KVPY Government Jobs Exams

The sum of (1^2 – 1 + 1)(1!) + (2^2 – 2 + 1)(2!) + …. + (n^2 – n + 1)(n!) is

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KVPY Other Question

Let a b cr r r , , be three vectors in the xyz space such that a ×b = b × c = c × a ≠ 0 r r r r r r If A, B, C are points with
position vectors a b cr r r , , respectively, then the number of possible positions of the centroid of triangle ABC is A narrow but tall cabin is falling freely near the earth's surface. Inside the cabin, two small stones A and B
are released from rest (relative to the cabin). Initially A is much above the centre of mass and B much below
the centre of mass of the cabin. A close observation of the motion of A and B will reveal that -
(A) both A and B continue to be exactly at rest relative to the cabin
(B) A moves slowly upward and B moves slowly downward relative to the cabin
(C) both A and B fall to the bottom of the cabin with constant acceleration due to gravity
(D) A and B move slightly towards each other vertically