Intersting Maths Questions

 Interesting maths Questions

1) If the sum of two prime numbers X and Y is odd, then the product of X and Y must be divisible by
(a) 2 (b) 3 (c) 4 (d) 8

2) If X is both cube and square of an integer and X is between 20 and 200, then the value of X will be
(a) 4 (b) 16 © 64 (d) 169

3) In the two-digit number X, both the sum and difference of its digit is 4. Then the value of X will be
(a) 13 (b) 31 (c) 40 (d) None of these

4) If the price of petrol is increased by 25%, what % must be reduce his consumption so that expenditure on, petrol may increase only 10%.
(a) 15% (b) 12% (c) 35% (d) none

5) A town has population growth rate of 10% per year. If the population in 1990 was 2000. What was the population in 1992?
(a) 1600 (b) 2200 © 2400 (d) 2800 (e) 2420

6) In a class of 200 students, 40% percent are girls . 25% of the boys and 10% the girls signed up for a tour. What percent of the class signed up for the tour?
(a) 19% (b) 23% © 25% (d) 27%

7) If 15% of the number is 4.5, then 45% of the same number will be.
(a) 10.5 (b) 15.3 (c) 13.5 (d) None of these

8) A school has total enrollment of 90 students there are 30 students taking physics, 25 taking English and 13 taking both what percentage of the students are taking either subjects.
(a) 36% (b) 47% (c) 51% (d) 58%

9) The triangle is formed by joining the points (3,5), (7,9) and ( 0,-3)
(a) Scalene (b)Right angled (c)Equilateral (d) Isosceles

10) Two acute angle of rt. Angled triangle are
(a) Complementary (b) Supplementary (c) Equal (d) None of these

11) In the triangle ABC, If A = 6B= 3C, what will be the Value of < B.
(a) 30 (b) 20 (c) 10 (d) 15

12) The difference between compound interest and simple interest on Rs 5120 for 3 years at 12.5% per annum will be
(a) 150 (b) 200 (c) 250 (d) 300

13) If A= {a, b,c} B= { b,c,d,e} then the Value of A Δ B will be
(a) {a, d,e} (b) {a,b,c,d,e} (c) {a,b} (d) none

14) In a mixture of 50 liters, the ratio of milk to water is 3:2, how much water must be added to make the ratio 2:3.
(a) 20 (b) 25 (c) 30 (d) 40

15) Two numbers are in the ratio 3:4 & their product is 192. then the numbers will be
(a) 16 & 48 (b) 12 & 48 (c) 12 & 16 (d) None of these

16 ) The radius of right circular cylinder is doubled. What is the ratio of old volume to new volume?
(a) 1: 2 (b) 2:1 (c) 1:4 (d) None of these

17) If x+2y= 20, y+ 2z = 9 and 2x+ z = 22 then the arithmetic mean of a, b and c will be
(a) 10/3 (b) 17/3 (c) 17 (d) 22/3

18) If x2 +y2 =25 and (x+y)2 = 169 then the value of xy is
(a) 62 (b) 72 (c) 82 (d) 92

19) If the sums of the three consecutive odd integers in 735, what is the largest of these integer
(a) 245 (b) 247 (c) 249 (d) None

20) The value of 4cosø + 3sin ø =5 then 3cos ø - 4sin ø equal to
(a) 3 (b) 4 (c) 5 (d) None

21) If x2=16, y2=4 which of the greatest possible value of (x-y) 2 ?
(a) 4 (b) 16 (c) 36 (d) 12

22) If x+1/x=2 then the value of x99+1/ x99 will be
(a) 0 (b) 1, (c) 2 (d) 3 (e) None

23) After increasing 12.5% a person gets Rs 2700 find his previous income. (a) Rs 2000 (b) Rs 2500 (c) Rs 2400
24) If 20% of 220 equal 5.5 % of P, what is P?
(a) 10 (b) 55 (c) 800 (d) 110 (e) None

25) If 20% of a is equal to the 80% of b, then a+b is
(a) 5a (b) 2a (c) 2.5a (d) None of these

26) In a mixture of 35 liters, the ratio of milk to water is 4:1 another 7 liters of water is added to the mixture then the ratio of milk to water in the mixture will be. (a) 1:2 (b) 2:1 (c) 2:3 (d) None

