Maths-
General
Easy

Question

In triangle A B C comma base B C and area of triangle increment are fixed. Locus of the centroid of triangle A B C is a straight line that is

  1. Parallel to side B C  
  2. Right bisector of side B C  
  3. Right angle of B C  
  4. Inclined at an angle sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator square root of increment over denominator B C end fraction close parentheses blankto side B C  

The correct answer is: Parallel to side B C


    increment equals fraction numerator 1 over denominator 2 end fraction open parentheses B C close parentheses h comma blankwhereblank h blankis the distance of vertexblank A from side B C
    increment subscript G B C end subscript equals fraction numerator increment over denominator 3 end fraction equals fraction numerator open parentheses B C close parentheses h over denominator 6 end fraction, where G is the centroid rightwards double arrow h equals fraction numerator 2 increment over denominator B C end fraction equalsconstant
    Thus, distance of vertex A from side is fixed. This, in turn, implies that distance of centroid from side B C will be fixed, hence locus of G will be a line parallel to B C

    Related Questions to study

    General
    Maths-

    The radii r subscript 1 end subscript comma blank r subscript 2 end subscript comma blank r subscript 3 end subscript of the escribed circles of the triangle A B C are in H.P. If the area of the triangle is 24 c m to the power of 2 end exponent and its perimeter is 24 cm, then the length of its largest side is

    The radii r subscript 1 end subscript comma blank r subscript 2 end subscript comma blank r subscript 3 end subscript of the escribed circles of the triangle A B C are in H.P. If the area of the triangle is 24 c m to the power of 2 end exponent and its perimeter is 24 cm, then the length of its largest side is

    Maths-General
    General
    Maths-

    In an acute angled triangle A B C comma blank r plus r subscript 1 end subscript equals r subscript 2 end subscript plus r subscript 3 end subscript blankandblank angle B greater than fraction numerator pi over denominator 3 end fraction comma then

    In an acute angled triangle A B C comma blank r plus r subscript 1 end subscript equals r subscript 2 end subscript plus r subscript 3 end subscript blankandblank angle B greater than fraction numerator pi over denominator 3 end fraction comma then

    Maths-General
    General
    Maths-

    If ´ O ´ is the circumcentre of increment A B C blankandblank R subscript 1 end subscript comma R subscript 2 end subscript blankandblank R subscript 3 end subscript are the radii of the circumcircles of triangles O B C comma blank O C A blankandblank O A B comma respectively, then fraction numerator a over denominator R subscript 1 end subscript end fraction plus fraction numerator b over denominator R subscript 2 end subscript end fraction plus fraction numerator c over denominator R subscript 3 end subscript end fraction has the value equal to

    If ´ O ´ is the circumcentre of increment A B C blankandblank R subscript 1 end subscript comma R subscript 2 end subscript blankandblank R subscript 3 end subscript are the radii of the circumcircles of triangles O B C comma blank O C A blankandblank O A B comma respectively, then fraction numerator a over denominator R subscript 1 end subscript end fraction plus fraction numerator b over denominator R subscript 2 end subscript end fraction plus fraction numerator c over denominator R subscript 3 end subscript end fraction has the value equal to

    Maths-General
    parallel
    General
    Physics-

    In a transformer, number of turns in the primary are 140 and that in the secondary are 280. If current in primary is 4 A, then that in the secondary is

    In a transformer, number of turns in the primary are 140 and that in the secondary are 280. If current in primary is 4 A, then that in the secondary is

    Physics-General
    General
    Physics-

    A transformer is often filled with oil. The oil used should have

    A transformer is often filled with oil. The oil used should have

    Physics-General
    General
    Physics-

    The figure shows three circuits with identical batteries, inductors and resistances. Rank the circuits according to the currents through the battery just after the switch is closed, greatest first

    The figure shows three circuits with identical batteries, inductors and resistances. Rank the circuits according to the currents through the battery just after the switch is closed, greatest first
    Physics-General

    parallel
    General
    Physics-

    A square coil of side 25 cm having 1000 turns is rotated with a uniform speed in a magnetic field about an axis perpendicular to the direction of the field. At an instant t, the emf induced in the coil is e =200sin 100pi t. The magnetic induction is

