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Priyanshu answered 2 year(s) , 1 month(s) ago

The ratio of the sum of n terms of two A.P.s is (7n+1):(4n+27).

Answer. Given ratio of sum of n terms of two AP’s = (7n+1):(4n+27)
Let’s consider the ratio these two AP’s mth terms as am : a’m →(2)
Recall the nth term of AP formula, an = a + (n – 1)d...

Nov 13

• 39 Likes
• 189269 Views

Nov 13

Syeda answered 2 year(s) , 6 month(s) ago

Show that one and only one out of n,n+2,n+4 is divisible by 3, where n is any positive integer.

We applied Euclid Division algorithm on n and 3.
a = bq +r  on putting a = n and b = 3
n = 3q +r  , 0 i.e n = 3q   -------- (1),n = 3q +1 --------- (2), n = 3...

Apr 15

• 32 Likes
• 171729 Views

Apr 15

Priyanshu answered 2 year(s) , 1 month(s) ago

What are the values of log from 1 to 10?

log 1 = 0
log 2 = 0.3010
log 3 = 0.4771
log 4 = 0.6020
log 5 = 0.6989
log 6 = 0.7781
log 7 = 0.8450
log 8 = 0.9030
log 9 = 0.9542 <...

Jan 18

• 14 Likes
• 145404 Views

Jan 18

Agam answered 2 year(s) , 4 month(s) ago

Least number to be added to make to make it a perfect square

Q1 find the least number which must be added to 7900 to obtain a perfect square?

Solution:

First let us find the square of 7900 using long division method.

The remainder is

...

Apr 14

• 35 Likes
• 144981 Views

Apr 14

Syeda answered 2 year(s) , 6 month(s) ago

Find 6 rational numbers between root 2 and root 3

We know
Root 2 = 1.414
Root 3 = 1.732

Now, we can write n number of rational number between these. That is just greater than 1.414 and less than 1.732 and it should be terminatin...

Jul 10

• 22 Likes
• 131013 Views

Jul 10

Yuvraj answered 2 year(s) , 2 month(s) ago

What is the fullform of CPCT?

Sol:
The full form of CPCT is Corresponding parts of Congruent Triangles.

Sep 18

• 33 Likes
• 127252 Views

Sep 18

Syeda answered 2 year(s) , 5 month(s) ago

Find the value of tan 15 degrees

Let  tan(15°) = tan(45°-30°)

We know that tan(A - B) = (tanA - tanB) /(1 + tan A tan B)

⇒tan(45°-30°) = (tan45°- tan30°)/(1+tan45°tan30°)

= {1-

...

Apr 20

• 12 Likes
• 125686 Views

Apr 20

Syeda answered 2 year(s) , 6 month(s) ago

Find the greatest 6 digits number exactly divisible by 24, 15,and 36.

We will find out the LCM of 24,15 and 36 is 360.

Now, greatest 6-digit number is 999999.

Now, We will divide this number by LCM of 24,15 and 36, we will get,

999999/360 will get remai

...

Apr 20

• 7 Likes
• 115056 Views

Apr 20

Syeda answered 2 year(s) , 6 month(s) ago

If the polynomial X4- 6X3+16X2-25X+10 is divided by X2-2X+k

Given that the remainder is (x + a)
⇒ (4k – 25 + 16 – 2k)x + [10 – k(8 – k) ] = x + a
⇒ (2k – 9)x + [10 – 8k + k 2 ] = x + a
On comparing both the sides, we get...

Aug 20

• 10 Likes
• 112687 Views

Aug 20

Syeda answered 2 year(s) , 6 month(s) ago

If x + 1/x = 3 , then find the value of x6+1/x6.

Assuming the question as (x + 1/x) = 3
Squaring on both the sides we get
(x + 1/x) 2 = 3 2
x 2 +(1/x 2) + 2 = 9
⇒ x 2...

Aug 19

• 30 Likes
• 106552 Views

Aug 19

Syeda answered 2 year(s) , 6 month(s) ago

A plane left 30 min later than the scheduled time and in order to reach the destination 1500km away in time it has to increase the speed by 250km/h from the usual speed. find its usual speed

Sol:
Let the usual time taken by the aeroplane = x km/hr
Distance to the destination = 1500 km
Case (i)
Speed = Distance / Time = (1500 / x) Hrs

Case (iI)...

Apr 28

• 6 Likes
• 101204 Views

Apr 28

Syeda answered 2 year(s) , 6 month(s) ago

If mth term of an A.P is 1/n and the nth term is 1/m

• SME Approved

Nov 24

• 9 Likes
• 98456 Views

Nov 24

Yogita answered 1 year(s) , 9 month(s) ago

In this solution triangle ABC and ACE is taken in place of ABC, ABE should be taken.

Sep 1

• 13 Likes
• 94605 Views

Sep 1

Syeda answered 2 year(s) , 6 month(s) ago

Find the largest number which divide 615 and 963 leaving remainder 6 in each case.

To find the largest number which divides 615 and 963 leaving remainder 6 in each case i.e. HCF.

Consider HCF be x.

In order to make 615 and 963 completely divisible by x, we need to deduct th

...

May 22

• 6 Likes
• 90372 Views

May 22

Syeda answered 2 year(s) , 5 month(s) ago

Prove that the product of three consecutive positive integer is divisible by 6.

Sol;
Let us three consecutive  integers be, n, n + 1 and n + 2.
Whenever a number is divided by 3 the remainder obtained is either 0 or 1 or 2.
let n = 3p or 3p + 1 or 3p + 2, where p is so...

Apr 27

• 6 Likes
• 89674 Views

Apr 27

Syeda answered 2 year(s) , 6 month(s) ago

Find the missing frequencies in the following frequency distribution

Given, mean = 50.25
Sum of observations = 80
That is (60 + x + y) = 80
(x + y) = 20 … (1)
Mean = (2880 + 45x + 75y)/80
That is (50.25 × 80) = 2880 + 45x + 75y...

Feb 9

• 11 Likes
• 86819 Views

Feb 9

Hhh answered 1 year(s) , 7 month(s) ago

Find integral of root tan x .

∫√(tan x) dx

Let tan x = t2

⇒ sec2 x dx = 2t dt

⇒ dx = [2t / (1 + t4)]dt

⇒ Integral  ∫ 2t2 / (1 + t4

...

Feb 11

• 14 Likes
• 85269 Views

Feb 11

Syeda answered 2 year(s) , 6 month(s) ago

To find 4th vertex of a parallelogram

Given three of vertices of a parallelogram are A(1,2), B (4,3), C (6,6).

Let the coordinates of fourth vertex be D (x, y)

In a parallelogram, diagonals bisect each other.

He

...

Feb 11

• 4 Likes
• 83033 Views

Feb 11

Syeda answered 2 year(s) , 6 month(s) ago

In an ap of 50 terms, the sum of 1st 10 terms is 210 and the sum of its last 15 terms is 2565. find the a.p.

Consider a and d as the first term and the common difference of an A.P. respectively.

n th term of an A.P., an = a + ( n – 1)d

Sum of n terms of an A.P., S n = n/

...

Feb 27

• 5 Likes
• 80322 Views

Feb 27

Syeda answered 2 year(s) , 6 month(s) ago

A traffic light at three different road crossing change

Given that traffic light at three different road crossing change after every 48 seconds,72 seconds and 108 seconds respectively.
48 = 2 × 2 × 2 × 2 × 3
72 = 2 × 2 × 2 × 3

...

Sep 16

• 5 Likes
• 77031 Views

Sep 16

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