If a→ and b→ are unit vec

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsShort Answer Type

21.

Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD = 8 m, BC = 11 m and AB = 10 m; then the distance (in meters) of a point M on AB from the point A such that MD2 + MC2 is minimums is ___


22.

Set A has m elements and Set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m - n is _____


23.

Let f : R   R be defined asfx = x5sin1x + 5x2, x < 00, x = 0x5cos1x + λx2, x > 0The value of λ for which f''0 exists, is


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24.

If a and b are unit vectors, then the greatest value of 3a + b + a - b = ?


Ans : 4

Let a  b = α3a + b + a - b = 32 + 2cosα= 32 × 2cos2α2  + 2 × 2sin2α2= 23cosα2 + sinα2Maximum value = 22 = 4


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25.

The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45°. After waling a distance of 80 meters towards the top, up a slope inclined at angle of 30° to the horizontal plane the angle of elevation of the top of the hill becomes 75°. Then the height of the hill (in meters) is _____.


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