Author Archives: Priyanka

In This Post we are  providing Chapter-4 Motion in a Plane NCERT MCQ for Class 11 Physics which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON MOTION IN A PLANE

Question 1.
Three vectors A, B and C satisfy the relation A.B = 0 and A.C = 0. The vector A is parallel to
(a) B
(b) C
(c) B × c
(d) B.C

Answer: (c) B × c

Question 2.
What is the minimum number of unequal forces whose resultant will be zero?
(a) 1
(b) 2
(c) 3
(d) 4

Answer: (c) 3

Question 3.
A body travelling in a circular path at uniform speed has :
(a) constant velocity
(b) tangential acceleration
(c) inward acceleration
(d) outward acceleration

Answer: (c) inward acceleration

Question 4.
When a disc containing mercury and water is rotated rapidly about a vertical axis, then the outermost place in the disc will be taken by:
(a) water
(b) mercury
(c) sometimes water and sometimes mercury
(d) none of these.

Answer: (b) mercury

Question 5.
The resultant of two forces P and Q is R. If one of the forces is reversed in direction, then the resultant becomes S. Then for the identity R² + S² = 2(P² + Q²) to hold good
(a) The forces are collinear
(b) The forces act as right angles to each other
(c) The forces are inclined at 45° to each other
(d) The forces can have any angle of inclination between them

Answer: (d) The forces can have any angle of inclination between them

Question 6.
A bus is moving on a straight road towards north with a uniform speed of 50 kmh^-1 when it turns left through 90°. If the speed remains unchanged after turning, the increase in the velocity of the bus in the turning process is :
(a) zero
(b) 50 kmh^-1
(c) 70.7 kmh^-1 along south-west direction
(d) 70.7 lcmh^-1 along north-west direction

Answer: (c) 70.7 kmh^-1 along south-west direction

Question 7.
Two bullets are fired simultaneously horizontally and with different speeds from the same place. Which bullet will hit the ground first?
(a) The slower one
(b) The faster one
(c) Both will reach simultaneously
(d) Depends on the masses

Answer: (c) Both will reach simultaneously

Question 8.
A particle is acted upon by a force of constant magnitude, which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that:
(a) its velocity is constant
(b) its acceleration is constant
(c) its kinetic energy is constant
(d) it moves in a circular path

Answer: (c) and (d).

Question 9.
The muzzle speed of a certain rifle is 330 ms^-1. At the end of one second, a bullet fired straight up into the air will travel a distance of:
(a) 330 m
(b) (330 – 4.9) m
(c) (330 – 9.8) m
(d) (330 + 4.9) m

Answer: (b) (330 – 4.9) m

Question 10.
If a body A of mass M is thrown with velocity v at angle of 30° to the horizontal and another body B of the same mass is thrown with the same speed at an angle of 60° to the horizontal, the ratio of the horizontal ranges of A and B will be
(a) 1 : 3
(b) 1 : 1
(c) √3 : 1
(c) 1 : √3

Answer: (b) 1 : 1

Question 11.
One body is dropped while a second body is thrown downwards with an initial velocity of 1 ms^-1 simultaneously. The separation between these is 18 m after a time
(a) 4.5 s
(b) 9 s
(c) 18 s
(d) 36 s

Answer: (c) 18 s

Question 12.
A boat which has the speed of 5 kmh^-1 still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water is
(a) 3 kmh^-1
(b) 4 kmh^-1
(c) 41−−√ kmh^-1
(d) 1 kmh^-1

Answer: (a) 3 kmh^-1

Question 13.
Which of the following vectors is perpendicular to i^ Pcos 9 +
(a) i^ Pcos θ + j^ Qsin θ
(b) i^ Qcos θ – j^ Psin θ
(c) i^ Psin θ + j^ Qcos θ
(d) i^ Qsin θ – j^Pcos θ

Answer: (d) i^ Qsin θ – j^Pcos θ

Question 14.
Which of the following operations between the two vectors can yield a vector perpendicular to either of them
(a) addition
(b) subtraction
(c) multiplication
(d) division

Answer: (c) multiplication

Question 15.
Which of the following is the essential characteristic of a projectile?
(a) Zero velocity at the highest point
(b) Initial velocity inclined to the horizontal
(c) Constant acceleration perpendicular to the velocity
(d) None of these

Answer (d) None of these

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In This Post we are  providing Chapter-3 Motion in a Straight Line NCERT MCQ for Class 11 Physics which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON MOTION IN A STRAIGHT LINE

Question 1.
The displacement in metres of a body varies with time t in second as y = t2 – t – 2. The displacement is zero for a positive of t equal to
(a) 1 s
(b) 2 s
(c) 3 s
(d) 4 s

Answer: (b) 2 s

Question 2.
A boy starts from a point A, travels to a point B at a distance of 3 km from A and returns to A. If he takes two hours to do so, his speed is
(a) 3 km/h
(b) zero
(c) 2 km/h
(d) 1.5 km/h

Answer: (a) 3 km/h

Question 3.
A 180 metre long train is moving due north at a speed of 25 m/s. A small bird is flying due south, a little above the train, with a speed of 5 m/s. The time taken by the bird to cross the train is
(a) 10 s
(b) 12 s
(c) 9 s
(d) 6 s

