﻿ Engineering Entrance Exam Question and Answers | Introduction To Three Dimensional Geometry - Zigya

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# Introduction To Three Dimensional Geometry

#### Multiple Choice Questions

1.

The number of common tangent to the circles x2+y2-4x-6y-12=0 and x2+y2+6x+18y+26 = 0 is

• 1

• 2

• 3

• 3

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2.

The angle between the lines whose direction cosines satisfy the equations l +m+n=0 and l2 = m2+n2 is

• π/3

• π/4

• π/6

• π/6

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3.

If PS is the median of the triangle with vertices P(2,1), Q(6,-1) and R (7,3), then equation of the line passing through (1,-1) and parallel to PS is

• 4x-7y - 11 =0

• 2x+9y+7=0

• 4x+7y+3 = 0

• 4x+7y+3 = 0

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4.

Let a,b,c and d be non-zero numbers. If the point of intersection of the lines 4ax +2ay +c= 0 and 5bx +2by +d = 0 lies in the fourth quadrant and is equidistant from the two axes, then

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5.

The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1) (1, 1) and (1, 0) is

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6.

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector.Then the maximum area (in sq. m) of the flower-bed, is

• 30

• 12.5

• 10

• 10

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7.

The projections of a vector on the three coordinate axis are 6, - 3, 2 respectively. The direction cosines of the vector are

•  6, –3, 2

• 6/5, -3/5, 2/5

• 6/7, -3/7, 2/7

• 6/7, -3/7, 2/7

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8.

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x. The maximum area enclosed by the park is

• 3x2/2

• x3/8

• x2/2

• x2/2

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9.

If (a, a2 ) falls inside the angle made by the lines y =x/2, x >0 and y = 3x, x > 0, then a belongs to

• (0,1/2)

• (3, ∞)

• (1/2, 3)

• (1/2, 3)

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10.

Let A(2,- 3) and B(- 2,1) be two angular points of AABC. If the centroid of the triangle moves on the line 2x + 3y = 1, then the locus of the angular point C is given by

• 2x + 3y = 9

• 2x - 3y = 9

• 3x + 2y = 5

• 3x + 2y = 3