1
IIT-JEE 1995 Screening
MCQ (Single Correct Answer)
+2
-0.5
$$\,3{\left( {\sin x - \cos x} \right)^4} + 6{\left( {\sin x + \cos x} \right)^2} + 4\left( {{{\sin }^6}x + {{\cos }^6}x} \right) = $$
A
11
B
12
C
13
D
14
2
IIT-JEE 1995 Screening
MCQ (Single Correct Answer)
+1
-0.25
The value of $$\int\limits_\pi ^{2\pi } {\left[ {2\,\sin x} \right]\,dx} $$ where [ . ] represents the greatest integer function is
A
$${{ - 5\pi } \over 3}$$
B
$$\pi $$
C
$${{ 5\pi } \over 3}$$
D
$$ - 2\pi $$
3
IIT-JEE 1995 Screening
MCQ (Single Correct Answer)
+3
-0.75
The value of the integral $$\int {{{{{\cos }^3}x + {{\cos }^5}x} \over {{{\sin }^2}x + {{\sin }^4}x}}} \,dx\,$$ is
A
$$\sin x - 6{\tan ^{ - 1}}\left( {\sin x} \right) + c$$
B
$$\sin x - 2{\left( {\sin x} \right)^{ - 1}} + c$$
C
$$\sin x - 2{\left( {\sin x} \right)^{ - 1}} - 6{\tan ^{ - 1}}\left( {\sin x} \right) + c$$
D
$$\,\sin x - 2{\left( {\sin x} \right)^{ - 1}} + 5{\tan ^{ - 1}}\left( {\sin x} \right) + c$$
4
IIT-JEE 1995 Screening
MCQ (Single Correct Answer)
+1
-0.25
The slope of the tangent to a curve $$y = f\left( x \right)$$ at $$\left[ {x,\,f\left( x \right)} \right]$$ is $$2x+1$$. If the curve passes through the point $$\left( {1,2} \right)$$, then the area bounded by the curve, the $$x$$-axis and the line $$x=1$$ is
A
$${5 \over 6}$$
B
$${6 \over 5}$$
C
$${1 \over 6}$$
D
$$6$$
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