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JEE Mathematics Solved Question Paper 2004

Match The Following

$α, β, γ$ are the roots of the equation x³ - 10x² + 7x + 8=0. Match the following and choose the correct answer.

$A . α + β + γ (1) - \frac{43}{7} B . α^{2} + β^{2} + γ^{2} (2) - \frac{7}{8} C . \frac{1}{α} + \frac{1}{β} + \frac{1}{γ} (3) 86 D . \frac{α}{βγ} + \frac{β}{γα} + \frac{γ}{αβ} (4) 0 (10)$

A. A B C D	(i) 5 3 1 2
B. A B C D	(ii) 4 3 1 2
C. A B C D	(iii) 5 3 2 1
D. A B C D	(iv) 5 2 3 1

Match the following elements of $[\begin{matrix} 1 & - 1 & 0 \\ 0 & 4 & 2 \\ 3 & - 4 & 6 \end{matrix}]$ with their co-factors and choose the correct answer

$Element Co - factor A - 1 (1) - 2 B 1 (2) 32 C 3 (3) 4 D 6 (4) 6 (5) - 6$

A. A B C D	(i) 2 4 1 3
B. A B C D	(ii) 2 4 3 1
C. A B C D	(iii) 4 2 1 3
D. A B C D	(iv) 4 1 2 3

Match the points on the curve 2y² = x + 1 with the slopes of normals at those points and choose the correct answer.

Point Slope of the normal

A (7, 2) 1 - 4 $\sqrt{2}$

B (0, $\frac{1}{\sqrt{2}}$ ) 2 - 8

C (1, - 1) 3, 4

D (3, $\sqrt{2}$ ) 4, 0

A. A B C D	(i) 2 4 3 1
B. A B C D	(ii) 2 5 3 1
C. A B C D	(iii) 2 3 5 1
D. A B C D	(iv) 2 5 1 3

Multiple Choice Questions

$If f : N \to Z is defined by f (n) = \{2 if n = 3 k, k \in Z 10 if n = 3 k + 1, k \in Z 0 if n = 3 k + 2, k \in Z\} Then, \{n \in N : f (n) > 2\} is equal to$

{3, 6, 4}
{1, 4, 7}
{4, 7}
{7}

The value of $\sqrt{42 + \sqrt{42 + \sqrt{42 + . . .}}}$ is equal to

$If \log_{27} (\log_{3} (x)) = \frac{1}{3}, then the value of x is$

S₁, S₃, ...... ,S₁₀are the speakers in a conference. If S₁addresses only after S₂,then the number of ways the speakers address iS

10!
9!
$10! \times 8!$
$\frac{10!}{2}$

The number of positive odd divisors of 216 is

9.
The binomial coefficients which are in decreasing order are

$^{15} C_{5,}^{15} C_{6,}^{15} C_{7,}$

$^{15} C_{10},^{15} C_{9},^{15} C_{8}$

$^{15} C_{6},^{15} C_{7},^{15} C_{8}$

$^{15} C_{7},^{15} C_{6},^{15} C_{5}$

$^{15} C_{7},^{15} C_{6},^{15} C_{5}$

$The series of binomial coefficient is^{15} C_{0},^{15} C_{1},^{15} C_{2} . . .^{15} C_{7},^{15} C_{8},^{15} C_{9} . . .^{15} C_{14},^{15} C_{15} \underset{decreasing}{\to} greatest \underset{decreasing}{\to} Form the above discussion, we can say that decreasing series^{15} C_{7},^{15} C_{6},^{15} C_{5} therefore option (d) is correct$