SECTION 3 (Maximum Marks: 16)
This section contains TWO questions
Each question contains two columns, Column I and Column II
Column I has four entries
Column – I | Column – II |
A. In R2, if the magnitude of the projection vector of the vector on is and if , then possible value(s) of is (are) | P. 1 |
B. Let a and b be real number such that the function is differentiable for all . Then possible value (s) of a is (are) | Q. 2 |
C. Let be a complex cube root of unit. If , then possible value(s) of n is (are) | R.3 |
D. Let the harmonic mean of two positive real number a and b be 4. If q is a positive real number such that a,5,q,b is an arithmetic progression, then the value(s) of |q-a| is (are) | S.4 |
T.5 |
Text Solution
Verified by ExpertsA
(P, Q), 
(P, Q), 
(P, Q, S, T), 
(Q, T)
… .. (1)
Given 
… .. (2)
From equation (1) and (2), we get 
= 2 or – 1
So | 
| = 1 or 2
For continuity – 3a – 2 = b + a 2
a 2 + 3a + 2 = – b … .. (1)
For differentiability – 6a = b
6a = – b
a 2 – 3a + 2 = 0
a = 1, 2
(3 – 3 
+ 2 
2 ) 4n + 3 + (2 + 3 
– 3 
2 ) 4n + 3 + ( – 3 + 2 
+ 3 
2 ) 4n + 3 = 0
(3 – 3 
+ 2 
2 ) 4n + 3 + ( 
(2 
2 + 3 – 3 
)) 4n + 3 + ( 
2 ( – 3 
+ 2 
2 + 3)) 4n + 3 = 0
(3 – 3 
+ 2 
2 ) 4n + 3 (1 + 
4n + 
8n ) = 0
n 
3k, k 
N
Let a = 5 – d
q = 5 + d
b = 5 + 2d
|q – a| = |2d|
Given 
(5 – d)(5 + 2d) = 2(5 – d + 5 + 2d) = 2(10 + d)
25 + 10d – 5d – 2d2 = 20 + 2d
2d 2 – 3d – 5 = 0
d = – 1, d = 
|2d| = 2, 5
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