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If the sum of first m term of an a.p is the same as the sum it's first n term show that the sum of its first m+n term is zero

Posted by Ashutosh Singh 2 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Preeti Dabral 2 years, 7 months ago

Let a be the first term and d be the com m on difference of the given A.P. Then,
S_m= S_n
{tex}\Rightarrow \frac{m}{2}{/tex}{2a + (m - 1) d} = {tex}\frac{n}{2}{/tex}{2a + (n - 1) d}
{tex}\Rightarrow{/tex} 2a(m - n) + {m(m - 1) - n(n - 1)} d = 0
{tex}\Rightarrow{/tex} 2a(m - n) + [(m²- n²) - (m - n)d = 0
{tex}\Rightarrow{/tex} (m - n){2a + (m + n - 1)d = 0
{tex}\Rightarrow{/tex} 2a + (m + n - 1)d = 0 [{tex}\because{/tex} m - n {tex}\ne{/tex} 0] ...(i)
{tex}\therefore {/tex} S_m+n= {tex}\frac{m+n}{2}{/tex} {2a + (m + n - 1) d} = {tex}\frac{m+n}{2} \times {/tex} 0 = 0 [Using (i)]
Hence proved on basis of above equation.

ANSWER

applying division algorithm prove that g(x)=ax²+3x+1 is a factor of the polynomial f(x)=3x⁴+5x³-7x²+2x+2.

Posted by Tanneru Sahithi 2 years, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Naman Sharma 2 years, 8 months ago

It is not in syllabus

Bikkina Sai Ram Teja 2 years, 8 months ago

Use division algorithm

ANSWER

Three circles each of radius 1 touch one another externally and they lie between two parallel lines. The maximum possible distance between the lines is.

Posted by Mayur Raj 2 years, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Taniya . 2 years, 8 months ago

h=23×2=√3 But the required length is L=1+h+1 So, L=2+√3

K. Hema 2 years, 8 months ago

H=root 3, l=1+h+1,=1+root 3+1 =2+ root 3 is the answer.

ANSWER

What do you mean by mathmatics class 10th cbse. And what you choose in 11th if you choose maths so what type of maths have you standard or basic. I choose bio to become a doctor.

Posted by Dev Sharma 2 years, 8 months ago

CBSE > Class 10 > Mathematics

4 answers

Dev Sharma 2 years, 8 months ago

But my class topper girl choose basic for bio so I can realise

Dev Sharma 2 years, 8 months ago

Because in the past I don't have idea about bio ; my thinking is when I take maths standard so we can select bio

Adiba Mansuri 2 years, 8 months ago

If you want to take maths in 11th so choose standard or you have to choose bio so you can choose basic maths...

Dev Sharma 2 years, 8 months ago

Can you hate maths while you choose maths with standard. So why you choose maths

ANSWER

Q1:What type of root exist in quadratic equations? give me most important questions of quadratic equations chapter!. Thanku.

Posted by Dev Sharma 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Naushad Alam 2 years, 8 months ago

The

ANSWER

For which value of P will the line represented by the following pair of linear equations P parallel 3x - 5 -y=0, 6x-2y-p=0 (a) all real values except 10 (b) 10 (c) 5/2 (d) 1/2

Posted by Rounak Gupta 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Aastik Singh 2 years, 8 months ago

a all real value except

ANSWER

Two vertices of an isoceles triangle are (2,0) and (2,5).find the third vertex if the length of the equal side is 3

Posted by Sahil Singh 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Dev Sharma 2 years, 8 months ago

∴ Coordinate of third vertex (a,b) = (22+11,25) and (22−11,25)

ANSWER

What do you mean by step deviation method ?

Posted by ._Nishant _. 2 years, 8 months ago

CBSE > Class 10 > Mathematics

3 answers

Aditya Sharma 2 years, 8 months ago

Sigma fidi divides by sigma fi

Dev Sharma 2 years, 8 months ago

The deviation method will be convenient to apply if all the (dí) have a common factor.

Amit Kumar 2 years, 8 months ago

Maths

ANSWER

What do you mean by step deviation metgod

Posted by ._Nishant _. 2 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Preeti Dabral 2 years, 7 months ago

Step deviation method can be defined as the method used to obtain the mean of large values which is divisible by a common factor. These values of deviations are reduced to a smaller value by dividing all the values by a common factor.

ANSWER

2 ×tan 30°÷1+tan×tan30°

Posted by Dev Lohia 2 years, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Naman Sharma 2 years, 8 months ago

2/1+tan

Kavya Sri 10-A ,12 Jnvo 2 years, 8 months ago

Ans cos 30° Steps tan 30°=1/√3 tan ×tan =tan² 30° Substitute the values. And you will get your answer

ANSWER

if alpha&beta are the zeroes of the polynomial x^2+6x-k such that 2 beta +alpha=11 then k is equal to

Posted by Kumar Soyambhuba 2 years, 8 months ago

CBSE > Class 10 > Mathematics

3 answers

Naman Sharma 2 years, 8 months ago

K=391

Omya Aryan 2 years, 8 months ago

k = 138

Soham Singh 2 years, 8 months ago

k=391

ANSWER

Graphically the pair of equations x=9 and y=17 represents two lines which are

Posted by Aarya Kamat 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Sk Classes 2 years, 8 months ago

Which are perpendicular lines

ANSWER

2x+3y=54 3x+2y=45

Posted by Shubh Chhirolya 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Soham Singh 2 years, 8 months ago

x=27/5, y=72/5

ANSWER

The angry Arjun carried some arrows for fighting with Bheeshm. With half the arrows, he cut down the arrows thrown by Bheeshm on him. Six arrows, he used to kill the rath driver of Bheeshm. With one arrow each he knocked down respectively the rath, flag and the bow of Bheeshm. Finally, with one more than four times the square root of arrows he laid Bheeshm unconscious on an arrow bed. Find the total number of arrows Arjun had.

