1
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let a, b, x and y be real numbers such that a $$-$$ b = 1 and y $$\ne$$ 0. If the complex number z = x + iy satisfies $${\mathop{\rm Im}\nolimits} \left( {{{az + b} \over {z + 1}}} \right) = y$$, then which of the following is(are) possible value(s) of x?
A
$$1 - \sqrt {1 + {y^2}}$$
B
$$- 1 - \sqrt {1 - {y^2}}$$
C
$$1 + \sqrt {1 + {y^2}}$$
D
$$- 1 + \sqrt {1 - {y^2}}$$
2
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
If $$2x - y + 1 = 0$$ is a tangent to the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {16}} = 1$$ then which of the following CANNOT be sides of a right angled triangle?
A
a, 4, 1
B
2a, 4, 1
C
a, 4, 2
D
2a, 8, 1
3
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let [x] be the greatest integer less than or equals to x. Then, at which of the following point(s) the function $$f(x) = x\cos (\pi (x + [x]))$$ is discontinuous?
A
x = $$-$$ 1
B
x = 1
C
x = 0
D
x = 2
4
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Which of the following is(are) NOT the square of a 3 $$\times$$ 3 matrix with real entries?
A
$$\left[ {\matrix{ 1 & 0 & 0 \cr 0 & 1 & 0 \cr 0 & 0 & { - 1} \cr } } \right]$$
B
$$\left[ {\matrix{ 1 & 0 & 0 \cr 0 & { - 1} & 0 \cr 0 & 0 & { - 1} \cr } } \right]$$
C
$$\left[ {\matrix{ { - 1} & 0 & 0 \cr 0 & { - 1} & 0 \cr 0 & 0 & { - 1} \cr } } \right]$$
D
$$\left[ {\matrix{ 1 & 0 & 0 \cr 0 & 1 & 0 \cr 0 & 0 & 1 \cr } } \right]$$
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