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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...

- 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...

- 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 =...

- 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-

- 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

- 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.

- 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

...- 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...

- 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

...- 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

...- 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., a_{n} = a + ( n – 1)d

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

...- 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...

- 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...

- 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)...

Asked by Rajesh kumar pandey

Aug 8

- 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:

- 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...

- 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....

- 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...

- 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...

Asked by Vaishali mathur

Aug 18

- 2 Answers
- 1 Like
- 56993 Views

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