    A square coil of side 25 cm having 1000 turns is rotated with a uniform speed in a magnetic field about an axis perpendicular to the direction of the field. At an instant t, the emf induced in the coil is e =200sin 100pi t. The magnetic induction is

    Physics-General
    General
    Physics-

    Quantity that remains unchanged in a transformer is

    Quantity that remains unchanged in a transformer is

    Physics-General
    General
    Physics-

    Two parallel rails of a railways track insulated from each other and with the ground are connected to a millivoltmeter. The distance between the rails is one metre. A train is travelling with a velocity of 72 km-h to the power of negative 1 end exponent along the track. The reading of the millivotmeter (in mV) is : (Vertical component of the earth’s magnetic induction isblank 2 cross times 10 to the power of negative 5 end exponent T right parenthesis

    Two parallel rails of a railways track insulated from each other and with the ground are connected to a millivoltmeter. The distance between the rails is one metre. A train is travelling with a velocity of 72 km-h to the power of negative 1 end exponent along the track. The reading of the millivotmeter (in mV) is : (Vertical component of the earth’s magnetic induction isblank 2 cross times 10 to the power of negative 5 end exponent T right parenthesis

    Physics-General
    parallel
    General
    Physics-

    A circular coil of diameter 21 cm is placed in a magnetic field of induction 10-4 T. the magnitude of flux linked with coil when the plane of coil makes an angle 30degree with the field is

    A circular coil of diameter 21 cm is placed in a magnetic field of induction 10-4 T. the magnitude of flux linked with coil when the plane of coil makes an angle 30degree with the field is

    Physics-General
    General
    Physics-

    A 50 turns circular coil has a radius of 3 cm, it is kept in a magnetic field acting normal to the area of the coil. The magnetic field B increased from 0.10 to 0.35 T in 2 millisecond. The average induced emf in the coil is

    A 50 turns circular coil has a radius of 3 cm, it is kept in a magnetic field acting normal to the area of the coil. The magnetic field B increased from 0.10 to 0.35 T in 2 millisecond. The average induced emf in the coil is

    Physics-General
    General
    Physics-

    A 50 blank v o l t potential difference is suddenly applied to a coil with L equals 5 cross times 10 to the power of negative 3 end exponent h e n r yand R equals 180 blank o h m. The rate of increase of current after 0.001 blank s e c o n d is

    A 50 blank v o l t potential difference is suddenly applied to a coil with L equals 5 cross times 10 to the power of negative 3 end exponent h e n r yand R equals 180 blank o h m. The rate of increase of current after 0.001 blank s e c o n d is

    Physics-General
    parallel
    General
    Physics-

    A solenoid is placed inside another solenoid, the length of both being equal carrying same magnitude of current. The parameters like radius and number of turns are in the ratio 1:2 for the two solenoids. The mutual inductance on each other would be

    A solenoid is placed inside another solenoid, the length of both being equal carrying same magnitude of current. The parameters like radius and number of turns are in the ratio 1:2 for the two solenoids. The mutual inductance on each other would be

    Physics-General
    General
    Maths-

    In a certain test ai students gave wrong answers to atleast i questions; where i = 1, 2, ---------k and no student gave wrong answers to more than k questions, then number of wrong answers is-

    In a certain test ai students gave wrong answers to atleast i questions; where i = 1, 2, ---------k and no student gave wrong answers to more than k questions, then number of wrong answers is-
    Maths-General

    General
    Maths-

    In a certain test there are n questions. In this test 2n–i student gave wrong answers to atleast i questions where i = 1, 2, 3 ..... n . If the total no. of wrong answer given is 2047. Then n is equal to-

    In a certain test there are n questions. In this test 2n–i student gave wrong answers to atleast i questions where i = 1, 2, 3 ..... n . If the total no. of wrong answer given is 2047. Then n is equal to-
    Maths-General

    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.