CBSE Class 10 - Social Science - Mid-Term Sample Question Paper - (2018-19)(#cbsepapers)(#eduvictors)

CBSE Class 10 - Social Science
 - Mid-Term Sample
Question Paper - (2018-19)

Divisibility Rules of Various Numbers - CBSE Class 6-12 - NTSE, Entrance Tests - Mathematics Tips (#cbsenotes)(#entrancetests)(#eduvictors)

Divisibility Rules of Various Numbers 

(2-25)

Divisibility by 2: 
A number is divisible by 2 if its unit’s digit is even or 0.

Divisibility by 3: 
A number is divisible by 3 if the sum of its digits are divisible by 3.

Divisibility by 4: 
A number is divisible by 4 if the last 2 digits are divisible by 4, or if the last two digits are 0’s.

Divisibility by 5: 
A number is divisible by 5 if its unit’s digit is 5 or 0.

Divisibility by 6: 
A number is divisible by 6 if it is simultaneously divisible by 2 and 3.

CBSE Class 10 - Pair of Linear Equations In Two Variables - Solved Examples (#cbsenotes)(#eduvictors)

Pair of Linear Equations In Two Variables 

Solved Examples 

☛Following questions have been asked in previous years of CBSE board examination.

Q1: Solve the following system of linear equations by elimination method (equating the coefficients).
6 (ax + by) = 3a + 2b
6 (bx – ay) = 3b – 2a

Answer:

Given equations :
6 (ax + by) = 3a + 2b ...(1)
6 (bx – ay) = 3b – 2a ...(2)

multiply eqn. (1) by a and equation (2) by b, and add, we get

6a²x + 6aby = 3a² + 2ab
6b²x – 6aby = 3b² – 2ab
────────────────────────
6 (a² + b²)x = 3(a + b)
────────────────────────

⇒ x = ½

Put x = ½ in equation (1), we have

6a × ½ + 6by = 3a + 2b

6by = 2b
⇒ y = ⅓

∴ x = ½ and y = ⅓        (Answer)

CBSE Class 10 - Maths - Introduction to Trigonometry - Short Q and A (#cbsenotes)(#eduvictors)

Introduction to Trigonometry

Short Q and A 

Q1: If sin 3A = cos (A – 26°), where 3A is an acute angle, find the value of A.

Answer: sin 3A = cos (A – 26°)

∵ sin 3A = cos (90° – 3A)
∴ cos (90° – 3A) = cos (A – 26°)

Since
90° – 3A and A – 26° are both acute angles, therefore,
90° – 3A = A – 26°
⇒ A = 29°

Q2: Express cot 85° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

Answer: cot 85° + cos 75° = cot (90° – 5°) + cos (90° – 15°)

= tan 5° + sin 15°

CBSE Class 10 - Maths - Real Numbers (NCERT Exemplar Solutions Ex 1.1 Q4-6) (#cbsenotes)(#eduvictors)

Real Numbers 

(NCERT Exemplar Solutions Ex 1.1)

Question 4:
If the HCF of 65 and 117 is expressible in the form 65m − 117, then the value of m is
(A) 4
(B) 2
(C) 1
(D) 3

Answer: (B) 2

Explanation:
Using Euclid’s division algorithm,
b = aq + r, 0 ≤ r < a [∵ dividend = divisor × quotient + remainder]
⇒ 117 = 65 × 1 + 52
⇒ 65 = 52 × 1 + 13
⇒ 52 = 13 × 4 + 0
∴ HCF (65, 117) = 13 .... (i)

Also, given that, HCF (65, 117) = 65m – 117 ... (ii)

From Equations (i) and (ii), we get
65m − 117 = 13
⇒ 65m = 130
⇒ m = 2

CBSE Class 10 - Maths - Real Numbers (NCERT Exemplar Solutions Ex 1.1 Q1-3) (#cbsenotes)(#eduvictors)

Real Numbers (NCERT Exemplar Solutions Ex 1.1)

Question 1:
For some integer m, every even integer is of the form

(A) m
(B) m + 1
(C) 2m
(D) 2m + 1


Answer: (C) 2m

Explanation:
Even integers are -4, -2, 0, 2, 4, 6 ...
Let m = integers[Since, here integer is represented by m]
such that m = ⋯ , −1, 0, 1, 2, 3, ...
∴ 2m = ⋯ , −2, 0, 2, 4, 6, ...
∴ even integers can be represented in the form of 2m

CBSE Class 9 - Lines and Angles - Brain Teaser (#cbsenotes)(#eduvictors)

Lines and Angles - Brain Teaser

Q: What is the measure of ∠A + ∠B + ∠C + ∠D + ∠E  in the figure given below, assuming no angles and sides are equal. Give reason to your answer.

Answer:

CBSE CLASS 10 - Maths - Real Numbers (NCERT Exercise 1.2) (#cbsenotes)(#eduvictors)

Real Numbers (NCERT Exercise 1.2)

Q1: Express each number as product of its prime factors:
(ⅰ) 140
(ⅱ) 156
(ⅲ) 3825
(ⅳ) 5005
(ⅴ) 7429

Answer:
(ⅰ)  140 = 2 × 2 × 5 × 7 = 2 2 × 5 × 7
(ⅱ)  156 = 2 × 2 × 3 × 13 = 2 2 × 3 × 13
(ⅲ)  3825 = 3 × 3 × 5 × 5 × 17 = 3 2 × 5 2 × 17
(ⅳ)  5005 = 5 × 7 × 11 × 13
(ⅴ)  7429 = 17 × 19 × 23

CBSE Class 10 - Final Examination Date Sheet - (2017-18) (#cbsenotes)(#eduvictors)

CBSE Class 10 - Final Examination Date Sheet - (2017-18)

CBSE Class 10 - Mathematics - Sample Question Paper - (2017-18) (#eduvictors)(#cbseNotes)

CBSE Class 10 - Mathematics - Sample
Question Paper - (2017-18)

CBSE Class 10 - Maths - Periodic Test Paper 2 - (2017-18) (#cbsePapers)

CBSE Class 10 - Maths -
Periodic Test Paper 2 - (2017-18)

Maths Pearls - What is so special about Srinivasa Ramanujan's Magic Square? (#cbseNotes)

What is so special about Srinivasa Ramanujan's Magic Square?