Answer: (d) 6 s

Question 4.
A boy starts from a point A, travels to a point B at a distance of 1.5 km and returns to A. If he takes one hour to do so, his average velocity is
(a) 3 km/h
(b) zero
(c) 1.5 km/h
(d) 2 km/h

Answer: (b) zero

Question 5.
A body starts from rest and travels with uniform acceleration on a straight line. If its velocity after making a displacement of 32 m is 8 m/s, its acceleration is
(a) 1 m/s²
(b) 2 m/s²
(c) 3 m/s²
(d) 4 m/s²

Answer: (a) 1 m/s²

Question 6.
Which one of the following is the unit of velocity?
(a) kilogram
(b) metre
(c) m/s
(d) second

Answer: (c) m/s

Question 7.
A body starts from rest and travels for t second with uniform acceleration of 2 m/s². If the displacement made by it is 16 m, the time of travel t is
(a) 4 s
(b) 3 s
(c) 6 s
(d) 8 s

Answer: (a) 4 s

Question 8.
The dimensional formula for speed is
(a) T^-1
(b) LT^-1
(c) L^-1T^-1
(d) L^-1T

Answer: (b) LT^-1

Question 9.
The dimensional formula for velocity is
(a) [LT]
(b) [LT^-1]
(c) [L2T]
(d) [L^-1T]

Answer: (b) [LT^-1]

Question 10.
A body starts from rest and travels with an acceleration of 2 m/s². After t seconds its velocity is 10 m/s . Then t is
(a) 10 s
(b) 5 s
(c) 20 s
(d) 6 s

Answer: (b) 5 s

Question 11.
A boy starts from a point A, travels to a point B at a distance of 1.5 km and returns to A. If he takes one hour to do so, his average velocity is
(a) 3 km/h
(b) zero
(c) 1.5 km/h
(d) 2 km/h

Answer: (b) zero

Question 12.
A body starts from rest. If it travels with an acceleration of 2 m/s², its displacement at the end of 3 seconds is
(a) 9 m
(b) 12 m
(c) 16 m
(d) 10 m

Answer: (a) 9 m

Question 13.
A body starts from rest and travels with uniform acceleration of 2 m/s². If its velocity is v after making a displacement of 9 m, then v is
(a) 8 m/s
(b) 6 m/s
(c) 10 m/s
(d) 4 m/s

Answer: (b) 6 m/s

Question 14.
A body starts from rest and travels with an acceleration of 2 m/s². After t seconds its velocity is 10 m/s. Then t is
(a) 10 s
(b) 5 s
(c) 20 s
(d) 6 s

Answer: (b) 5 s

Question 15.
A body starts from rest and travels for five seconds to make a displacement of 25 m if it has travelled the distance with uniform acceleration a then a is
(a) 3 m/s²
(b) 4 m/s²
(c) 2 m/s²
(d) 1 m/s²

Answer: (c) 2 m/s²

In This Post we are  providing Chapter-2 Units and Measurement NCERT MCQ for Class 11 Physics which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON UNITS AND MEASUREMENT

Question 1 :  One second is defined to be equal to

• a) 9192631770 periods of the cesium clock
• b) 1650763.73 periods of the cesium clock
• c) 652189.63 periods of the krypton clock
• d) 1650763.73 periods of the krypton clock

Answer :  9192631770 periods of the cesium clock

Question 2 :  One yard in SI unit is equal to

• a) 0.9144 metre
• b) 1.0936 kilometre
• c) 1.9144 metre
• d) 0.09144 kilometre

Answer :  0.9144 metre

Question 3 :  One pico farad is equal to

• a) 10^–12 farad
• b) 10^–24 farad
• c) 10^–18 farad
• d) 10^–6 farad

Answer :  10^–12 farad

Question 4 :  ‘Torr’ is the unit of

• a) pressure
• b) volume
• c) density
• d) flux

Answer :  pressure

Question 5 :  Very large distances such as the distance of a Planet or a star from Earth can be measured by

• a) Parallax method
• b) All of these
• c) Millikan’s oil drop method
• d) Spectrograph

Answer :  Parallax method

Question 6 :  Joule second is a unit of

• a) angular momentum
• b) torque
• c) energy
• d) power

Answer :  angular momentum

Question 7 :  Temperature can be expressed as derived quantity in terms of

• a) None of these
• b) mass and time
• c) length and mass
• d) length, mass and time

Answer :  None of these

Question 8 :  Unit of specific resistance is

• a) ohm – m
• b) ohm/m
• c) ohm m³
• d) ohm/m²

Answer :  ohm – m

Question 9 :  Unit of magnetic moment is

• a) ampere–metre²
• b) weber–metre²
• c) ampere–metre
• d) weber/metre

Answer :  ampere–metre²

 

Question 10 :  Dimensional analysis can be applied to

• a) All of these
• b) to convert from one system of units to another
• c) deduce relations among the physical quantities
• d) check the dimensional consistency of equations

Answer :  All of these

Question 11 :  The dimensions of pressure is equal to

• a) energy per unit volume
• b) energy
• c) force
• d) force per unit volume

Answer :  energy per unit volume

Question 12 :  Which is dimensionless?

• a) Force/acceleration
• b) Velocity/acceleration
• c) Energy/work
• d) Volume/area

Answer :  Force/acceleration

Question 13 :  The dimensions of torque are

• a)
• b)
• c)
• d)

Answer :

Question 14 :  The division of energy by time is X. The dimensional formula of X is same as that of

• a) power
• b) electric field
• c) momentum
• d) torque

Answer :  power

Question 15 :  Which of the following is a dimensional constant?

