35 Year JEE Previous Questions: Miscellaneous Sets, Relations, Statistics

In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls? [2002]

The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12 N. The magnitude of the two forces are [2002]

A bead of weight w can slide on smooth circular wire in a vertical plane. The bead is attached by a light thread to the highest point of the wire and in equilibrium, the thread is taut and make an angle θ with the vertical then tension of the thread and reaction of the wire on the bead are

The median of a set of  9 distinct observations  is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set [2003]

A couple is of moment and the force forming the couple is is turned through a right angle the moment of the couple thus formed is . If instead , the force are turned through an angle α, then the moment of couple becomes [2003]

The resultant of forces  is doubled then is d oubled. If the direction of is reversed,then is again doubled. Then P 2 : Q 2 : R 2 is [2003]

A body travels a distance s in t seconds. It starts from rest and ends at rest. In the first part of the journey, it moves with constant acceleration f and in the second  part with constant retardation r. The value of t is given by

Two  stones  are  projected  from  the top of  a cliff  h metres high , with the same speed  u, so as to hit the ground  at  the same  spot.  If  one  of  the  stones is projected  horizontally and the other is projected horizontally and the other is projected at  an  angle  θ  to  the  horizontal then tanq equals [2003]

Two  particles   start  simultaneously    from   the same point and  move  along  two  straight  lines, one with uniform velocity and the other from rest with  uniform acceleration . Let α be   the angle between  their directions  of motion.
The relative velocity  of the  second particle  w.r.t. the first is least after a time [2003]

The upper  th portion of a vertical pole subtends an angle  at a point in the  horizontal plane through its foot and at  a distance 40 m from the foot. A possible height of the vertical pole is [2003]

Let R₁ and R₂ respectively be the  maximum ranges up and down an inclined plane and R be the maximum range on the horizontal plane. Then R₁, R, R₂ are in [2003]

In  an experiment with 15 observations on x, the following results were available : [2003]

∑x² = 2830, ∑x= 170

One observation that was 20  was found to be wrong and was replaced  by the correct value  30. The corrected variance is [2003]

Let R = {(1, 3), ( 4, 2), (2, 4), (2, 3), (3,1)} be a relation on the set A = {1,2, 3,4}. . The relation R is [2004]

Consider the following statements :
(A) Mode can be computed from histogram
(B) Median is not independent of change of scale
(C) Variance is independent of change of origin and scale.Which of these is / are correct ? [2004]

In a series of 2 n observations, half of them equal a and remaining half equal –a. If the standard deviation of the observations is 2, then |a| equals. [2004]

With two forces acting at point, the maximum affect is obtained when their resultant is 4N. If they act at right angles, then their resultant is 3N. Then the forces are                                            [2004]

In a right angle ΔABC , ∠A = 90° and sides a, b,  c are respectively, 5 cm, 4 cm and 3 cm. If a force has moments 0, 9 and 16 in N cm. units respectively about vertices A, B and C, then magnitude of is [2004]

Three forces acting along IA, IB and IC, where I is the incentre of a ΔABC are in equilibrium. Then  [2004]

A paticle moves towards east from a point A to a point B at the rate of 4 km/h and then towards north from B to C at the rate of 5km/hr. If AB = 12 km and BC = 5 km, then its average speed for its journey from A to C and resultant average velocity direct from A to C are respectively [2004]

A velocity m / s  is resolved into two components along OA and OB making angles 30° and 45° respectively with the given velocity. Then the component along OB is [2004]

If t₁ and t₂ are the times of flight of two particles  having the same initial velocity u and range R on the horizontal , then t₁² + t₂² is equal to [2004]

Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. The relation is [2005]

ABC is a triangle. Forces acting along IA, IB, and IC respectively are in equilibrium, where I is the incentre of D ABC. Then P : Q : R is

If  in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately [2005]

A lizard, at an initial distance of 21 cm behind an insect, moves from rest with an acceleration of 2 cm /s² and pursues the insect which is crawling uniformly along a straight line at a speed of 20 cm/s. Then the lizard will catch the insect after [2005]