Skip to main content

Posts

FEATURED ARTICLES

Volume and surface area | short tricks and fast track arithmetic formulae in Hindi | LAWS OF NATURE

आयतन तथा पृष्ठिय क्षेत्रफल (VOLUME AND SURFACE AREA)
1). यदि किसी गोले, घनाभ, घन, बेलन तथा शंकु के आयतन में सम्मिलित तीनों कोरो या विमाओ में क्रमशः x%, y% व z% का परिवर्तन कर दिया जाए, तो उनके आयतनों में परिवर्तन होगा।     = {x +y + z +([xy+ yz + zx]/100) + xyz/100^2}
2). यदि किसी गोले व घन के आयतन में सम्मिलित तीनों कोरो या विमाओ में x% का परिवर्तन कर दिया जाए, तो उनके आयतनों में परिवर्तन होगा = (3x+3x^2/100+x^3/100^2) या [(1+x/100)^3 - 1]×100%
3). यदि किसी बेलन की त्रिज्या को स्थिर रखकर उसके ऊंचाई में x% की वृद्धि कर दी जाए, तो उसके आयतन में प्रतिशत वृद्धि = x% 
4). यदि बेलन की त्रिज्या, घन का किनारा तथा गोले की त्रिज्या में x% का परिवर्तन किया जाता है, जबकि ऊंचाई स्थिर रखा गया है, तब आयतन में परिवर्तन = (2x + x^2/100)%
5). यदि बेलन तथा शंकु के त्रिज्या तथा ऊंचाई में x% तथा y% का बदलाव किया गया है, तब आयतन में प्रतिशत बदलाव =     [ 2x + y + (x^2+2xy/100) + x^2.y/100^2]
6). यदि बेलन तथा शंकु के त्रिज्या तथा ऊंचाई में x% का बदलाव किया जाए, तब आयतन में परिवर्तन =      [(1+x/100)^3 - 1]×100%
7). ध…
Recent posts

Area and perimeter | short - tricks and fast track arithmetic formulae in Hindi | LAWS OF NATURE

क्षेत्रफल एवं परिमाप (AREA AND PERIMETER)
1). a भुजा वाले संबाहू त्रिभुज के अंत:वृत की त्रिज्या तथा क्षेत्रफल होता है। = a/2√3 तथा πa^2/12
2). a भुजा वाले संबाहु त्रिभुज के परी वृत की त्रिज्या तथा क्षेत्रफल होता है। = a/√3 तथा πa^2/3
3). a भुजा वाले वर्ग के अन्तर्गत खिंचे जाने वाले अधिकतम त्रिज्या के वृत का क्षेत्रफल = πa^2/4
4). यदि एक आयत की लंबाई व चौड़ाई क्रमशः एल व b हैं, तब इसके अंदर खिंचे जाने वाले अधिकतम त्रिज्या के वृत का क्षेत्रफल = πb^2/4
5). यदि किसी आकृति की एक भुजा को m गुना तथा दूसरी भुजा को n गुना कर दिया जाए तो क्षेत्रफल में आवश्यक वृद्धि = (mn -1)×100%
6). यदि किसी आयत की लंबाई व चौड़ाई में क्रमशः x% व y% की वृद्धि कर दी जाए तो उस आयत के क्षेत्रफल में वृद्धि =        (x+y+xy/100)%
7). यदि किसी आयत की लंबाई में x% की वृद्धि तथा चौड़ाई में y% की कमी कर दी जाए तो उस आयत के क्षेत्रफल में वृद्धि/कमी होगी = (x-y -xy/100)%
8). यदि किसी आयत की लंबाई में x% की वृद्धि /कमी कर दी जाए, तो उस आयत के क्षेत्रफल को मूल स्थिति में रखने के लिए उसकी चौड़ाई में आवश्यक वृद्धि/कमी = (100x/100+-x)%

क्या श्रीनिवास रामानुजन का परग्रहियों के साथ कोई संबंध था?

