Mathematics NDA/NA SOLVED PAPER 2021-II (51 to 100)

Total Questions: 50

21. Consider the following relations for two events E and F:

1. P(E ∩ F) > P(E) + P(F) - 1
2. P(E ∪ F) = P(E) + P(F) +P(E ∩ F)
3. P(E ∪ F) < P(E) + P(F)
Which of the above relations is/are correct?

Correct Answer: (c) 1 and 3 only
Solution:

22. If P(A | B)< P(A), then which one of the following is correct?

Correct Answer: (a) P(B | A) < P(B)
Solution:

23. When the measure of central tendency is available in the form of mean, which one of the following is the most reliable and accurate measure of variability?

Correct Answer: (c) Standard deviation
Solution:Coefficient of variation ( C.V.)= S.D /mean × 100
We know that the series having greater C.V. is said to be more variable.

24. A problem is given to three students A, B and C, whose probabilities of solving the problem independently are 1/2, 3/4 and p respectively. If the probability that the problem can be solved is 29/32, then what is the value of p?

Correct Answer: (d) 1/4
Solution:

25. In a cricket match, a batsman hits a six 8 times out of 60 balls he plays. What is the probability that on a ball played he does not hit a six?

Correct Answer: (d) 13/15
Solution:Let probability of hitting P(H) = 8/60
P(H') = 1 - 8/60 = 52/60 = 13/15

26. The locus of a point P(x, y, z) which moves in such a way that z = 7 is a

Correct Answer: (d) plane parallel to xy-plane
Solution:The locus of a point P(x, y, z) which moves in such a way that z = 7 is a plane parallel to xy plane at distance 7 unit from xy plane.

27. Consider the following statements:

1. A line in space can have infinitely many direction ratios.
2. It is possible for certain line that the sum of the squares of direction cosines can be equal to sum of its direction cosines.
Which of the above statements is/are correct?

Correct Answer: (c) Both 1 and 2
Solution:There are infinitely many different line present in space with different direction ratios.
So, statement 1 is correct
1² + 1²+ 1² = 1 + 1 + 1 so, line have direction cosines 1, 1, 1. Such that sum of the squares of direction cosines can be equal to sum of its direction cosines.

28. The xy-plane divides the line segment joining the points (-1, 3, 4) and (2, -5, 6)

Correct Answer: (c) externally in the ratio 2: 3
Solution:

29. The number of spheres of radius r touching the coordinate axes is

Correct Answer: (c) 8
Solution:There are 8 octants in coordinate system so, 8 spheres of radius r touching the coordinate axes.

30. ABCDEFGH is a cuboid with base ABCD. Let 4(0, 0, 0) B (12, 0, 0), C(12, 6, 0) and G(12, 6, 4) be the vertices. If α is the angle between AB and AG; β is the angle between AC and AG, then what is the value of cos 2α + cos 2β?

Correct Answer: (b) 64/49
Solution: