1
AIEEE 2005
+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
+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
+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
$${{ - 5} \over {3}}$$
4
AIEEE 2004
+4
-1
The coefficient of $${x^n}$$ in expansion of $$\left( {1 + x} \right){\left( {1 - x} \right)^n}$$ is
A
$${\left( { - 1} \right)^{n - 1}}n$$
B
$${\left( { - 1} \right)^n}\left( {1 - n} \right)$$
C
$${\left( { - 1} \right)^{n - 1}}{\left( {n - 1} \right)^2}$$
D
$$\left( {n - 1} \right)$$
EXAM MAP
Medical
NEET