1
JEE Advanced 2015 Paper 1 Offline
Numerical
+4
-0
The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least $$0.96,$$ is
2
JEE Advanced 2015 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
In $${R^3},$$ consider the planes $$\,{P_1}:y = 0$$ and $${P_2}:x + z = 1.$$ Let $${P_3}$$ be the plane, different from $${P_1}$$ and $${P_2}$$, which passes through the intersection of $${P_1}$$ and $${P_2}.$$ If the distance of the point $$(0,1, 0)$$ from $${P_3}$$ is $$1$$ and the distance of a point $$\left( {\alpha ,\beta ,\gamma } \right)$$ from $${P_3}$$ is $$2,$$ then which of the following relations is (are) true?
A
$$2\alpha + \beta + 2\gamma + 2 = 0$$
B
$$2\alpha - \beta + 2\gamma + 4 = 0$$
C
$$2\alpha + \beta - 2\gamma - 10 = 0$$
D
$$2\alpha - \beta + 2\gamma - 8 = 0$$
3
JEE Advanced 2015 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
In $${R^3},$$ let $$L$$ be a straight lines passing through the origin. Suppose that all the points on $$L$$ are at a constant distance from the two planes $${P_1}:x + 2y - z + 1 = 0$$ and $${P_2}:2x - y + z - 1 = 0.$$ Let $$M$$ be the locus of the feet of the perpendiculars drawn from the points on $$L$$ to the plane $${P_1}.$$ Which of the following points lie (s) on $$M$$?
A
$$\left( {0, - {5 \over 6}, - {2 \over 3}} \right)$$
B
$$\left( { - {1 \over 6}, - {1 \over 3},{1 \over 6}} \right)$$
C
$$\left( { - {5 \over 6},0,{1 \over 6}} \right)$$
D
$$\left( { - {1 \over 3},0,{2 \over 3}} \right)$$
4
JEE Advanced 2015 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$\Delta PQR$$ be a triangle. Let $$\vec a = \overrightarrow {QR} ,\vec b = \overrightarrow {RP}$$ and $$\overrightarrow c = \overrightarrow {PQ} .$$ If $$\left| {\overrightarrow a } \right| = 12,\,\,\left| {\overrightarrow b } \right| = 4\sqrt 3 ,\,\,\,\overrightarrow b .\overrightarrow c = 24,$$ then which of the following is (are) true?
A
$${{{{\left| {\overrightarrow c } \right|}^2}} \over 2} - \left| {\overrightarrow a } \right| = 12$$
B
$${{{{\left| {\overrightarrow c } \right|}^2}} \over 2} + \left| {\overrightarrow a } \right| = 30$$
C
$$\left| {\overrightarrow a \times \overrightarrow b + \overrightarrow c \times \overrightarrow a } \right| = 48\sqrt 3$$
D
$$\overrightarrow a .\overrightarrow b = - 72$$
EXAM MAP
Medical
NEET