1
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
2
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 =
3
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?
4
JEE Advanced 2017 Paper 1 Offline
Numerical
+3
-0
Let f : R $$\to$$ R be a differentiable function such that f(0) = 0, $$f\left( {{\pi \over 2}} \right) = 3$$ and f'(0) = 1.

If $$g(x) = \int\limits_x^{\pi /2} {[f'(t)\text{cosec}\,t - \cot t\,\text{cosec}\,t\,f(t)]dt}$$

for $$x \in \left( {0,\,{\pi \over 2}} \right]$$, then $$\mathop {\lim }\limits_{x \to 0} g(x)$$ =
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