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Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1


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25 Questions MCQ Test Maths 35 Years JEE Main & Advanced Past year Papers | Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1

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Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 1

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 1

Total student = 100;
for 70 stds. total marks = 75 x 70 = 5250
⇒ Total marks of  girls = 7200 – 5250 = 1950 Average of girls =   = 65

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 2

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 2

Given P + Q = 18 .......(1)
P2 + Q2 + 2PQ cosα = 144 ......(2)

⇒ P + Q cosα = 0   ......(3)
From (2) and (3),
Q2 – P2 = 144 ⇒ (Q – P) (Q + P) = 144

From (1), On solving, we get Q = 13, P = 5

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 3

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

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 3

∠ TQW = 180 – θ ;  ∠ RQW = 2θ  ; ∠ RQT = 180 – θ

Applying Lami's theorem at Q,

⇒ R = W and T = 2W cosθ

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 4

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 4

n = 9 then median term  term. Last

four observations are increased by 2. The  median is 5th observation which is remaining  unchanged.

∴ there will be no change in median.

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 5

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 5

 

...........(2)

...........(3)

From (1),  (2) & (3), 

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 6

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 6

.......(1)

.......(2)

.......(3)

.......(4)

.....(5)

.....(6)

....(7)

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 7

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

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 7

Let the body travels from A to B with constant accelerationt and from B to C with constant retardation r.

If AB = x, BC = y, time taken from A to B = t1
and time taken from B to C = t2,
then s = x + y and
t = t1 + t2
For the motion from A to B

v2 = u2 + 2 fs ⇒ v2 = 2 fx (∵u=0)

....(1)

and v = u + ft ⇒ v= ft1

...(2)

For the motion from B to C

Adding equations (1) and (3), we get

Adding equations (2) and (4), we get

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 8

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 8

For the stone projected horizontally, for horizontal motion, using
distance = speed × time ⇒ R = ut and for vertical motion

∴ We get   ....(1)

For the stone projected at an angle θ, for horizontal and vertical motions, we have

R = u cosθ x t ....(2)

and ....(3)

From (1) and (2) we get

Substituting this value of t in eq (3) we get

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 9

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 9

We can consider the two velocities as

and 

∴ Relative velocity of second with respect to first

= f 2t2 + u2 - 2uft cosα

Forto be min we should have

Also 

∴ |v|2 and hence |v| is least at the time  

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 10

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 10

or β = θ - α

or 

  = 40 or 160 metre

∴  Possible height = 40 metre  

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 11

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 11

Let β be the inclination of the plane to the horizontal and u be the velocity of projection of the projectile

 and 

 

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 12

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 12

∑x = 170, ∑x2 = 2830 increase in ∑x = 10 , then ∑x' = 170 + 10 = 180
Increase in ∑x2 = 900 - 400 = 500 then ∑x'2 = 2830 + 500 = 3330

Variance 

= 222 - 144= 78

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 13

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 13

∵ (1, 1) ∉ R ⇒ R is not reflexive (2,3) ∈ R but (3, 2) ∉ R
∴ R is not symmetric

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 14

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 14

Only first (A) and second (B) statements are correct.

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 15

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 15

Clearly mean A = 0

Standard deviation  

Hence | a | = 2

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 16

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 16

Let forces be P and Q. then P +Q= 4   ....(1)

and P2 +Q2= 32    ....(2)

Solving we get the forces

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 17

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 17

Since, the moment about A is zero, hence passes through A. Taking A as origin. Let the line of action of force be y = mx.(see figure)

Moment about

Moment about C

Dividing (1) by (2), we get   

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 18

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

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 18

IA, IB, IC are bisectors of the angles A, B and C as  I is incentre of ΔABC.

Now ∠BIC 

Applying Lami’s theorem at I

⇒ P : Q : R = 

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 19

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 19

Time taken by the particle in complete journey

∴ Average speed

Average velocity =  [using vector addition]

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 20

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 20

If  component along OB

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 21

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 21

For same horizontal range the angles of projection must

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 22

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 22

Reflexive and transitive only. e.g. (3, 3), (6, 6), (9, 9), (12, 12)
[Reflexive] (3, 6), (6, 12), (3, 12)
[Transitive]. (3, 6) ∈ R but (6, 3) ∉  R [ non symmetric]

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 23

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

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 23

IA, IB, IC are bisectors of the angles A, B and C as  I is incentre of ΔABC.

Now ∠BIC 

Applying Lami’s theorem at I

  

⇒ P : Q : R = 

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 24

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

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 24

Mode + 2Mean = 3 Median
⇒ Mode = 3 × 22 – 2 × 21 = 66 – 42 = 24.

Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 25

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]

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) - 1 - Question 25

Let the lizard catches the insect after time t then distance covered by lizard = 21cm + distance covered by insect

⇒ t2 - 20t - 21=0 ⇒ t = 21 sec

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