Q15.) (P) is the plane with Cartesian equation x + y- 3z + 4 = 0 and (S) is a sphere x? + y2 + z2 – 2x + 4y – 4 = 0. The intersection of (S) and (P) is A.) the point I(1, –5,0) B.) the circle of center 2) and radius 3 C.) the circle of center 1(1, -2,0) and radius 2 D.) the circle of center (- and radius 3/10 E.) None of the above 11
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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Answer Q15, 16, 17
![Q15.) (P) is the plane with Cartesian equation x + y – 3z + 4 = 0 and (S) is a sphere x? + y? +
z2 – 2x + 4y – 4 = 0. The intersection of (S) and (P) is
8
25 9
A.) the point I (1, -5,0)
B.) the circle of center
and radius 3
11
25
C.) the circle of center N(1, –2,0) and radius 2 D.) the circle of center
and radius
11
3/10
E.) None of the above
11
Q16.) Consider a discrete random variable, X of values in N such that Vk E N, p(X = k) = ,
where a is a positive real constant. The value of a is:
A.) Ve
B.)
C.) e
D.) Does not exist
E.) None of the above
Q17.) z is a complex number whose modulus is p and whose argument is 0. The modulus and
argument of the complex number z' given by z' = z - (cos+ isin") z in terms of p and 0 are
respectively:
A.) plsine| and pn + 0
В.)
2
plsine|
and 0 – pn C.) p sin (0 +) and (2n]
D.)P sin (0 - and "(7] E.) None of the above](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a6d9c67-6f13-49d2-ac4d-2d996f90a88b%2Fff940828-830e-4ec5-a9b5-5638c73d4946%2F7kxt3ji_processed.jpeg&w=3840&q=75)
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