27) The difference between C.I and S.I on the sum of Rs 4800 for 2 years at 5% pa will be
(a) Rs 10 (b) Rs 12 (c) Rs 30 d) None

28) A rectangle with one side 4cm is inscribed in a circle of radius 2.5 cm. Then the Area of the rectangle will be
(a) 12cm2 (b) 14cm2 (c) 10cm2 (d) None

29) The largest sphere is carved out of a cube of side 21cm. Then the volume of the remaining wood of cube will be
(a) 4410cm3 (b) 4010 cm3 (c) 4900 cm3 (d) None
30) If 6a+3b=20 and 4a+7b= 10 then the arithmetic mean of a and b is
(a) 25 (b) 15 (c) 20 (d) None

31) If 0.1% of m =10% of n then m is what % of 10n?
(a) 1% (b) 10% © 1000% (d) 100% (e) None

32) If 120% of a is equal to 80% of b, which of the following is equal to a+b
(a) 1.5a (b) 2.5a (c) 3a (d) None

33) If the sides of a square increase by 40%, then the area of the square increases by
(a) 50% (b) 80% (c) 96% (d) 95%

34) If X is an odd positive integer then other consecutive odd integer is
(a) X+2 (b) X+1 (c) X2 (d) 2X

35) If X is increased by 25% then by what percent is X2 increased?
(a) 56.25% (b) 62.25 (c) 50.25% (d) None

36) The selling price of two radios for 960 each. Gained 20% in 1st & loss 20% in the 2nd then loss % on his total outlay will be.
(a) 1% (b) 2% (c) 3% (d) None of these

37) A single discount is equivalent to the successive discount 10% and 5% will be
(a) 14.5% (b) 15% (c) 10% (d) None

38) If a:b=6:7 and b:c= 8:7 than a:c will be
(a) 48:49 (b) 7:9 (c) 30:7 (d) None

39) The points (3,3), (9.0) and (12,21) are the vertices of
(a) Isosceles triangle (b) Equilateral triangle(c) Right angled triangle (d) None of these

40) From a cube of side 21cm, a cone of maximum size is carried out then the volume of the cone will be
(a) 720 cm3 (b) 618 cm3 (c) 718.6 cm3 (d) None

41) If the sum of two sides of a right angled triangle is 17 cm and the hypotenuse is 13cm then the length of sides are
(a) 15 cm and 2 cm (b) 12cm and 5cm (c) 10cm and 7cm (d) None

42) One of the factors of 2x3+7x2-4x-14=0 is will be
(a) x-5 (b) 2x+7 (c) x-3 (d) None

43) David’s income was increased by 10% and later decreased by 10% what is the change percent in his income
(a) 0% (b) 1% (c) 2% (d) 25%

44) If the number 8 and 12 are increased by 25% and 33 1/3% respectively what will be the average incensement?
(a) 30% (b) 25% (c) 20% (d) None

45) Two dice are tossed then the probability of getting a sum of 6 or 5 will be
(a) 7/18 (b) ¼ (c) ¾ (d) None

46) If 3x+2y=11 and 2x+3y= 17, then the average value of x and y will be
(a) 2.5 (b) 2.8 (b) 5.6 (c) 5.8 (d) None

47) If a-b=10 and a2-b2=20 than the value of a+b will be
(a) -6 (b) -4 (c) 2 (d) 6

48) If f(x) = x2+3, then the value of f(-8) will be
(a) 66 (b) 67 (c) 68 (d) 69

49) If tan α+ sin α = m & tan α- sin α = n then the value of m2-n2 will be
(a) mn (b) m2n (c) 2mn ( d) None

50) What is the value of sin α if X= (1+ sin α)/ cos α
(a) (1-X2)/(1+ X2) (b) (-1+X2)/(1+ X2) (c) ) (1+X)/(1- X) (d) (1-X)/(1+ X)

Tricky Maths

Try this simple Maths trick

Try this out???

Step1 : Think of any number.
Step2 : Subtract the number you have thought with 1.
Step3 : Multiply the result with 3.
Step4 : Add 12 with the result.
Step5 : Divide the answer by 3.
Step6 : Add 5 with the answer.
Step7 : Take away the number you have thought from the answer, that is, subtract the answer from the number you have thought.