• a) Gravitational constant
• b) Dielectric constant
• c) Refractive index
• d) Relative density

Answer :  Gravitational constant

In This Post we are  providing Chapter-1 Physical World NCERT MCQ for Class 11 Physics which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON PHYSICAL WORLD

Question 1 :  Which of the following is true regarding the physical science?

• a) Both
• b) The study of matter are conducted at atomic or ionic levels
• c) None of these
• d) They deal with non-living things

Answer :  Both

Question 2 :  The scientific principle involves in production of ultra high magnetic fields is

• a) super conductivity
• b) photoelectric effect
• c) digital logic
• d) laws of thermodynamics

Answer :  super conductivity

Question 3 :  Louis de-Broglie is credited for his work on

• a) matter waves
• b) law of distribution of velocities
• c) electromagnetic theory
• d) theory of relativity

Answer :  matter waves

Question 4 :  Madam Marie Curie won Nobel Prize twice which were in the field of

• a) Physics and chemistry
• b) Physics only
• c) Chemistry only
• d) Biology only

Answer :  Physics and chemistry

Question 5 :  Scientific way of doing things involve

• a) All of the above
• b) hypothesising a possible theory
• c) collecting data
• d) identifying the problem

Answer :  All of the above

Question 6 :  The exchange particles for the electromagnetic force are

• a) photons
• b) gravitons
• c) gluons
• d) mesons

Answer :  photons

Question 7 :  Which of the following is the weakest force?

• a) Gravitational force
• b) None of these
• c) Nuclear force
• d) Electromagnetic force

Answer :  Gravitational force

Question 8 :

Assertion : Electromagnetic force is much stronger than the gravitational force.
Reason : Electromagnetic force dominates all phenomena at atomic and molecular scales

• a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
• b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
• c) Assertion is correct, reason is incorrect
• d) Assertion is incorrect, reason is correct

Answer :  Assertion is correct, reason is correct; reason is a correct explanation for assertion.

Question 9 :  When we hold a book in our hand, we are balancing the gravitational force on the book due to

• a) normal force provided by our hand
• b) friction force provided by our book
• c) both
• d) None of these

Answer :  normal force provided by our hand

Question 10 :   Which of the following has infinite range?

• a) Both
• b) Electromagnetic force
• c) Gravitational force
• d) None of these

Answer :  Both

Question 11 :  Which of the following statements is/are correct?

I. Strong nuclear force binds protons and neutrons in a nucleus.
II. In twentieth century, silicon chip triggered a revolutionary changes in technology of computer system.
III. The fossil fuels of the planet are dwindling fast and there is urgent need to discover new source of energy.

• a) I, II and III
• b) Only III
• c) I and II
• d) Only I

Answer :  I, II and III

Question 12 :  The field of work of S. Chandrashekar is

• a) theory of black hole
• b) theory of relativity
• c) Cosmic rays
• d) X-rays

Answer :  theory of black hole

Question 13 :  Who discovered X-rays?

• a) Roentgen
• b) Madam Curie
• c) Chadwick
• d) Thomson

Answer :  Roentgen

Question 14 :  Who gave general theory of relativity?

• a) Einstein
• b) Marconi
• c) Ampere
• d) Newton

Answer :  Einstein

Question 15 :  Which of the following is wrongly matched ?

• a) Humidity-Calorimeter
• b) Coulomb’s law-charges
• c) Lactometer-Milk
• d) Barometer-Pressure

Answer :  Humidity-Calorimeter

In This Post we are  providing Chapter-16 Probability NCERT MCQ for Class 11 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON PROBABILITY

Question 1.
Two cards from a pack of 52 cards are lost. One card is drawn from the remaining cards. If drawn card is diamond then the probability that the lost cards were both hearts is
(a) 143/1176
(b) 143/11760
(c) 143/11706
(d) 134/11760

Answer: (b) 143/11760

Question 2.
If four whole numbers taken at random are multiplied together, then the chance that the last digit in the product is 1, 3, 5, 7 is
(a) 16/25
(b) 16/125
(c) 16/625
(d) none of these

Answer: (c) 16/625

Question 3.
Three identical dice are rolled. The probability that the same number will appear on each of them is
(a) 1/6
(b) 1/36
(c) 1/18
(d) 3/28

Answer: (b) 1/36

Question 4.
There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed is
(a) 1/3
(b) 1/6
(c) 1/2
(d) 1/4

Answer: (b) 1/6

Question 5.
Two unbiased dice are thrown. The probability that neither a doublet nor a total of 10 will appear is
(a) 3/5
(b) 2/7
(c) 5/7
(d) 7/9

Answer: (d) 7/9

Question 6.
Two dice are thrown the events A, B, C are as follows A: Getting an odd number on the first die. B: Getting a total of 7 on the two dice. C: Getting a total of greater than or equal to 8 on the two dice. Then AUB is equal to
(a) 15
(b) 17
(c) 19
(d) 21

Answer: (d) 21

Question 7.
Two numbers are chosen from {1, 2, 3, 4, 5, 6} one after another without replacement. Find the probability that the smaller of the two is less than 4.
(a) 4/5
(b) 1/15
(c) 1/5
(d) 14/15

