Match the following :
Column IColumn II(i) If nCr – 1 = nCr = 35 and nCr + 1 = 21, then r is equal …

Question

Match the following :
Column IColumn II(i) If nCr – 1 = nCr = 35 and nCr + 1 = 21, then r is equal to[A] 7(ii) The product of perpendiculars drawn from (–1, 2) to the pair of lines 2x2 – 5xy + 2y2 = 0 is[B] 5(iii) The square of the length of intercept on the x-axis cut by the pair of lines 2x2 + 5xy + 3y2 + 6x + 7y + 1 = 0 is[C] 4(iv) For a complex number, z (z + ) = 12 – 4 |z|2, then maximum value of |z|2 is equal to[D] 2

CGP EDU Academic Team · Accepted Answer

The correct answer is (i) [C]; (ii) [C]; (iii) [A]; (iv) [C]. Ans.
(i) [C]
(ii) [C]
(iii) [A]
(iv) [C]
Sol. (i) n = 7, r = 4
(ii) p 1 . p 2 =  = 4
(iii) y = 0 ⇒ 2x 2 + 6x + 1 = 0
⇒ x 1 + x 2 = – 3, x 1 x 2 = 
| x 1 – x 2 | 2 = (x 1 + x 2 ) 2 – 4x 1 x 2 = 7
(iv) 2x = 12 – 4 (x 2 + y 2 )
x 2 + y 2 = –  + 3
 + y 2 =  ⇒ max. value of |z| 2 i.e. |z| =  +  = 2
|z
2 | = 4

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Column I	Column II
(i) If nCr – 1 = nCr = 35 and nCr + 1 = 21, then r is equal to	[A] 7
(ii) The product of perpendiculars drawn from (–1, 2) to the pair of lines 2x2 – 5xy + 2y2 = 0 is	[B] 5
(iii) The square of the length of intercept on the x-axis cut by the pair of lines 2x2 + 5xy + 3y2 + 6x + 7y + 1 = 0 is	[C] 4
(iv) For a complex number, z (z + ) = 12 – 4 \|z\|2, then maximum value of \|z\|2 is equal to	[D] 2

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