1
IIT-JEE 2008 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Let $$a,\,b,c$$, $$p,q$$ be real numbers. Suppose $$\alpha ,\,\beta $$ are the roots of the equation $${x^2} + 2px + q = 0$$ and $$\alpha ,{1 \over \beta }$$ are the roots of the equation $$a{x^2} + 2bx + c = 0,$$ where $${\beta ^2} \in \left\{ { - 1,\,0,\,1} \right\}$$

STATEMENT - 1 : $$\left( {{p^2} - q} \right)\left( {{b^2} - ac} \right) \ge 0$$

and STATEMENT - 2 : $$b \ne pa$$ or $$c \ne qa$$

A
STATEMENT - 1 is True, STATEMENT - 2 is True;
STATEMENT - 2 is a correct explanation for
STATEMENT - 1
B
STATEMENT - 1 is True, STATEMENT - 2 is True;
STATEMENT - 2 is NOT a correct explanation for
STATEMENT - 1
C
STATEMENT - 1 is True, STATEMENT - 2 is False
D
STATEMENT - 1 is False, STATEMENT - 2 is True
2
IIT-JEE 2008 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1

Consider all possible permutations of the letters of the word ENDEANOEL. Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.

Column I Column II
(A) The number of permutations containing the word ENDEA is (P) 5!
(B) The number of permutations in which the letter E occurs in the first and the last position is (Q) 2 $$\times$$ 5!
(C) The number of permutations in which none of the letters D, L, N occurs in the last five positions is (R) 7 $$\times$$ 5!
(D) The number of permutations in which the letters A, E, O occur only in odd positions is (S) 21 $$\times$$ 5!

A
(A) - p ; (B) - s; (C) - q ; (D) - q
B
(A) - q ; (B) - q ; (C) - s ; (D) - p
C
(A) - p ; (B) - s; (C) - p ; (D) - r
D
(A) - p ; (B) - r ; (C) - q ; (D) - p
3
IIT-JEE 2008 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Suppose four distinct positive numbers $${a_1},\,{a_{2\,}},\,{a_3},\,{a_4}\,$$ are in G.P. Let $${b_1} = {a_1},{b_2} = {b_1} + {a_2},\,{b_3} = {b_2} + {a_{3\,\,}}\,\,\,and\,\,\,{b_4} = {b_3} + {a_4}$$.

STATEMENT-1: The numbers $${b_1},\,{b_{2\,}},\,{b_3},\,{b_4}\,$$ are neither in A.P. nor in G.P. and

STATEMENT-2 The numbers $${b_1},\,{b_{2\,}},\,{b_3},\,{b_4}\,$$ are in H.P.

A

STATEMENT-1 is True, STATEMENT-2 is True;
STATEMENT-2 is a correct explanation for
STATEMENT-1
B

STATEMENT-1 is True, STATEMENT-2 is True;
STATEMENT-2 is NOT a correct explanation for
STATEMENT-1
C
STATEMENT-1 is True, STATEMENT-2 is False
D
STATEMENT-1 is False, STATEMENT-2 is True
4
IIT-JEE 2008 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Consider

$$\,{L_1}:\,\,2x\,\, + \,\,3y\, + \,p\,\, - \,\,3 = 0$$

$$\,{L_2}:\,\,2x\,\, + \,\,3y\, + \,p\,\, + \,\,3 = 0$$

where p is a real number, and $$\,C:\,{x^2}\, + \,{y^2}\, + \,6x\, - 10y\, + \,30 = 0$$

STATEMENT-1 : If line $${L_1}$$ is a chord of circle C, then line $${L_2}$$ is not always a diameter of circle C
and

STATEMENT-2 : If line $${L_1}$$ is a diameter of circle C, then line $${L_2}$$ is not a chord of circle C.

A
Statement-1 is True, Statement-2 is True; Statement-2 is a correct rexplanation for Statement-1
B
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct rexplanation for Statement-1
C
Statement-1 is True, Statement-2 is False
D
Statement-1 is False, Statement-2 is True
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