Answer: (a) 4/5

Question 8.
The probability that when a hand of 7 cards is drawn from a well-shuffled deck of 52 cards, it contains 3 Kings is
(a) 1/221
(b) 5/716
(c) 9/1547
(d) None of these

Answer: (c) 9/1547

Question 9.
A certain company sells tractors which fail at a rate of 1 out of 1000. If 500 tractors are purchased from this company, what is the probability of 2 of them failing within first year
(a) e^-1/2/2
(b) e^-1/2/4
(c) e^-1/2/8
(d) none of these

Answer: (c) e^-1/2/8

Question 10.
The probability that in a random arrangement of the letters of the word INSTITUTION the three T are together is
(a) 0.554
(b) 0.0554
(c) 0.545
(d) 0.0545

Answer: (d) 0.0545

Question 11.
Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is
(a) 2/9
(b) 1/9
(c) 8/9
(d) 7/9

Answer: (b) 1/9

Question 12.
A bag contains 5 brown and 4 white socks . A man pulls out two socks. The probability that both the socks are of the same colour is
(a) 9/20
(b) 2/9
(c) 3/20
(d) 4/9

Answer: (d) 4/9

Question 13.
When a coin is tossed 8 times getting a head is a success. Then the probability that at least 2 heads will occur is
(a) 247/265
(b) 73/256
(c) 247/256
(d) 27/256

Answer: (c) 247/256

Question 14.
A couple has two children. The probability that both children are females if it is known that the elder child is a female is
(a) 0
(b) 1
(c) 1/2
(d) 1/3

Answer: (c) 1/2

Question 15.
A certain company sells tractors which fail at a rate of 1 out of 1000. If 500 tractors are purchased from this company, what is the probability of 2 of them failing within first year
(a) e^-1/2/2
(b) e-^-1/2/4
(c) e^-1/2/8
(d) none of these

Answer: (c) e^-1/2/8

In This Post we are  providing Chapter-15 Statistics NCERT MCQ for Class 11 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON STATISTICS

Question 1: What is the standard deviation of the following series ? 
Measurements 0 -10   10 – 20    20 -30   30 – 40
Frequency           1          3             4           2
(a) 81
(b) 7.6
(c) 9
(d) 2.26

Answer :  C

Question 2: The mean deviation from the mean of the following data : 
Marks   0-10    10-20    20-30    30-40   40-50
No. of     5         8          15         16         6
Students
is
(a) 10
(b) 10.22
(c) 9.86
(d) 9.44

Answer :  D

Question 3 : The standard deviation for the following data is 
Wages per week upto  15   30   45    60     75     90     105    120
Number of Workers      12   30   65   107   157    202    222   230
(a) 26.75
(b) 24.46
(c) 25.89
(d) none

Answer :  C

Question 4 : The mean of 13 observations is 14. If the mean of the first 7 observations is 12 and that of the last 7 observations is 16, what is the value of the 7th observation ? 
(a) 12
(b) 13
(c) 14
(d) 15

Answer :  C

Question 5: A batsman scores runs in 10 innings 38, 70, 48,34, 42, 55, 63, 46, 54 and 44, then the mean deviation is 
(a) 8.6
(b) 6.4
(c) 10.6
(d) 9.6

Answer :  A

Question 6 : Let x1, x2, …..xn be n observations. Let wi = l xi + k for i = 1, 2, … n, where l and k are constants. If the mean of xi’s is 48 and their standard deviation is 12, the mean of w’is is 55 and standard deviation of w’is is 15, the values of l and k should be 
(a) l = 1.25, k = – 5
(b) l = –1.25, k = 5
(c) l = 2.5, k = – 5
(d) l = 2.5, k = 5

Answer :  A


Question 7 : Standard deviations for first 10 natural numbers is 
(a) 5.5
(b) 3.87
(c) 2.97
(d) 2.87

Answer :  D

Question 8 : The standard deviation of some temperature data in °C is 5. If the data were converted into °F, the variance would be 
(a) 81
(b) 57
(c) 36
(d) 25

Answer :  A

Question 9 : The variance of the following distribution is 
x₁ 2 3 11
f(x₁) 1/3 1/2 1/6
(a) 10
(b) 16
(c) 8
(d) 7.5

Answer :  A

Question 10 : In an experiment with 15 observations on x, the following results were available :Sx2 = 2830, Sx =170One observation that was 20 was found to be wrong and was replaced by the correct value 30. The corrected variance is 
(a) 8.33
(b) 78.00
(c) 188.66
(d) 177.33

Answer :  B

Question 11 : 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. 
(a) √2 / n
(b) √2
(c) 2 
(d) 1/n

Answer :  C

Question 12 : A scientist is weighing each of 30 fishes. Their mean weight worked out is 30 gm and a standarion deviation of 2 gm. Later, it was found that the measuring scale was misaligned and always under reported every fish weight by 2 gm. The correct mean and standard deviation (in gm) of fishes are respectively : 
(a) 32, 2
(b) 32, 4
(c) 28,2
(d) 28, 4

Answer :  A


Question 13 : In a batch of 15 students, if the marks of 10 students who passed are 70, 50, 95, 40, 60, 70, 80, 90, 75, 80 then the median marks of all the 15 students is: 
(a) 40
(b) 50
(c) 60
(d) 70

Answer :  C

Question 14 : If f (x + y, x – y) = xy, then the arithmetic mean of f (x, y) and f(y, x) is : 
(a) x
(b) y
(c) 0
(d) none of these

