1
BITSAT 2022
MCQ (Single Correct Answer)
+3
-1

Let $$A = \left[ {\matrix{ 1 & { - 1} & 1 \cr 2 & 1 & { - 3} \cr 1 & 1 & 1 \cr } } \right]$$ and $$10B = \left[ {\matrix{ 4 & 2 & 2 \cr { - 5} & 0 & \alpha \cr 1 & { - 2} & 3 \cr } } \right]$$

If B is the inverse of A, then the value of $$\alpha$$ is

A
4
B
$$-$$4
C
3
D
5
2
BITSAT 2022
MCQ (Single Correct Answer)
+3
-1

If $$x \in \left( {0,{\pi \over 2}} \right)$$, then the value of $${\cos ^{ - 1}}\left( {{7 \over 2}(1 + \cos 2x) + \sqrt {({{\sin }^2}x - 48{{\cos }^2}x)\sin x} } \right)$$ is equal to

A
$$x - {\cos ^{ - 1}}(7\cos x)$$
B
$$x + {\sin ^{ - 1}}(7\cos x)$$
C
$$x + {\cos ^{ - 1}}(6\cos x)$$
D
$$x + {\cos ^{ - 1}}(7\cos x)$$
3
BITSAT 2022
MCQ (Single Correct Answer)
+3
-1

A running track of 440 ft is to be laid out enclosing a football field, the shape of which is a rectangle with a semi-circle at each end. If the area of the rectangular portion is to be maximum, then the lengths of its side are

A
70 ft and 110 ft
B
80 ft and 120 ft
C
35 ft and 110 ft
D
35 ft and 120 ft
4
BITSAT 2022
MCQ (Single Correct Answer)
+3
-1

$$\left( {{{dy} \over {dx}}} \right)\tan x = y{\sec ^2}x + \sin x$$, find general solution

A
$$y = \tan x(\log |{\mathop{\rm cosec}\nolimits} x - \cot x| + \cos x + c)$$
B
$$y = {\sec ^2}x + \tan x + c$$
C
$$y = \log |\sec x + \tan x| + {\mathop{\rm cosec}\nolimits} \,x + c$$
D
$$y = {\tan ^2}x + \sin x + c$$
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