boards.

1. There are three coins. One is a two-headed coin, another is a biased coin that comes up heads 75% of the time and the third is an unbiased coin. One of the three coins is chosen at random and tossed. If it shows heads, what is the probability that it is the two-headed coin?
2. Find the equation of the line passing through (2, – 1, 2) and (5, 3, 4) and of the plane passing through (2, 0, 3), (1, 1, 5) and (3, 2, 4). Also, find their point of intersection.
3. Find the vector and Cartesian equations of the plane passing through the points having position vectors i + j – 2k, 2i – j + k and i + 2j + k. Write the equation of a plane passing through a point (2, 3, 7) and parallel to the plane obtained above. Hence, find the distance between the two parallel planes.
4. If a line has the direction ratios – 18, 12, – 4, then what are its direction cosines?
5. Form the differential equation representing the family of curves y² = m (a² – x²) by eliminating the arbitrary constants ‘m’ and ‘a’.

1. Mother, father and son line up at random for a family photo. If A and B are two events given by A = Son on one end, B = Father in the middle, find P(B/A).
2. Let X be a random variable which assumes values x1, x2, x3, x4 such that 2P(X = x1) = 3P(X = x2) = P(X = x3) = 5P(X = x4). Find the probability distribution of X.
3. A coin is tossed 5 times. Find the probability of getting (i) at least 4 heads, and (ii) at most 4 heads.
4. Show that the relation R on the set Z of all integers, given by R = {(a, b): 2 divides (a – b)} is an equivalence relation.
5. Show that the height of a cylinder, which is open at the top, having a given surface area and greatest volume, is equal to the radius of its base.

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