Answer :  C

Question 15: If a variable takes discrete values x + 4, x – 7/2 , x – 5/2 , x – 3 , x – 2 , x + 1/2 , x – 1/2 , x + 5 (x is positive), then the median is : 
(a) x – 5/4
(b) x – 1/2
(c) x – 2 
(d) x + 5/4

Answer :  A

In This Post we are  providing Chapter-14 Mathematical Reasoning NCERT MCQ for Class 11 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON MATHEMATICAL REASONING

Question 1.
The connective in the statement 2 + 7 > 9 or 2 + 7 < 9 is
(a) and
(b) or
(c) >
(d) <

Answer: (b) or

Question 2.
Which of the following is not a negation of the statement A natural number is greater than zero
(a) A natural number is not greater than zero
(b) It is false that a natural number is greater than zero
(c) It is false that a natural number is not greater than zero
(d) None of these

Answer: (c) It is false that a natural number is not greater than zero.

Question 3.
Which of the following is the conditional p → q
(a) q is sufficient for p
(b) p is necessary for q
(c) p only if q
(d) if q then p

Answer: (c) 6 is a natural number

Question 4.
The contra-positive of the statement If a triangle is not equilateral, it is not isosceles is
(a) If a triangle is not equilateral, it is not isosceles
(b) If a triangle is equilateral, it is not isosceles
(c) If a triangle is not equilateral, it is isosceles
(d) If a triangle is equilateral, it is isosceles

Answer: (d) If a triangle is equilateral, it is isosceles

Question 5.
Which of the following is a statement
(a) I will go tomorrow
(b) She will come today
(c) 3 is a prime number
(d) Tomorrow is Friday

Answer: (c) 3 is a prime number

Question 6.
The contra-positive of the statement if p then q is
(a) if ~p then q
(b) if p then ~q
(c) if q then p
(d) if ~q then ~p

Answer: (d) if ~q then ~p

Question 7.
Which of the following is not a statement
(a) The product of (-1) and 8 is 8
(b) All complex number are real number
(c) Today is windy day
(d) All of the above

Answer: (d) All of the above

Question 8.
If (p or q) is true, then
(a) p is true and q is false
(b) p is true and q is true
(c) p is false and q is true
(d) All of the above

Answer: (d) All of the above

Question 9.
Which of the following statement is a conjunction
(a) Ram and Shyam are friends
(b) Both Ram and Shyam are friends
(c) Both Ram and Shyam are enemies
(d) None of these

Answer: (d) None of these

Question 10.
Which of the following is a compound statement
(a) Sun is a star
(b) I am a very strong boy
(c) There is something wrong in the room
(d) 7 is both odd and prime number.

Answer: (d) 7 is both odd and prime number.

Question 11.
Which of the following is a statement
(a) x is a real number
(b) Switch of the fan
(c) 6 is a natural number
(d) Let me go

Answer: (c) 6 is a natural number

Question 12.
Which of the following is not a statement
(a) 8 is less than 6.
(b) Every set is finite set.
(c) The sun is a star.
(d) Mathematics is fun.

Answer: (d) Mathematics is fun.

Question 13.
Which of the following is true
(a) A prime number is either even or odd
(b) √3 is irrational number.
(c) 24 is a multiple of 2, 4 and 8
(d) Everyone in India speaks Hindi.

Answer: (d) Everyone in India speaks Hindi.

Question 14.
If (p and q) is false then
(a) p is true and q is false
(b) p is false and q is false
(c) p is false and q is true
(d) all of the above

Answer: (d) all of the above

Question 15.
The converse of the statement p ⇒ q is
(a) p ⇒ q
(b) q ⇒ p
(c) ~p ⇒ q
(d) ~q ⇒ p

Answer: (b) q ⇒ p

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In This Post we are  providing Chapter-13 Limits and Derivatives NCERT MCQ for Class 11 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON LIMITS AND DERIVATIVES

Question 1. lim_x→4 |x-4 | /x – 4 is equal to     
(a) 1
(b) –1
(c) does not exist
(d) None of these

Answer :  C

Question 2. If y = √x + 1/√x , then dy/dx at x = 1 is

(a) 1
(b) 1/2
(c) 1/√2
(d) 0

 Answer :  D

Question 3. lim_x→0 |Sinx | /x  is      
(a) 1
(b) –1
(c) does not exist
(d) None of these

Answer :  C

Question 4. If y =

(a) -4x / (x² – 1)2

(b) -4x / (x² – 1)
(c)  1 – x² / 4x
(d) 4x / x² – 1
 

Answer :  A

Question 5. lim_x→0 tan2x – x / 3x – Sinx      
(a) 2
(b) 1/2
(c) -1/2
(d) 1/4

Answer :  B

Question 6. The derivative of (3x + 5)(1 + tan x) is     
(a) 3x sec² x 6 sec2 x 3 + 3 tan x
(b) 3x sec² x  5 sec2 x 3 3 tan x
(c) 3x sec² x + 5 sec2 x + 3 + 3 tan x
(d) None of the above

Answer :  C

Question 7. The derivative of (ax² + cot x)( p + q cos x) is     
(a) ax² cot (q sin ) + ( p+ q cosx )(2ax cosec²x )
(b) ax² cot (q sin ) + ( p+ q cosx )(2ax cosec²x )
(c) ax² cot (q sin ) + ( p q cosx )(2ax cosec²x )
(d) None of the above

