JEE Questions for Maths Statistics Quiz 4 - MCQExams.com

A uniform beam of length 2a rests in equilibrium against a smooth vertical plane and over a smooth peg at a distance h from the plane. If θ be the inclination of the beam to the vertical, then sin3θ is

  • Maths-Statistics-50877.png
  • 2)
    Maths-Statistics-50878.png

  • Maths-Statistics-50879.png

  • Maths-Statistics-50880.png
Let ABC be an equilateral triangle formed by weightless inextensible strings, the side AB is horizontal. A and B are tied to fixed points D and E by equal weightless inextensible strings AD, BE; a weight of W gm is attached at C. The angle DAB, ABE are each 150°. Then which of the following statements is true
  • The tensions in the strings AB, BC and CA are equal
  • The tensions in the strings BE, AD are inversely proportional
  • The tension in BE is less than the tension in AB
  • The tension in AD is twice the tension in BC
With two forces acting at a point, the maximum effect is obtained when their resultant is 4 N. If they act at right angles, then their resultant is 3 N. Then the forcesare

  • Maths-Statistics-50804.png
  • 2)
    Maths-Statistics-50805.png

  • Maths-Statistics-50806.png

  • Maths-Statistics-50807.png
If the resultant of two forces of magnitudes P and Q acting at a point at an angle of 60° is √7 Q, then P/Q is
  • 1
  • 2)
    Maths-Statistics-50809.png
  • 2
  • 4
The resultant of two forces acting on a particle is at right angles to one of them and its magnitude is one third of the magnitude of the other. The ratio of thelarger force to the smaller is

  • Maths-Statistics-50811.png
  • 2)
    Maths-Statistics-50812.png
  • 3 : 2
  • 4 : 3
If two forces P and Q act on such an angle that their resultant force R is equal to force P, then if P is doubled then the angle between new resultant force and Q willbe
  • 30°
  • 60°
  • 45°
  • 90°
The resultant of two forces P and Q is R. If the direction of P is reversed keeping the direction Q same, the resultant remains unaltered. The angle between P andQ is
  • 90°
  • 60°
  • 45°
  • 30°

Maths-Statistics-50816.png

  • Maths-Statistics-50817.png
  • 2)
    Maths-Statistics-50818.png

  • Maths-Statistics-50819.png
  • None of these
Forces M and N acting at a point Omake an angle 150°. Their resultant acts at Ohas magnitude 2 unit and is perpendicular to M. Then, in the same unit, the magnitudes of M and N are

  • Maths-Statistics-50821.png
  • 2)
    Maths-Statistics-50822.png
  • 3, 4
  • 4, 5
If the resultant of two forces of magnitude P and 2P is perpendicular to P, then the angle between the forces is
  • 2π/ 3
  • 3π/ 4
  • 4π/5
  • 5π/6
Like parallel forces act at the vertices A, B and C of atriangle ABC and are proportional to the lengths BC, AC and AB respectively. The centre of the forces is at the
  • Centroid
  • Circum-centre
  • Incentre
  • None of these
Two like parallel forces P and 3P act on a rigid body at points A and B respectively. If the forces are interchanged in position, the resultant will be displaced through a distance of

  • Maths-Statistics-50826.png
  • 2)
    Maths-Statistics-50827.png

  • Maths-Statistics-50828.png

  • Maths-Statistics-50829.png
Three forces P, Q, R act along the sides BC, CA, AB oftriangle ABC, taken in order. If their resultant passes through the incentre of ∆ABC, then

  • Maths-Statistics-50831.png
  • 2)
    Maths-Statistics-50832.png

  • Maths-Statistics-50833.png
  • None of these
The resultant of two like parallel forces is 12 N. The distance between the forces is 18 m. If one of the force is 4 N, then the distance of the resultant from thesmaller force is
  • 4 m
  • 8 m
  • 12 m
  • None of these
The resultant of three equal like parallel forces actingat the vertices of a triangle act at its
  • Incentre
  • Circumcentre
  • Orthocentre
  • Centroid

Maths-Statistics-50836.png
  • P = Q
  • P = 2Q
  • 2P = Q
  • None of these
Two parallel forces not having the same line of action form a couple if they are
  • Like and unlike
  • Like and equal
  • Unequal and unlike
  • Equal and unlike
Two like parallel forces P and 3P are 40 cm apart. If the direction of P is reversed, then their resultant shifts through a distance of
  • 30 cm
  • 40 cm
  • 50 cm
  • 60 cm
Two like parallel forces of 5 N and 15 N, act on a lightrod at two points A and B respectively 6 m apart. The resultant force and the distance of its point of a application from the point A are
  • 10 N, 4.5 m
  • 20 N, 4.5 m
  • 20 N, 1.5 m
  • 10 N, 15 m

Maths-Statistics-50840.png
  • 9
  • 4
  • 5
  • 3
A man carries a hammer on his shoulder and holds it at the other end of its light handle in his hand. If he changes the point of support of the handle at the shoulder and if x is the distance between his hand and the point of support, then the pressure on his shoulderis proportional to

  • Maths-Statistics-50842.png
  • 2)
    Maths-Statistics-50843.png

  • Maths-Statistics-50844.png

  • Maths-Statistics-50845.png
If a couple is acting on 2 particles of mass 1 kg attached with a rigid rod of length 4 m, fixed at centre, acting at the end and the angular acceleration of system about centre is 1 rad/s2, then magnitude of force is
  • 2 N
  • 4 N
  • 1 N
  • None of these

Maths-Statistics-50848.png
  • 0
  • 2)
    Maths-Statistics-50849.png

  • Maths-Statistics-50850.png
  • 5
A couple is of moment G and the force forming the couple is P. If P is turned through a right angle, the moment of the couple thus formed is H. If instead, the force P are turned an angle α, then the moment ofcouple becomes
  • G sin α –H cos α
  • H cos α+ G sin α
  • G cos α + H sin α
  • H sin α –G cos α
The resultant of the forces 4, 3, 4 and 3 unit actingalong the lines AB, BC, CD and DA of a square ABCD of side \'a\' respectively is
  • A force 5√2 through the centre of the square
  • A couple of moment 7a
  • A null force
  • None of the above
Three like parallel forces P, Q, R act at the corner pointsof a triangle ABC. Their resultant passes through the circumcentre, if

  • Maths-Statistics-50854.png
  • 2)
    Maths-Statistics-50855.png

  • Maths-Statistics-50856.png
  • None of these
A and B are two like parallel forces. A couple of moment H lies in the plane of A and B contained with them. The resultant of A and B after combining isdisplaced through a distance

  • Maths-Statistics-50858.png
  • 2)
    Maths-Statistics-50859.png

  • Maths-Statistics-50860.png

  • Maths-Statistics-50861.png
A system of five forces whose directions and non-zero magnitudes can be chosen arbitrarily, will never be in equilibrium if n of the forces are concurrent, where
  • n = 2
  • n = 3
  • n = 4
  • n = 5
A uniform rod of weight W and length 2l is resting in a smooth spherical bowl of radius r. The rod is inclined to the horizontal at an angle of
  • 0°
  • 2)
    Maths-Statistics-50863.png

  • Maths-Statistics-50864.png

  • Maths-Statistics-50865.png
There is a system of coplanar forces acting on a rigid body represented in magnitude, direction and sense by the sides of a polygon taken in order, then the system is equivalent to
  • A single non-zero force
  • A zero force
  • A couple, where moment is equal to the area of polygon
  • A couple, where moment is twice the area of polygon
0:0:1


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