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New Mathematics Short Tricks Notes

   Published Date: 5th August 2023
New Mathematics Short Tricks Notes

New Mathematics Short Tricks Notes

Hello Aspirants,

1. Number System:

Natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers.
2. Algebra:

Equations, inequalities, polynomials, factoring, algebraic expressions, and solving linear and quadratic equations.
3. Geometry:

Points, lines, angles, polygons, triangles, circles, congruence, similarity, and properties of shapes.
4. Trigonometry:

Trigonometric functions (sine, cosine, tangent), identities, trigonometric ratios, and solving trigonometric equations.
5. Calculus:

Differentiation: Derivatives, rules, rates of change.
Integration: Antiderivatives, definite and indefinite integrals, applications in finding area and volume.
6. Statistics and Probability:

Data analysis, measures of central tendency, measures of dispersion, probability theory, and basic counting principles.
7. Linear Algebra:

Vectors, matrices, systems of linear equations, determinants, eigenvalues, eigenvectors.
8. Coordinate Geometry:

Equations of lines, slopes, distance formula, midpoint formula, conic sections.
9. Discrete Mathematics:

Sets, relations, functions, logic, combinatorics, graph theory, and number theory.
10. Applied Mathematics:

Calculus in physics, engineering, economics, and other fields.
Optimization, differential equations, and mathematical modeling.
11. Mathematical Proof:

Understanding and constructing proofs to establish the validity of mathematical statements.
12. Mathematical Notation:

Symbols, notation, and conventions used in mathematics.

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Important Question & Answer Mathematics Formula 

  • प्राकृतिक संख्या (Natural Numbers) – an – bn = (a – b)(an-1 + an-2 +…+ bn-2a + bn-1)
  • सम संख्या (Even) –  (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)
  • विषम संख्या (Odd) – (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1)
  • (a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….
  • घातांक के नियम (Low Of Formula Exponents)
  • 1. (am)(an) = am+n
  • 2. (ab)m = ambm
  • 3. (am)n = amn
  • a2 – b2 = (a – b)(a + b)
  • (a+b)2 = a2 + 2ab + b2
  • a2 + b2 = (a – b)2 + 2ab
  • (a – b)2 = a2 – 2ab + b2
  • (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
  • (a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc
  • (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
  • (a – b)3 = a3 – 3a2b + 3ab2 – b3
  • a3 – b3 = (a – b)(a2 + ab + b2)
  • a3 + b3 = (a + b)(a2 – ab + b2)
  • (a + b)3 = a3 + 3a2b + 3ab2 + b3
  • (a – b)3 = a3 – 3a2b + 3ab2 – b3
  • (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)
  • (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)
  • a4 – b4 = (a – b)(a + b)(a2 + b2)
  • a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)

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Maths QUESTION ANSWER

1. The average of first 50 natural numbers is …………..

A. 25.30
B. 25.5
C. 25.00
D. 12.25Answer- B. 25.52. A fraction which bears the same ratio to 1/27 as 3/11 bear to 5/9 is equal to ……….. .

A. 1/55
B. 55
C. 3/11
D. 1/11
Answer- A. 1/55

3. The number of 3-digit numbers divisible by 6, is ………….. .

A. 149
B. 166
C. 150
D. 151Answer- C. 1504. What is 1004 divided by 2?

A. 52
B. 502
C. 520
D. 5002
Answer- B. 502

 5. A clock strikes once at 1 o’clock, twice at 2 o’clock, thrice at 3 o’clock and so on. How many times will it strike in 24 hours?

A. 78
B. 136
C. 156
D. 196Answer- C. 156

6. 106 × 106 – 94 × 94 = ?

A. 2004
B. 2400
C. 1904
D. 1906

Answer- B. 2400

7. Which of the following numbers gives 240 when added to its own square?

A. 15
B. 16
C. 18
D. 20

Answer- A. 15

8. The simplest form of 1.5 : 2.5 is …………… .

 A. 6 : 10
B. 15 : 25
C. 0.75 : 1.25
D. 3 : 5
Answer-  D. 3 : 5
9. 125 gallons of a mixture contains 20% water. What amount of additional water should be added such that water content be raised to 25%?
A. 15/2 gallons.
B. 17/2 gallons.
C. 19/2 gallons.
D. 81/3 gallons.

Answer- D. 81/3 gallons.

10. Evaluation of 83 × 82 × 8-5 is …………. .

A. 1
B. 0
C. 8
D. None of these.
Answer- A. 1

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