Answer :  A

Question 8. The derivative of (x sinx cosx) 2 + 2 is      
(a) x² cos x + 2x sin x sin 2x
(b) x² cos x + 2x sin x sin 2x
(c) x² cos x + x sin x sin 2x
(d) x² cos x + 2x sin x + sin 2x

Answer :  B

Question 9. The derivative of sin³x cos³x xis       
(a) 3 /5 sin² 2x cos 2x
(b) 3 /4 sin² 2x cos 2x
(c) 3 /4 sin 2x cos² 2x 
(d) 3 /2 sin² 2x cos 2x

Answer :  B

Question 10. The derivative of x⁵ cos x /sinx is

Answer :  B

Question 11. Find the differentiation of x^2/3 by using first principle.     
(a) 2/3 x^-1/3
(b) -2/3 x^-1/3
(c) 2/3 x ^1/3
(d) None of these

Answer :  A

Question 12. Find the differentiation of cos (x² + 1 ) by using first principle.      
(a) 2x sin (x² + 1 )
(b) 2x sin (x² + 1 )
(c) -2x sin (x² – 1 )
(d) None of these

Answer :  B

Question 13. If  f (x )= x-4 /2√x then f ‘(1) is

(a) 5/4
(b) 4/5
(c) 1
(d) 0

Answer :  A

Question 14. Find the differentiation of x cos x by using first principle.   
(a) x sin x + cos x
(b) x sin x + cos x
(c) x cos x cos x
(d) None of these

Answer :  A

Question 15. If y = Sin (x+9) / Cos x , then dy/dx at x = 0 is    
(a) cos 9
(b) sin 9
(c) 0
(d) 1

Answer :  A

In This Post we are  providing Chapter-12 Introduction to Three Dimensional Geometry NCERT MCQ for Class 11 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

Question 1. The coordinates of a point which is equidistant from the points (0, 0, 0), (a, 0, 0), (0, b, 0), (0, 0, c) are given by
(a) (a/2 , b/2 , c/2,)
(b)  ( -a/2 , -b/2 , c/2,)
(c)  (a/2 , -b/2 , c/2,)
(d) (-a/2 , b/2 , c/2,)

Answer :   A

Question 2. If x2+y2 = 1, then the distance from the point (x, y, 1-x2-y2 )  to the origin is 
(a) 1
(b) – 1
(c) 0
(d) 2

Answer :   A

Question 3. Three vertices of a parallelogram ABCD are A(1, 2, 3), B(-1, -2, -1) and C(2, 3, 2). Find the fourth vertex D. 
(a) (– 4, – 7, – 6)
(b) (4, 7, 6)
(c) (4, 7, – 6)
(d) None of these

Answer :   B

Question 4. If a parallelopiped is formed by planes drawn through the points (5, 8, 10) and (3, 6, 8) parallel to the coordinate planes, then the length of diagonal of the parallelopiped is 
(a)2 √3
(b)3√2
(c) √2
(d) √3

Answer :   A

Question 5. The points (5, – 4, 2),(4,– 3, 1), (7, -6, 4) and (8, – 7, 5) are the vertices of 
(a) a rectangle
(b) a square
(c) a parallelogram
(d) None of these

Answer :   C

Question 6. If the coordinates of the vertices of a ΔABC are A(-1, 3, 2), B(2, 3, 5) and C(3, 5, – 2), then ? ∠A is equal to
(a) 45°
(b) 60°
(c) 90°
(d) 30°

Answer :   A

Question 7.  Find the ratio in which the YZ-plane divides the line segment formed by joining the points (– 2, 4, 7) and (3, – 5, 8).
(a) externally 2 : 3
(b) internally 2 : 3
(c) internally 3 : 2
(d) externally 3 : 2

Answer :   B

Question 8. Find the coordinates of the point which divides the line segment joining the points (– 2, 3, 5) and (1, -4, 6) in the ratio 2 : 3 externally.
(a) (– 8, – 17, 3)
(b) (– 8, 17, 3)
(c) (8, – 17, 3)
(d) None of these

Answer :   B

Question 9. Find the length of the medians of the triangle with vertices A(0, 0, 6), B(0, 4, 0) and C(6, 0, 0).
(a) 7, 7, √34
(b) 7, 8, √34
(c) 7, 9, √34
(d) None of these

Answer :   A

Question 10. Find the coordinates of the points which trisect the line segment joining the points P(4 , 2, -6) and Q(10, -16, 6).
(a) (6, – 4, – 2), (8, – 10, 2)
(b) (6, 4, – 2), (8, – 10, 2)
(c) (6, – 4, – 2), (8, 10, 2)
(d) None of these

Answer :   B

Question 11. Find the centroid of a triangle, the mid-point of whose sides are D(1, 2, -3), E(3, 0, 1) and F (-1, 1, -4).
(a) (1, 1, 2)
(b) (1, 1, – 2)
(c) (– 1, –1, –2)
(d) (1, –1, –2)

Answer :   B

Question 12. The points A(5, -1, 1), B(7, -4, 7), C(1, -6, 10) and D(-1, -3, 4) are vertices of a 
(a) square
(b) rhombus
(c) rectangle
(d) None of these

