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Priyanshu answered 1 year(s) , 7 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

• 38 Likes
• 187523 Views

Nov 13

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
• 167000 Views

Apr 15

Priyanshu answered 1 year(s) , 7 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

• 12 Likes
• 140087 Views

Jan 18

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
• 118206 Views

Apr 20

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
• 108822 Views

Apr 20

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
• 107121 Views

Aug 20

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
• 100681 Views

Apr 28

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

• SME Approved

Nov 24

• 9 Likes
• 96458 Views

Nov 24

Yogita answered 1 year(s) , 3 month(s) ago

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

Sep 1

• 13 Likes
• 94234 Views

Sep 1

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
• 87693 Views

May 22

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
• 85379 Views

Apr 27

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
• 81634 Views

Feb 11

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
• 79408 Views

Feb 27

A circle is touching the side BC of a triangle ABC at P and is touching AB and AC when produced Q and R respectively. prove that AQ = 1/2(perimeter of triangle ABC)

Sol:

Given:  A circle touching the side BC of ΔABC at P and AB, AC produced at Q and R respectively.

RTP: AP = 1/2 (Perimeter of ΔABC)

Proof: Lengths of tangents...

Dec 15

• 2 Likes
• 70992 Views

Dec 15

Agam answered 1 year(s) , 10 month(s) ago

If the roots of the equation (a-b)x2 + (b-c)x + (c-a) = 0 are equal

Given quadratic equation is (a – b)x 2 + (b – c)x + (c – a) = 0
Since the root are equal, discriminent of the quadritic equation = 0
Hence (b – c) 2 = 4(a – b)(c – a)...

Aug 8

• 8 Likes
• 69918 Views

Aug 8

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

Prove that. tan/1-cot+cot/1-tan=(1+sec cosec)

Consider LHS:

Aug 26

• 8 Likes
• 69173 Views

Aug 26

Find the point on the x-axis which is equidistant from (2,-5) and (-2,9)

Let the point of x-axis be P(x, 0)
Given A(2, -5) and B(-2, 9) are equidistant from P
That is PA = PB
Hence PA 2 = PB 2  → (1)
Distan...

Dec 25

• 3 Likes
• 67402 Views

Dec 25

1] what is the smallest no. that when divided by 35,56,91 leaves a remainder 7 in each case?

Sol:
The smallest number which when divided by 35, 56 and 91 = LCM of 35, 56 and 91

35 = 5 x 7
56 = 2 x 2 x 2 x 7
91 = 7 x 13

LCM = 7 x 5 x 2 x 2 x 2 x 13...

Sep 9

• 1 Like
• 66694 Views

Sep 9

show that (n2-1) Is divisible by 8??

Sol:

If 'n' is an odd positive integer, show that (n 2-1) Is divisible by 8??

Any odd positive integer is in the form of 4p + 1 or 4p+ 3 for some integer p.
...

Aug 16

• 3 Likes
• 66550 Views

Aug 16

Two water tap together can fill a tank in 75/8 hours. The tap of larger daimeter takes 10 hours less than the smaller one to fill the tank saparately. Find the time in which each tap can saparately fi

Sol :
Let the tap of the larger diameter fills the tank alone in ( x – 10) hours.

In 1 hour, the tap of the  smaller diameter can fill 1/ x part of the tank....

Jun 21

• 8 Likes
• 64272 Views

Jun 21

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