NCERT Solutions for Class 12 Maths Exercise 9.5

Class XII Mathematics Ex. 9.5 Solutions are in PDF format updated for new academic session 2024-25 for all students. UP Board students who are following NCERT Books 2024-25 can take the benefits of these solutions. Download NCERT Books and for all subjects and NCERT Solutions Apps for offline use, which work without internet.

NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5 in PDF format to free download based on latest NCERT Books 2024-25. Offline Apps are prepared for new session following the new CBSE Syllabus. Ask your doubts in Discussion forum regarding to CBSE or NIOS board.

1. If A and B are symmetric matrices, such that AB and BA are both defined, then prove that AB – BA is a skew symmetric matrix.
2. 12 cards numbered 1 to 12 (one number on one card), are placed in a box and mixed up thoroughly. Then a card is drawn at random from the box. If it is known that the number on the drawn card is greater than 5, find the probability that the card bears an odd number.
3. Out of 8 outstanding students of a school, in which there are 3 boys and 5 girls, a team of 4 students is to be selected for a quiz competition. Find the probability that 2 boys and 2 girls are selected.
4. In a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?
5. Find the value of x, for which the four points A(x, –1, –1), B(4, 5, 1), C(3, 9, 4) and D(– 4, 4, 4) are coplanar.

1. A ladder 13 m long is leaning against a vertical wall. The bottom of the ladder is dragged away from the wall along the ground at the rate of 2 cm/sec. How fast is the height on the wall decreasing when the foot of the ladder is 5 m away from the wall?
2. Find the vector equation of the plane determined by the points A(3, –1, 2), B(5, 2, 4) and C(–1, –1, 6). Hence, find the distance of the plane, thus obtained, from the origin.
3. An insurance company insured 3000 cyclists, 6000 scooter drivers and 9000 car drivers. The probability of an accident involving a cyclist, a scooter driver and a car driver are 0·3, 0·05 and 0·02 respectively. One of the insured persons meets with an accident. What is the probability that he is a cyclist?
4. Using matrices, solve the following system of linear equations: x + 2y – 3z = – 4, 2x + 3y + 2z = 2, 3x – 3y – 4z = 11.
5. Using the method of integration, find the area of the region bounded by the lines 3x – 2y + 1 = 0, 2x + 3y – 21 = 0 and x – 5y + 9 = 0.

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