श्रीनिवास रामानुजन का परग्रही संबंध
हर युग में जन्म लेते हैं, कुछ ऐसे बच्चे, जिनमें ऐसी गजब कि काबिलियत होती है, जो हमेशा से ही साधारण जन मानस को हैरान करते आए हैं। ये बच्चे बचपन से ही विलक्षण प्रतिभा के धनी होते हैं, ये कम उम्र में ही ऐसी चीजे सीख लेते हैं, जिनका किसी भी तरह से उस छोटी उम्र में सीख पाना मुश्किल होता है।
एक ऐसे ही विलक्षण बुद्धि वाले बालक(श्रीनिवास रामानुजन) का जन्म तमिलनाडु राज्य के इरोड गांव में 22 दिसम्बर 1887 को हुआ, जो भारत में स्थित है। हालांकि श्रीनिवास रामानुजन एक लम्बी आयु नहीं प्राप्त कर पाए और 32 वर्ष की उम्र में हेपटिक अमोबियासिस नामक बीमारी के वजह से 26 अप्रैल 1920 को दीर्घ निंद्रा में सो गए। 
लेकिन इन 32 वर्षो के जीवनकाल में इन्होंने जो कर दिखाया, शायद कोई सैकड़ों वर्षों की जीवन अवधि में भी ना कर पाए।  एमोरी यूनिवर्सिटी, अटलांटा जॉर्जिया, दिसंबर 2012 - एक लंबे समय के अध्ययन के बाद गणितज्ञ केन ऑनो और उनके दो साथियों ने एक ऐसे मैथमेटिकल फार्मूले को पाया जो ब्लैक होल को एक नए तरीके से अध्ययन करने में मदद करता है।  केन ऑनो ने उस गणितीय फॉर्म्युले के कुछ पैराग्रा…

Short-tricks and fast track arithmetic formulae on COMPOUND INTEREST | Laws Of Nature

ARITHMETIC FORMULAE ON COMPOUND INTEREST
1). If P principle is invested with r% pa for n years at compound interest-
*. If Interest is compounded annually then amount is , A = P(1+r/100)^n
*. If Interest is compounded half yearly then amount is , A = P(1+r/200)^2n
*. If interest is compounded quarterly then amount is , A = P(1+r/400)^4n
2). If a city population is P , and it is increasing at the rate of r% annually then-
*. Population after n years -     Population = P(1+r/100)^n
*. Population before n years -     Population = P/(1+r/100)^n
3). If any principle on compound interest become x times in n1 years and y times in n2 years, then = [x^(1/n1) = y^(1/n2)]
4). If the simple interest of any principle for 2 years at the rate of r% annually is SI , then -   Compound Interest = SI(1+r/200)
5). If the simple interest of any principle for 2 years at the rate of r% annually is SI , then the difference between the compound interest and the simple interest is = SI×r/200
6). At compound i…

SIMPLE INTEREST | fast track arithmetic formulae | shortcut tricks for all competitive examination| Laws Of Nature

ARITHMETIC FORMULAE ON SIMPLE INTEREST
1). Principle = Simple interest ×100/rate×Time
2). Simple interest = principle × rate × time/100
3). Rate = simple interest ×100/principle × time
4). Time = simple interest × 100/ principle × rate
5). Amount = principle + simple interest
6). Principle = amount - simple interest
7). Principle = amount ×100/[100+(rate×time)]
8). If r1% changes to r2% and in t years Rs x receive more , then principle is = 100×x/(r2 - r1)t
9). Time taken by the principle to become n time of itself with r% simple interest is = 100(n-1)/r
10). If any principle become n times of itself in t years then the interest rate = 100(n-1)/t
11). If any principle become n1 times of itself with r1% in any time period , then in same time period, rate required to become n2 times of itself is          = (n2-1)r1/(n1-1)%
12).  If any principle become n1 times of itself in t1 time period in any interest rate, then in same interest rate, time period required to become n2 times of itsel…

Fast track arithmetic formulae on DISCOUNT | shortcut tricks for all competitive examination| LAWS OF NATURE

ARITHMETIC FORMULAE ON DISCOUNTYOU MAY ALSO LIKE
Important arithmetic formulae on PERCENTAGE
Important arithmetic formulae on LCM and HCF
Important arithmetic formulae on AVERAGE
Important arithmetic formulae on NUMBER SYSTEM
Important arithmetic formulae on ratio & proportion


1). Discount = marked price - selling price
2). Selling price = marked price - discount
3). Marked price = selling price + discount
4). Discount = marked price × discount rate/100
5). Selling price = MP(100-r)/100
6). Discount percent = r ×100/MP
7). If successive discount on marked price is n1% , n2% and n3% , then equivalent discount rate  = 100[1-(100-n1)/100][(100-n2)/100][(100-n3)/100]%
8). If anyone wants to earn R% profit after giving r% discount , then for this the marked price is      = CP(100+R/100-r) , CP = MP(100-r/100+R)
9). Single discount equivalent to two discount rates is = (r1+r2 -r1r2/100)%
10). If marked price and successive discount rates is given as MP and n1, n2 and n3, then the selling pr…

What is escape velocity?| Derivation for escape velocity. | step by step process.

