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By using1,3,5,7,9,11,13,15 Add five times and get 30

If there will be leniency of factorials use, then the answers will be
3!+1+9+3+11=30

3!+1+1+7+15=30

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Deependra Verma

When the length of each side of a cube is increased by 3 cm, its volume is increased by 2457 cm3. Find its side. How much will its volume decrease, if length of each side of it is reduced by 20%?

When length of each side of a cube is increased by 3 cm, its volume is increased by 2457

(a+3)^3-a^3=2457;;;;;;(ecause Volume;of ;cube=a^3)

a^3+3^3+3 imes a^2 imes (3)+3 imes a imes 3^2-a^3=2457

27+9 imes a^2+27 imes a=2457

a^2+3a-270=0

a^2+18a-15a-270=0

a(a+18)-15(a+18)=0

(a-15)(a+18)=0

a=(-18) ;;;;not possible

So, a=15;cm

If side reduced by 20% then  it becomes 12 cm 

then volume reduced by 

=15^3-12^3=3375-1728=1647 cm^3

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Deependra Verma

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Which of the following sets have closure property with respect to addition and multiplication? 1. 1 2. 2,-1 3.1,-1?

For this question go by options is the best approach

Option 1) 1

As only 1 element so it definitely holds closure property.

Option 2)  2,-1

2 imes-1=-2;;;;;2+(-1)=1

Both multiplication and addition are not contained in the given set so this set does not hold closure property.

Option 3) 1,-1

1 imes-1=-1;;;;;1+(-1)=0

The addition is not contained in the given set so this set does not hold closure property.

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Deependra Verma

Which of the following sequences are A.P.?If they are A.P. find the common difference.is 0.3,0.33,0.333,......

The given sequence is 0.3,0.33,0.333,0.3333

a_2-a_1=0.33-0.3=0.03

a_3-a_2=0.333-0.33=0.003

a_3-a_2 eq a_2-a_1

Means common difference is not same 

So, this is not A.P.

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Deependra Verma

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What is the contribution of the Thales of Miletus?

Thales ;has ; been ; credited ; with ; the ; discovery ; of ;five ;geometric ; theorems:

(1) Opposite angles formed by intersecting straight lines are equal

(2) Angle inscribed inside a semicircle is a right angle

(3) A circle is bisected by its diameter

(4) Angles in a triangle opposite two sides of equal length are equal

(5) A triangle is determined if its base and the two angles at the base are given

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Deependra Verma

In the given figure,AB//QRand PA=2cm and PB=3cm,then find the ratio of the areas of the?PQR and?PAB

PA = 2cm;    AQ = 3cm

PQ = PA+AQ= 2+3= 5cm

fracArea; Delta; PQRArea ;Delta; PAB=fracPQ^2PA^2=frac5^22^2=frac254

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Deependra Verma

NEET 2024 Most scoring concepts

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(C) Find out Median from the following seriesSizeFrequency 0-10 02 10-20 18 20-30 30 30–40 45 40–50 35 50-60 30 60-70 06 70-80 03?

Data Range Frequency Cumulative Frequency
0-10 02 02
10-20 18 20
20-30 30 50
30-40 45 95
40-50 35 130
50-60 30 160
60-70 06 166
70-80 03 169
Total 169  

 

First, add the total number of frequencies.

Here, F=169

fracF2=frac1692=84.5

Hence, the value 84.5 lies in the class interval 30-40 from the cumulative frequency table.

So, 30-40 is the median class.

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Deependra Verma

Trignometry identites

Some of the important trigonometry identities are

sin^2 heta+cos^2 heta=1

csc^2 heta-cot^2 heta=1

sec^2 heta- an^2 heta=1

sin(90- heta)=cos heta

cos(90- heta)=sin heta

an(90- heta)=cot heta

cot(90- heta)= an heta

sec(90- heta)=csc heta

csc(90- heta)=sec heta

sin(A+B)=sin A cos B+cos A sin B

sin(A-B)=sin A cos B-cos A sin B

cos(A+B)=cos A cos B-sin A sin B

cos(A-B)=cos A cos B+sin A sin B

an(A+B)=frac an A+ an B1- an A an B

an(A-B)=frac an A- an B1+ an A an B

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Challenge to all those whose fav. subject is math 987654321×987654321 show me with full calculations

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Deependra Verma

Express the rational number with numerators 15 and denominator (-10) with: 1)numerator 75, 2)denominator -40

1)numerator 75

Rational; number=frac15 imes5-10 imes 5=frac75-50

2)denominator (-40)

Rational; number=frac15 imes4-10 imes4=frac60-40

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Deependra Verma

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