Answer :   B

Question 13. If vertices of a triangle are A(1, -1, 2), B(2, 0, -1) and C(0, 2, 1), then the area of a triangle is (a) √6
(b) 2√6
(c) 3√6
(d) 4√6

Answer :   B

Question 14. The point ( -2, -3, -4) lies in the  
(a) first octant
(b) seventh octant
(c) second octant
(d) eight octant

Answer :   B

Question 15. The mid-points of the sides of a triangle are (5, 7, 11), (0, 8, 5) and (2, 3, – 1). Then, the vertices are
(a) (7, 2, 5), (3, 12, 17), (– 3, 4, – 7)
(b) (7, 2, 5), (3, 12, 17), ( 3, 4, 7)
(c) (7, 2, 5), (– 3, 12, 17), (– 3, – 4, – 7)
(d) None of the above

Answer :   A

In This Post we are  providing Chapter-11 Conic Sections NCERT MCQ for Class 11 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON CONIC SECTIONS

Question 1.
The straight line y = mx + c cuts the circle x² + y² = a² in real points if
(a) √{a² × (1 + m²)} < c
(b) √{a² × (1 – m²)} < c
(c) √{a² × (1 + m²)} > c
(d) √{a² × (1 – m²)} > c

Answer: (c) √{a² × (1 + m²)} > c
The straight line y = mx + c cuts the circle x² + y² = a² in real points if
√{a² × (1 + m²)} > c

Question 2.
Equation of the directrix of the parabola x² = 4ay is
(a) x = -a
(b) x = a
(c) y = -a
(d) y = a

Answer: (c) y = -a
Given, parabola x² = 4ay
Now, its equation of directrix = y = -a

Question 3.
The equation of parabola with vertex at origin and directrix x – 2 = 0 is
(a) y² = -4x
(b) y² = 4x
(c) y² = -8x
(d) y² = 8xAnswer

Answer: (c) y² = -8x
Since the line passing through the focus and perpendicular to the directrix is x-axis,
therefore axis of the required parabola is x-axis.
Let the coordinate of the focus is S(a, 0).
Since the vertex is the mid point of the line joining the focus and the point (2, 0) where the directix is x – 2 = 0 meets the axis.
So, 0 = {a – (-2)}/2
⇒ 0 = (a + 2)/2
⇒ a + 2 = 0
⇒ a = -2
Thus the coordinate of focus is (-2, 0)
Let P(x, y) be a point on the parabola.
Then by definition of parabola
(x + 2)² + (y – 0)² = (x – 2)²
⇒ x² + 4 + 4x + y² = x² + 4 – 4x
⇒ 4x + y² = – 4x
⇒ y² = -4x – 4x
⇒ y² = -8x
This is the required equation of the parabola.

Question 4.
The perpendicular distance from the point (3, -4) to the line 3x – 4y + 10 = 0
(a) 7
(b) 8
(c) 9
(d) 10Answer

Answer: (a) 7
The perpendicular distance = {3 × 3 – 4 × (-4) + 10}/√(3² + 4²)
= {9 + 16 + 10}/√(9 + 16)
= 35/√25
= 35/5
= 7

Question 5.
The equation of a hyperbola with foci on the x-axis is
(a) x²/a² + y²/b² = 1
(b) x²/a² – y²/b² = 1
(c) x² + y² = (a² + b²)
(d) x² – y² = (a² + b²)

Answer: (b) x²/a² – y²/b² = 1
The equation of a hyperbola with foci on the x-axis is defined as
x²/a² – y²/b² = 1

Question 6.
If the line 2x – y + λ = 0 is a diameter of the circle x² + y² + 6x − 6y + 5 = 0 then λ =
(a) 5
(b) 7
(c) 9
(d) 11

Answer: (c) 9
Given equation of the circle is
x² + y² + 6x − 6y + 5 = 0
Center O = (-3, 3)
radius r = √{(-3)² + (3)² – 5} = √{9 + 9 – 5} = √13
Since diameter of the circle passes through the center of the circle.
So (-3, 3) satisfies the equation 2x – y + λ = 0
⇒ -3 × 2 – 3 + λ = 0
⇒ -6 – 3 + λ = 0
⇒ -9 + λ = 0
⇒ λ = 9

Question 7.
The number of tangents that can be drawn from (1, 2) to x² + y² = 5 is
(a) 0
(b) 1
(c) 2
(d) More than 2Answer

Answer: (b) 1
Given point (1, 2) and equation of circle is x² + y² = 5
Now, x² + y² – 5 = 0
Put (1, 2) in this equation, we get
1² + 2² – 5 = 1 + 4 – 5 = 5 – 5 = 0
So, the point (1, 2) lies on the circle.
Hence, only one tangent can be drawn.