 Your answer is 8 

Quick Square Trick

Step1 : If you need to square a 2 digit number ending in 5, you can do so very easily with this trick.
Step2 : Mulitply the first digit by itself + 1, and put 25 on the end.
Step3 :That is all!
Step4 : Ex:25 ie(2*(2+1))&25

Be a better Person

Some tips for improving your personality

Success - That's what we want!

1. Be a better listener.


2. Read more and expand your interests.


3. Be a good conversationalist.


4. Have an Opinion.


5. Meet New People.


6. Be yourself.


7. Have a positive outlook and attitude.


8. Be fun and see the humorous side of life.


9. Be supportive of others.
10. Have Integrity and treat people with respect..

Organic Nomenclature

Organic Nomenclature

IUPAC Rules for Alkane Nomenclature

 1.   Find and name the longest continuous carbon chain.
 2.   Identify and name groups attached to this chain.
 3.   Number the chain consecutively, starting at the end nearest a substituent group. 
 4.   Designate the location of each substituent group by an appropriate number and name.
 5.   Assemble the name, listing groups in alphabetical order using the full name (e.g. cyclopropyl before isobutyl). 
    The prefixes di, tri, tetra etc., used to designate several groups of the same kind, are not considered when alphabetizing.

IUPAC Rules for Cycloalkane Nomenclature

 1.   For a monosubstituted cycloalkane the ring supplies the root name (table above) and the substituent group is named as usual. A location number is unnecessary.
 2.   If the alkyl substituent is large and/or complex, the ring may be named as a substituent group on an alkane.
 3.   If two different substituents are present on the ring, they are listed in alphabetical order, and the first cited substituent is assigned to carbon #1. The numbering of ring carbons then continues in a direction (clockwise or counter-clockwise) that affords the second substituent the lower possible location number.
 4.   If several substituents are present on the ring, they are listed in alphabetical order. Location numbers are assigned to the substituents so that one of them is at carbon #1 and the other locations have the lowest possible numbers, counting in either a clockwise or counter-clockwise direction. 
 5.   The name is assembled, listing groups in alphabetical order and giving each group (if there are two or more) a location number. The prefixes di, tri, tetra etc., used to designate several groups of the same kind, are not considered when alphabetizing.\

IUPAC Rules for Alkene and Cycloalkene Nomenclature  1.   The ene suffix (ending) indicates an alkene or cycloalkene.  2.   The longest chain chosen for the root name must include both carbon atoms of the double bond.   3.   The root chain must be numbered from the end nearest a double bond carbon atom. If the double bond is in the center of the chain, the nearest substituent rule is used to determine the end where numbering starts.  4.   The smaller of the two numbers designating the carbon atoms of the double bond is used as the double bond locator. If more than one double bond is present the compound is named as a diene, triene or equivalent prefix indicating the number of double bonds, and each double bond is assigned a locator number.  5.   In cycloalkenes the double bond carbons are assigned ring locations #1 and #2. Which of the two is #1 may be determined by the nearest substituent rule.  6.   Substituent groups containing double bonds are:             H2C=CH–   Vinyl group             H2C=CH–CH2–   Allyl group

 

Physics Quotes

Physics  quotations : from great people to great people

I ask you to look both ways. For the road to a knowledge of the stars leads through the atom; and important knowledge of the atom has been reached through the stars.
Sir Arthur Eddington

All science is either physics or stamp collecting.
Ernest Rutherford

In physics, your solution should convince a reasonable person. In math, you have to convince a person who's trying to make trouble. Ultimately, in physics, you're hoping to convince Nature. And I've found Nature to be pretty reasonable.
Frank Wilczek

It is impossible to trap modern physics into predicting anything with perfect determinism because it deals with probabilities from the outset.
Sir Arthur Eddington

When you are courting a nice girl an hour seems like a second. When you sit on a red-hot cinder a second seems like an hour. That's relativity.
Albert Einstein

When you sit with a nice girl for two hours, you think it's only a minute. But when you sit on a hot stove for a minute, you think it's two hours. That's relativity.
Albert Einstein

Not only is the universe stranger than we imagine, it is stranger than we can imagine.
Sir Arthur Eddington

When a man sits with a pretty girl for an hour, it seems like a minute. But let him sit on a hot stove for a minute-and it's longer than any hour. That's relativity.
Albert Einstein

When forced to summarize the general theory of relativity in one sentence: Time and space and graviton have no separate existence from matter.
Albert Einstein

