32. . Let f be a function which is continuous on the closed interval [a.b] and differentiahle on the open interval (a.b) such that f(a) = f(b). The Rolle's theorem states that [A) There exists ce (a,b) such that S'(c) = 0 [B] There exists ce[a,b] such that f'(c) = 0 (C) There exists ce(a,b) such that f(c) = (6)=T(-)- b-a (D] There exists ee[a,b] such that b-a 33. A position vectörs of two points P and Q are p= Si-j-k and q = 4i- 3j + 6k respectively. The vect equation of the line through P and Q is (A]. r= Si-j-k+2(4i–3j+6k)) (B] r= Si-j-k+ 2(-i-2j+?k) ) (C) r=-i-2j+7k+ 2(-i-2j+7k). (D]-r=-i-2j-7k +2(4i– 3j+6k«)
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.
Show all working explaining detailly each step
Answer must be typewritten with a computer keyboard!
Answer 32, 33
![32. ·
Let f be a function which is continuous on the closed
interval [a,b] and differentiatle on the open
interval (a,b) such that f(a) = f(b). The Rolle's
theorem states that
[A] There exists ce(a,b) such that f'(e) = 0
[B] There exists ee[a,b] such that f'(c) = 0
(C] There exists ce (a,b) such
that f'(c) = L6)-T (1) -
b-a
[D] There exists ce[a.b] such that
j'(c)=
S(b)- S(a)
b-a
33.
A position vectors of two points P and Q are
p= 5i-j-k and q = 4i-3j + 6k respectively. The vect-
equation of the line through P andQ is
[A] . r= Si-j-k+2(4i-3j+ 6k))
[B] r= Si-j-k+2(-i-2j+7k) )
(C]
r=-i-2j+7k+ 2(--i-2j+7k).
[D]---r=-i-2j- 7k+2(4i– 3j+6k)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4957fe4-4c01-40d3-938e-f3efa5fe6d1c%2F60268687-d4ae-4562-8b37-dac4b5e79781%2Febw2bh_processed.jpeg&w=3840&q=75)
Step by step
Solved in 2 steps