Question 8.
The equation of the circle x² + y² + 2gx + 2fy + c = 0 will represent a real circle if
(a) g² + f² – c < 0
(b) g² + f² – c ≥ 0
(c) always
(d) None of these

Answer: (b) g² + f² – c ≥ 0
Given, equation of the circle is: x² + y² + 2gx + 2fy + c = 0
This equation can be written as
{x – (-g)}² + {y – (-f)}² + = √{g² + f² – c}²
So, the circle is real is g² + f² – c ≥ 0

Question 9.
The equation of parabola whose focus is (3, 0) and directrix is 3x + 4y = 1 is
(a) 16x² – 9y² – 24xy – 144x + 8y + 224 = 0
(b) 16x² + 9y² – 24xy – 144x + 8y – 224 = 0
(c) 16x² + 9y² – 24xy – 144x – 8y + 224 = 0
(d) 16x² + 9y² – 24xy – 144x + 8y + 224 = 0

Answer: (d) 16x² + 9y² – 24xy – 144x + 8y + 224 = 0
Given focus S(3, 0)
and equation of directrix is: 3x + 4y = 1
⇒ 3x + 4y – 1 = 0
Let P (x, y) be any point on the required parabola and let PM be the length of the perpendicular from P on the directrix
Then, SP = PM
⇒ SP² = PM²
⇒ (x – 3)² + (y – 0)² = {(3x + 4y – 1) /{√(3² + 4²)}²
⇒ x² + 9 – 6x + y² = (9x² + 16y² + 1 + 24xy – 8y – 6x)/25
⇒ 25(x² + 9 – 6x + y²) = 9x² + 16y² + 1 + 24xy – 8y – 6x
⇒ 25x² + 225 – 150x + 25y² = 9x² + 16y² + 1 + 24xy – 8y – 6x
⇒ 25x² + 225 – 150x + 25y² – 9x² – 16y² – 1 – 24xy + 8y + 6x = 0
⇒ 16x² + 9y² – 24xy – 144x + 8y + 224 = 0
This is the required equation of parabola.

Question 10.
If the parabola y² = 4ax passes through the point (3, 2), then the length of its latusrectum is
(a) 2/3
(b) 4/3
(c) 1/3
(d) 4

Answer: (b) 4/3
Since, the parabola y² = 4ax passes through the point (3, 2)
⇒ 2² = 4a × 3
⇒ 4 = 12a
⇒ a = 4/12
⇒ a = 1/3
So, the length of latusrectum = 4a = 4 × (1/3) = 4/3

Question 11.
The eccentricity of an ellipse is?
(a) e = 1
(b) e < 1
(c) e > 1
(d) 0 < e < 1

Answer: (d) 0 < e < 1
The eccentricity of an ellipse e = √(1 – a²/b²) and 0 < e < 1

Question 12.
If the length of the tangent from the origin to the circle centered at (2, 3) is 2 then the equation of the circle is
(a) (x + 2)² + (y – 3)² = 3²
(b) (x – 2)² + (y + 3)² = 3²
(c) (x – 2)² + (y – 3)² = 3²
(d) (x + 2)² + (y + 3)² = 3²

Answer: (c) (x – 2)² + (y – 3)² = 3²
Radius of the circle = √{(2 – 0)² + (3 – 0)² – 2²}
= √(4 + 9 – 4)
= √9
= 3
So, the equation of the circle = (x – 2)² + (y – 3)² = 3²

Question 13.
If the length of the major axis of an ellipse is three times the length of the minor axis then its eccentricity is
(a) 1/3
(b) 1/√3
(c) 1/√2
(d) 2√2/√3

Answer: (d) 2√2/√3
Given, the length of the major axis of an ellipse is three times the length of the minor axis
⇒ 2a = 3(2b)
⇒ 2a = 6b
⇒ a = 3b
⇒ a² = 9b²
⇒ a² = 9a² (1 – e²) {since b² = a²(1 – e²)}
⇒ 1 = 9(1 – e²)
⇒ 1/9 = 1 – e²
⇒ e² = 1 – 1/9
⇒ e² = 8/9
⇒ e = √(8/9)
⇒ e = 2√2/√3
So, the eccentricity of the ellipse is 2√2/√3

Question 14.
The equation of parabola with vertex at origin and directrix x – 2 = 0 is
(a) y² = -4x
(b) y² = 4x
(c) y² = -8x
(d) y² = 8x

Answer: (c) y² = -8x
Since the line passing through the focus and perpendicular to the directrix is x-axis,
therefore axis of the required parabola is x-axis.
Let the coordinate of the focus is S(a, 0).
Since the vertex is the mid point of the line joining the focus and the point (2, 0) where the directix is x – 2 = 0 meets the axis.
So, 0 = {a – (-2)}/2
⇒ 0 = (a + 2)/2
⇒ a + 2 = 0
⇒ a = -2
Thus the coordinate of focus is (-2, 0)
Let P(x, y) be a point on the parabola.
Then by definition of parabola
(x + 2)² + (y – 0)² = (x – 2)²
⇒ x² + 4 + 4x + y² = x² + 4 – 4x
⇒ 4x + y² = – 4x
⇒ y² = -4x – 4x
⇒ y² = -8x
This is the required equation of the parabola.

Question 15.
In an ellipse, the distance between its foci is 6 and its minor axis is 8 then its eccentricity is
(a) 4/5
(b) 1/√52
(c) 3/5
(d) 1/2

Answer: (c) 3/5
Given, distance between foci = 6
⇒ 2ae = 6
⇒ ae = 3
Again minor axis = 8
⇒ 2b = 8
⇒ b = 4
⇒ b² = 16
⇒ a² (1 – e²) = 16
⇒ a² – a² e² = 16
⇒ a² – (ae)² = 16
⇒ a² – 3² = 16
⇒ a² – 9 = 16
⇒ a² = 9 + 16
⇒ a² = 25
⇒ a = 5
Now, ae = 3
⇒ 5e = 3
⇒ e = 3/5
So, the eccentricity is 3/5

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