1
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
If $${\cos ^{ - 1}}x - {\cos ^{ - 1}}{y \over 2} = \alpha ,$$ then $$4{x^2} - 4xy\cos \alpha + {y^2}$$ is equal to :
A
$$2\sin 2\alpha $$
B
$$4$$
C
$$4{\sin ^2}\alpha $$
D
$$-4{\sin ^2}\alpha $$
2
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
The value of integral, $$\int\limits_3^6 {{{\sqrt x } \over {\sqrt {9 - x} + \sqrt x }}} dx $$ is
A
$${1 \over 2}$$
B
$${3 \over 2}$$
C
$$2$$
D
$$1$$
3
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
The differential equation representing the family of curves $${y^2} = 2c\left( {x + \sqrt c } \right),$$ where $$c>0,$$ is a parameter, is of order and degree as follows:
A
order $$1,$$ degree $$2$$
B
order $$1,$$ degree $$1$$
C
order $$1,$$ degree $$3$$
D
order $$2,$$ degree $$2$$
4
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
If $$x{{dy} \over {dx}} = y\left( {\log y - \log x + 1} \right),$$ then the solution of the equation is :
A
$$y\log \left( {{x \over y}} \right) = cx$$
B
$$x\log \left( {{y \over x}} \right) = cy$$
C
$$\log \left( {{y \over x}} \right) = cx$$
D
$$\log \left( {{x \over y}} \right) = cy$$
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