1
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
$$\left[ {\matrix{ 1 & 0 & 0 \cr 0 & 1 & 0 \cr 0 & 0 & 1 \cr } } \right]$$
2
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
If a chord, which is not a tangent, of the parabola y2 = 16x has the equation 2x + y = p, and mid-point (h, k), then which of the following is(are) possible value(s) of p, h and k?
A
p = $$-$$1, h = 1, k = $$-$$3
B
p = 2, h = 3, k = $$-$$4
C
p = $$-$$2, h = 2, k = $$-$$4
D
p = 5, h = 4, k = $$-$$3
3
JEE Advanced 2017 Paper 1 Offline
Numerical
+3
-0
For a real number $$\alpha$$, if the system

$$\left[ {\matrix{ 1 & \alpha & {{\alpha ^2}} \cr \alpha & 1 & \alpha \cr {{\alpha ^2}} & \alpha & 1 \cr } } \right]\left[ {\matrix{ x \cr y \cr z \cr } } \right] = \left[ {\matrix{ 1 \cr { - 1} \cr 1 \cr } } \right]$$

of linear equations, has infinitely many solutions, then 1 + $$\alpha$$ + $$\alpha$$2 =
4
JEE Advanced 2017 Paper 1 Offline
Numerical
+3
-0
The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side?