You may be familiar with magic squares. Srinivasa Ramanujan also designed his own magic square.

This magic square looks similar to any other square. What is so special about it?


Sum of any rows is 139

CBSE Class X Mathematics - Chapter 3 - Linear equation in two variables - Revision Questions (#cbseNotes)

Chapter 3 - Linear equation in two variables - Revision Assignment 

Class X Mathematics 

1. The sum of two numbers is 6 and their difference is 4. Find the numbers


2. The sum of two numbers is 15. If the sum of their reciprocals is 3/10. Find the numbers


3. The sum of two numbers as well as the difference between their squares is 9. Find the numbers


4. If we add 5 to the denominator and subtract 5 from the numerator of a fraction, it reduces to 1/8. If we subtract 3 from the numerator and add 3 to its denominator, it reduces to 2/7. Find the fraction

CBSE Class 10 - Maths - Number Systems - Problems and Solutions (#cbsenotes)

Number Systems

Problems and Solutions

(CBSE Class 10)

Q1: Find HCF and LCM of 126 and 156 using prime factorization method.

Answer: HCF of 126 is:

           126
           ╱╲
          2  63
             ╱╲
            3 21
              ╱╲
             3  7

∴ 126 = 2 × 3 × 3 × 7 = 2 × 3² × 7

    HCF of 156 is:

           156
           ╱╲
          2 78
            ╱╲
           2 39
             ╱╲
            3 13

∴ 156 = 2 × 2 × 3 × 13 = 2² × 3 × 13  

∴ HCF (126, 156) = product of common factors with lowest power

= (2ⁱ × 3ⁱ) = 6

CBSE Class 10 - SA2 Maths Sample Question Paper (2016-17)(#cbsepapers)(#cbsenotes)

CBSE Class 10 - SA2 Maths Sample Question Paper (2016-17)

CBSE Class 10 - Maths Sample Question Paper and Marking Scheme (2016-17)(#cbsepapers)

CBSE Class 10  - Maths Sample Question Paper and Marking Scheme (2016-17)

CBSE Class 10 - Pre-Board Maths SA2 Sample Question Paper (2016-17) (#cbsePapers)

CBSE Class 10  - Pre-Board Maths SA2  Sample Question Paper (2016-17)

CBSE Class 10 - Maths - Arithmetic Progressions ( Questions and Answers)

Arithmetic Progressions

Class 10 NCERT Exemplar Chapter Solutions

Q 1(MCQ): In an AP, if d=-4,a_n=7 and a_n=4, then a is equal to

(a) 6

(b) 7

(c) 20

(d) 28

Answer: (d) In an AP, a_n=a+(n-1)d
⇒ 4=a+(7-1) (-4)
⇒ 4=a+6(-4)
⇒ 4+24=a
∴ a=28


Q 2(mcq): In an AP, if a=3.5,d=0 and n=101, then a_n will be
(a) 0

(b) 3.5

(c) 103.5

(d) 104.5

Answer: (b) 3.5
For an AP, a_n =a+(n-1)d=3.5+(101-1)×0
∴ =3.5


Q 3(mcq): The list of numbers are -10,-6,-2,2,.... is

(a) an AP with d=-16

(b) an AP with d=4

(c) an AP with d=-4

(d) not an AP

Answer: (b) The given numbers are -10,-6,-2,2...is
Here, a₁ = -10,
          a₂ = -6,
          a₃ = -2
    and a₄ =2...

Since, a₂ - a₁ = -6-(-10)

           = -6+10=4

   a₃-a₂= -2-(-6)

           =-2+6=4

   a₄-a₃=2-(-2)
            =2+2=4
Each successive term of given list has the same difference i.e.,4.
So, the given list forms an AP with common difference, d=4.


Q 4(mcq): The first four terms of an AP whose first term is -2 and the common difference is -2 are

(a) -2,0,2,4

(b) -2,4,-8,16

(c) -2,-4,-6,-8

(d) -2,-4,-8,-16

Answer: (c) -2,-4,-6,-8
Let the first four terms of an AP are a,a+d,a+2d and a+3d.
Given, that first term, a=-2 and common difference, d=-2, then we have an AP as follows
     -2,-2,-2,-2+2(-2),-2+3(-2)
= -2,-4,-6,-8

CBSE Class 9, 10, 11, 12 - Mathematics - Know about Special Constants

Know about Special Constants

Change is the only constant in our lives. However, there are constants or constant numbers that are frequently used in the domains of Science, Mathematics, Economics etc.

Do you know what is golden ratio?

What is the value of Pi?

What are transcendental numbers?

What's the value of cube root of 2?

CBSE - Class 6-12 - Mathematics - Important Formulas

Mathematics - Important  Formulas 

eduvictors.com has added a new section "Mathematics" and has compiled important formulas on different topics.

Here is the list of Mathematics formulas:

1. Algebra Formulas

⓵ Polynomials
⓶ Fractions
⓷ Algebraic Identities
⓸ Exponents
⓹ Roots