WHAT IS ESCAPE VELOCITY?
It is the minimum velocity with which a body is projected vertically upward to escape out of the Gravitational pull of any planet. Every planets have different escape velocity and it depends upon the mass (M) of the planets, radius (R) , acceleration due to gravity (g) of the planet. Escape velocity of earth is 11.2 Km/sec.  If you want to go out of the earth then you have to go upward with the velocity of 11.2 Km/sec. DERIVATION FOR ESCAPE VELOCITY Here we are going to derive the expression for escape velocity of the earth.
Let's take a body of mass (m) , which is lying at distance x from the centre of the earth. M is the mass of the earth and R is the radius of the earth. According to the Newton's laws of Gravitation, the Gravitational force between the body and the earth is F. And it is given as-
F = GMm/x^2
And if dW be the small work done to displace the body to small distance dx. then 
dW = Fdx = (GMm/x^2)dx
And the total work done in taking the…

Hydrodynamics : fluid at motion , study notes for IIT JEE | concept booster, chapter highlights |

HYDRODYNAMICS : FLUID IN MOTION
FLUID MOTIONSTREAMLINE FLOWIt is the type of flow in which the path taken by the fluid particles under a steady flow is streamline in the direction of the fluid velocity at that point. LAMINAR FLOW
In this type of flow, fluid flows in steady state and moves in the form of layers of different velocities and never intermix while flowing. TURBULENT FLOW
It is also a type of the fluid motion in which velocity of the particles is greater than its critical velocity and particles become irregular during motion. CRITICAL VELOCITYIt is the maximum velocity of the fluid up to which the flow is streamline and above which it become turbulent is called critical velocity.
Mathematically ; Vc = kη/ρr , where η is viscosity of liquid, ρ  is the density of the liquid, r is the radius of the tube. REYNOLDS NUMBERIt is the number scale which determines the nature of the motion of the liquid through the pipe. Reynolds number is given as- = (Inertial force per unit area/viscous force …

Hydrostatic : fluids at rest | concept booster , chapter highlights | study notes for IIT JEE |

HYDROSTATIC : FLUIDS AT REST
PRESSURE DUE TO LIQUID*. Pressure is thrust applied by the liquids at rest per unit surface area of the objects when it is in contact with the liquid. If F is the force applied by the liquid on the small surface area of ∆A then Pressure is given in the form of limit as follows :
*. In CGS system unit of pressure is dyne/cm^2 and in SI system it is N/m^2. A pressure of one  N/m^2 is called a Pascal.
PASCAL LAW Pascal law states that pressure applied by a enclosed liquid is transmitted equally in all directions , to every position of the liquid and wall of the container. HYDROSTATIC PRESSURE OF A LIQUID COLUMN*. Pressure is given as = force / area = ρgh Where ρ is the liquid density and h is height of the liquid column.
*. All hydraulic press and brakes are based on Pascal law.
*. Unit of pressure is Pascal and it denoted as Pa.
*. 1 Bar = 10^5 Pa and 1 torr = 1 mm of Hg. DENSITY AND RELATIVE DENSITY*. Density is given by = mass /volume For water it is = 10^3 kg / m^3  1…

What happened to our solar system, if the mass of the Jupiter became as equal to the mass of the sun?

What if ! The mass of the Jupiter became as equal to the mass of the sun? All we know that our solar system have 8 planets and a sun. Among all the planets Jupiter has the largest mass or you can say Jupiter is the second largest mass body in our solar system.

Now let's imagine a situation in our solar system that, what will happened if the mass of the Jupiter became equal to the mass of the sun?
According to the general theory of relativity universe is infinitely stretched space time fabrics on which all the celestial bodies are kept. All the celestial bodies which are in the outer space haves different masses, so due to their different masses, the depression in the space time fabrics are also different. However here masses of Jupiter and sun are equal then the depression in the space time fabrics are also equal. Below some high probable possibilities are given on the basis of the imagination. If the mass of the Jupiter been equal to the mass of the sun.If the masses of the Jupiter an…