I am acutely aware of the fact that the marriage between mathematics and physics, which was so enormously fruitful in past centuries, has recently ended in divorce.
Freeman John Dyson

God does not care about our mathematical difficulties. He integrates empirically.
Albert Einstein

Something unknown is doing we don't know what.
Sir Arthur Eddington

I think that a particle must have a separate reality independent of the measurements. That is an electron has spin, location and so forth even when it is not being measured. I like to think that the moon is there even if I am not looking at it.
Albert Einstein

Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute. That's relativity.
Albert Einstein

We have found a strange footprint on the shores of the unknown. We have devised profound theories, one after another, to account for its origins. At last, we have succeeded in reconstructing the creature that made the footprint. And lo! It is our own.
Sir Arthur Eddington

God does not play dice
Albert Einstein

I don't believe in mathematics.
Albert Einstein

99 Physics Facts

Mechanics

1. Weight (force of gravity) decreases as you move away from the earth by distance squared.
2. Mass and inertia are the same thing.
3. Constant velocity and zero velocity means the net force is zero and acceleration is zero.
4. Weight (in newtons) is mass x acceleration (w = mg). Mass is not weight!
5. Velocity, displacement [s], momentum, force and acceleration are vectors.
6. Speed, distance [d], time, and energy (joules) are scalar quantities.
7. The slope of the velocity-time graph is acceleration.
8. At zero (0) degrees two vectors have a resultant equal to their sum. At 180 degrees two vectors have a resultant equal to their difference. From the difference to the sum is the total range of possible resultants.
9. Centripetal force and centripetal acceleration vectors are toward the center of the circle- while the velocity vector is tangent to the circle.
10. An unbalanced force (object not in equilibrium) must produce acceleration.
11. The slope of the distance-tine graph is velocity.
12. The equilibrant force is equal in magnitude but opposite in direction to the resultant vector.
13. Momentum is conserved in all collision systems.
14. Magnitude is a term use to state how large a vector quantity is.
 

Energy

1. Mechanical energy is the sum of the potential and kinetic energy.
2. Units: a = [m/sec²], F = [kg•m/sec²] (newton), work = pe= ke = [kg•m²/sec²] (joule)
3. An ev is an energy unit equal to 1.6 x 10^-19 joules
4. Gravitational potential energy increases as height increases.
5. Kinetic energy changes only if velocity changes.
6. Mechanical energy (pe + ke) does not change for a free falling mass or a swinging pendulum. (when ignoring air friction)
7. The units for power are [joules/sec] or the rate of change of energy.

Electricity

8. A coulomb is charge, an amp is current [coulomb/sec] and a volt is potential difference [joule/coulomb].
9. Short fat cold wires make the best conductors.
10. Electrons and protons have equal amounts of charge (1.6 x 10^-19 coulombs each).
11. Adding a resistor in parallel decreases the total resistance of a circuit.
12. Adding a resistor in series increases the total resistance of a circuit.
13. All resistors in series have equal current (I).
14. All resistors in parallel have equal voltage (V).
15. If two charged spheres touch each other add the charges and divide by two to find the final charge on each sphere.
16. Insulators contain no free electrons.
17. Ionized gases conduct electric current using positive ions, negative ions and electrons.
18. Electric fields all point in the direction of the force on a positive test charge.
19. Electric fields between two parallel plates are uniform in strength except at the edges.
20. Millikan determined the charge on a single electron using his famous oil-drop experiment.
21. All charge changes result from the movement of electrons not protons (an object becomes positive by losing electrons)


Magnetism

22. The direction of a magnetic field is defined by the direction a compass needle points.
23. Magnetic fields point from the north to the south outside the magnet and south to north inside the magnet.
24. Magnetic flux is measured in webers.
25. Left hands are for negative charges and right hands are for positive charges.
26. The first hand rule deals with the B-field around a current bearing wire, the third hand rule looks at the force on charges moving in a B-field, and the second hand rule is redundant.
27. Solenoids are stronger with more current or more wire turns or adding a soft iron core.


