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Priyanshu answered 1 year(s) , 5 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...

Asked by Venkatesh

Nov 13

  • 5 Answers
  • 37 Likes
  • 183924 Views
Syeda answered 1 year(s) , 10 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.

Answer.

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...

Asked by Hyadarani

Apr 15

  • 2 Answers
  • 28 Likes
  • 149884 Views
Priyanshu answered 1 year(s) , 5 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
log 10 =...

Asked by Yash

Jan 18

  • 3 Answers
  • 12 Likes
  • 122926 Views
Syeda answered 1 year(s) , 9 month(s) ago

Find the value of tan 15 degrees

Answer.

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-

...

Asked by Chundi

Apr 20

  • 3 Answers
  • 10 Likes
  • 105529 Views
Syeda answered 1 year(s) , 10 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)...

Asked by P duraisami

Apr 28

  • 2 Answers
  • 6 Likes
  • 98811 Views
Syeda answered 1 year(s) , 10 month(s) ago

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

Answer.


  • SME Approved

Asked by Lavanya

Nov 24

  • 2 Answers
  • 9 Likes
  • 93770 Views
Yogita answered 1 year(s) , 1 month(s) ago

Prove that 9AD2 = 7AB2

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

Asked by Pranav

Sep 1

  • 3 Answers
  • 13 Likes
  • 93379 Views
Syeda answered 1 year(s) , 10 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

...

Asked by BAISHALI

Apr 20

  • 2 Answers
  • 7 Likes
  • 92087 Views
Syeda answered 1 year(s) , 10 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...

Asked by Krishna

Aug 20

  • 3 Answers
  • 8 Likes
  • 91910 Views
Syeda answered 1 year(s) , 10 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

...

Asked by Pragasam

May 22

  • 2 Answers
  • 6 Likes
  • 79119 Views
Syeda answered 1 year(s) , 10 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

...

Asked by Rutul

Feb 11

  • 2 Answers
  • 4 Likes
  • 76489 Views
Syeda answered 1 year(s) , 10 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/

...

Asked by Ishita

Feb 27

  • 2 Answers
  • 5 Likes
  • 75951 Views
Syeda answered 1 year(s) , 9 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...

Asked by Sparsh

Apr 27

  • 2 Answers
  • 6 Likes
  • 75676 Views
Syeda answered 1 year(s) , 9 month(s) ago

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...

Asked by Shrey

Dec 15

  • 2 Answers
  • 2 Likes
  • 70019 Views
Agam answered 1 year(s) , 7 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)...

  • 4 Answers
  • 8 Likes
  • 67011 Views
Priyanshu answered 1 year(s) , 5 month(s) ago

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

Consider LHS:

Asked by Anjali

Aug 26

  • 3 Answers
  • 8 Likes
  • 65620 Views
Syeda answered 1 year(s) , 10 month(s) ago

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

Answer.

    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...

Asked by Rrahul

Dec 25

  • 2 Answers
  • 3 Likes
  • 65176 Views
Syeda answered 1 year(s) , 9 month(s) ago

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....

Asked by Aman

Jun 21

  • 2 Answers
  • 8 Likes
  • 63205 Views
Syeda answered 1 year(s) , 10 month(s) ago

D,E,F are the mid-points of the sides AB, BC and CA of triangle ABC


Given in ΔABC, D, E and F are midpoints of sides AB, BC and CA respectively.
BC = EC
Recall that the line joining the midpoints of two sides of a triangle is parallel to third side and ha...

Asked by Swetcha

Aug 9

  • 2 Answers
  • 5 Likes
  • 61312 Views
Syeda answered 1 year(s) , 10 month(s) ago

Prove that the sum of the squares of the diagonals of parallelogram


In parallelogram ABCD, AB = CD, BC = AD
Draw perpendiculars from C and D on AB as shown.
In right angled ΔAEC, AC 2 = AE 2 + CE 2 [By Pythagoras theore...

  • 2 Answers
  • 1 Like
  • 56993 Views
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