1
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
For natural numbers $$m$$ , $$n$$, if $${\left( {1 - y} \right)^m}{\left( {1 + y} \right)^n}\,\, = 1 + {a_1}y + {a_2}{y^2} + ..........$$ and $${a_1} = {a_2} = 10,$$ then $$\left( {m,\,n} \right)$$ is
A
$$\left( {20,\,45} \right)$$
B
$$\left( {35,\,20} \right)$$
C
$$\left( {45,\,35} \right)$$
D
$$\left( {35,\,45} \right)$$
2
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
The value of $$\,{}^{50}{C_4} + \sum\limits_{r = 1}^6 {^{56 - r}} {C_3}$$ is
A
$${}^{55}{C_4}$$
B
$${}^{55}{C_3}$$
C
$${}^{56}{C_3}$$
D
$${}^{56}{C_4}$$
3
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
If the coefficient of $${x^7}$$ in $${\left[ {a{x^2} + \left( {{1 \over {bx}}} \right)} \right]^{11}}$$ equals the coefficient of $${x^{ - 7}}$$ in $${\left[ {ax - \left( {{1 \over {b{x^2}}}} \right)} \right]^{11}}$$, then $$a$$ and $$b$$ satisfy the relation
A
$$a - b = 1$$
B
$$a + b = 1$$
C
$${a \over b} = 1$$
D
$$ab = 1$$
4
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
$${x \over 2} - {3 \over 8}{x^2}$$
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