Wave Phenomena

28. Sound waves are longitudinal and mechanical.
29. Light slows down, bends toward the normal and has a shorter wavelength when it enters a higher (n) value medium.
30. All angles in wave theory problems are measured to the normal.
31. Blue light has more energy. A shorter wavelength and a higher frequency than red light (remember- ROYGBIV).
32. The electromagnetic spectrum (radio, infrared, visible. Ultraviolet x-ray and gamma) are listed lowest energy to highest.
33. A prism produces a rainbow from white light by dispersion (red bends the least because it slows the least).
34. Light wave are transverse (they can be polarized).
35. The speed of all types of electromagnetic waves is 3.0 x 10⁸ m/sec in a vacuum.
36. The amplitude of a sound wave determines its energy.
37. Constructive interference occurs when two waves are zero (0) degrees out of phase or a whole number of wavelengths (360 degrees.) out of phase.
38. At the critical angle a wave will be refracted to 90 degrees.
39. According to the Doppler effect a wave source moving toward you will generate waves with a shorter wavelength and higher frequency.
40. Double slit diffraction works because of diffraction and interference.
41. Single slit diffraction produces a much wider central maximum than double slit.
42. Diffuse reflection occurs from dull surfaces while regular reflection occurs from mirror type surfaces.
43. As the frequency of a wave increases its energy increases and its wavelength decreases.
44. Transverse wave particles vibrate back and forth perpendicular to the wave direction.
45. Wave behavior is proven by diffraction, interference and the polarization of light.
46. Shorter waves with higher frequencies have shorter periods.
47. Radiowaves are electromagnetic and travel at the speed of light (c).
48. Monochromatic light has one frequency.
49. Coherent light waves are all in phase.

Geometric Optics

50. Real images are always inverted.
51. Virtual images are always upright.
52. Diverging lens (concave) produce only small virtual images.
53. Light rays bend away from the normal as they gain speed and a longer wavelength by entering a slower (n) medium {frequency remains constant}.
54. The focal length of a converging lens (convex) is shorter with a higher (n) value lens or if blue light replaces red.

Modern Physics

55. The particle behavior of light is proven by the photoelectric effect.
56. A photon is a particle of light {wave packet}.
57. Large objects have very short wavelengths when moving and thus can not be observed behaving as a wave. (DeBroglie Waves)
58. All electromagnetic waves originate from accelerating charged particles.
59. The frequency of a light wave determines its energy (E = hf).
60. The lowest energy state of a atom is called the ground state.
61. Increasing light frequency increases the kinetic energy of the emitted photo-electrons.
62. As the threshold frequency increase for a photo-cell (photo emissive material) the work function also increases.
63. Increasing light intensity increases the number of emitted photo-electrons but not their KE.

Internal Energy

64. Internal energy is the sum of temperature (ke) and phase (pe) conditions.
65. Steam and liquid water molecules at 100 degrees have equal kinetic energies.
66. Degrees Kelvin (absolute temp.) Is equal to zero (0) degrees Celsius.
67. Temperature measures the average kinetic energy of the molecules.
68. Phase changes are due to potential energy changes.
69. Internal energy always flows from an object at higher temperature to one of lower temperature.

Nuclear Physics

70. Alpha particles are the same as helium nuclei and have the symbol .
71. The atomic number is equal to the number of protons (2 for alpha)
72. Deuterium () is an isotope of hydrogen ()
73. The number of nucleons is equal to protons + neutrons (4 for alpha)
74. Only charged particles can be accelerated in a particle accelerator such as a cyclotron or Van Der Graaf generator.
75. Natural radiation is alpha (), beta () and gamma (high energy x-rays)
76. A loss of a beta particle results in an increase in atomic number.
77. All nuclei weigh less than their parts. This mass defect is converted into binding energy. (E=mc²)
78. Isotopes have different neutron numbers and atomic masses but the same number of protons (atomic numbers).
79. Geiger counters, photographic plates, cloud and bubble chambers are all used to detect or observe radiation.
80. Rutherford discovered the positive nucleus using his famous gold-foil experiment.
81. Fusion requires that hydrogen be combined to make helium.
82. Fission requires that a neutron causes uranium to be split into middle size atoms and produce extra neutrons.
83. Radioactive half-lives can not be changed by heat or pressure.
84. One AMU of mass is equal to 931 meV of energy (E = mc²).
85. Nuclear forces are strong and short ranged.

What is Maths?

What is Maths?

Maths is the  collection of mathematical operations and processes involved in the solution of a problem or study of some scientific field.

Mathematics is a group of related sciences, including algebra, geometry, and calculus, concerned with the study of number, quantity, shape, and space and their interrelationships by using a specialized notation.