1
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
If $$x$$ is so small that $${x^3}$$ and higher powers of $$x$$ may be neglected, then $${{{{\left( {1 + x} \right)}^{{3 \over 2}}} - {{\left( {1 + {1 \over 2}x} \right)}^3}} \over {{{\left( {1 - x} \right)}^{{1 \over 2}}}}}$$ may be approximated as
A
$$1 - {3 \over 8}{x^2}$$
B
$$3x + {3 \over 8}{x^2}$$
C
$$ - {3 \over 8}{x^2}$$
D
$${x \over 2} - {3 \over 8}{x^2}$$
2
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
If the coefficients of rth, (r+1)th, and (r + 2)th terms in the binomial expansion of $${{\rm{(1 + y )}}^m}$$ are in A.P., then m and r satisfy the equation
A
$${m^2} - m(4r - 1) + 4\,{r^2} - 2 = 0$$
B
$${m^2} - m(4r + 1) + 4\,{r^2} + 2 = 0$$
C
$${m^2} - m(4r + 1) + 4\,{r^2} - 2 = 0$$
D
$${m^2} - m(4r - 1) + 4\,{r^2} + 2 = 0$$
3
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
Let $$S(K)$$ $$ = 1 + 3 + 5... + \left( {2K - 1} \right) = 3 + {K^2}.$$ Then which of the following is true
A
Principle of mathematical induction can be used to prove the formula
B
$$S\left( K \right) \Rightarrow S\left( {K + 1} \right)$$
C
$$S\left( K \right) \ne S\left( {K + 1} \right)$$
D
$$S\left( 1 \right)$$ is correct
4
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
The coefficient of the middle term in the binomial expansion in powers of $$x$$ of $${\left( {1 + \alpha x} \right)^4}$$ and $${\left( {1 - \alpha x} \right)^6}$$ is the same if $$\alpha $$ equals
A
$${3 \over 5}$$
B
$${10 \over 3}$$
C
$${{ - 3} \over {10}}$$
D
$${{ - 5} \over {3}}$$
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