Posted by Soham Singh 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Sk Classes 2 years, 8 months ago

100

ANSWER

one zero of the quadratic polynomial x2 + 3x + k is 2, then the value of k is 10 -10 5

Posted by Mukul Kumar 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Soham Singh 2 years, 8 months ago

Given, x=2 p(x)=x²+3x+k Putting the value of x p(2)=2²+3(2)+k => 4+6+k=0 k=-10

ANSWER

If two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar

Posted by Arpita Yadav 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Aman Sharma 2 years, 8 months ago

Yes it is similar

ANSWER

In triangles, weather the area of triangle is included or excluded...?

Posted by Omya Aryan 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Vijay Kumar 2 years, 8 months ago

Included

ANSWER

Explain whether 3*5*13*46+23 is prime or composite

Posted by Poorvi Shukla 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

K. Hema 2 years, 8 months ago

(3×5×13×46)+23 (3×5×13×2×23)+23 23(3×5×13×2)+1 Since the number is divisible by only 23. Therefore (3×5×13×46)+23 is a composite number.

ANSWER

The difference between 2 numbers is 26 the larger no. Increase the 3times the smaller no. By 4 find the numbers

Posted by Jasmine . 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Omya Aryan 2 years, 8 months ago

Let the larger number be x, then the smaller number is (x-26). ATQ, x+4 = 3(x-26)…, x+4 = 3x- 78…, 4+78 = 3x-x…, 82 = 2x…, x = 41. The smaller number is 41-26 = 15. Hence, the required numbers are 41 and 15.

ANSWER

A man goes 24 m due west and then 10m due north. How far is he from the starting point

Posted by Shivangi Dixit 2 years, 8 months ago

CBSE > Class 10 > Mathematics

4 answers

Naman Sharma 2 years, 8 months ago

26m

Krish Raj 2 years, 8 months ago

26m.

Anku Mandal 2 years, 8 months ago

By pythagoras theorem, distance from the starting point = √24^2+10^2 = √576+100 = √676 = 26m.

Omya Aryan 2 years, 8 months ago

By pythagoras theorem, distance from the starting point = √24^2+10^2 = √576+100 = √676 = 26m.

ANSWER

Sum of traingle

Posted by Ritik Tomar (Rk) 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Krish Raj 2 years, 8 months ago

180°

ANSWER

The sum of 2 positive numbers is 12 and one number is less than the twice of other number find the number

Posted by Lakshaya Swarnareka 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Puja Rani 2 years, 8 months ago

4 & 8

ANSWER

The 8th term of an AP is zero. Then find its 38th term?

Posted by Rajat Kumar 2 years, 8 months ago

CBSE > Class 10 > Mathematics

3 answers

Saksham Bhardwaj 2 years, 8 months ago

30d, where d is common difference

Rajat Kumar 2 years, 8 months ago

Yes

Raksha Trivedi 2 years, 8 months ago

Is this que complete?

ANSWER

Find the sum of ap 7 10.5 14.........84

Posted by Ali Ahamad Khan 2 years, 8 months ago

CBSE > Class 10 > Mathematics

3 answers

Krish Raj 2 years, 8 months ago

1001

Arpit Singh 2 years, 8 months ago

Sn=n/2(a+l) where a=first term & l=last term then put the value in formula

K. Hema 2 years, 8 months ago

The sum of the first n terms of an Arithmetic Progression is given by Sₙ = n/2 [2a + (n - 1) d] or Sₙ = n/2 [a + l], and the nth term of an AP is aₙ = a + (n - 1)d Here, a is the first term, d is the common difference and n is the number of terms and l is the last term. (i) 7 + 10 ½ + 14 + .... + 84 Given, First-term, a = 7Common Difference, d = 10 ½ - 7 = 21/2 - 7 = 7/2Last term, l = 84 To find the total number of terms, we will use the formula a + (n - 1) d. l = aₙ = a + (n - 1) d 84 = 7 + (n - 1) 7/2 77 = (n - 1) 7/2 22 = n - 1 n = 23 Hence, n = 23 Sₙ = n/2 [a + l] S₂₃ = 23/2 [7 + 84] = (23/2) × 91 = 2093/2 = 1046 ½

ANSWER

Prove that 1/ root 2 is irrational

Posted by Shanmuga Lakshmi 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

K. Hema 2 years, 8 months ago

Rationalize factor =root 2 =1/root 2×root 2/root 2 =Root 2/2 =root 2/2 is a rational number. Let us assume that root 2/2 is a rational number. root 2/2=p/q, q is not equal to 0 Where p and q are co-prime number. root 2/2=p/q Root 2=p/q×2 Multiplication of two rational number is a rational number. Thus root 2 is a rational number. But this contradicts the fact that root 2 is a irrational number. This contradiction arises because of our incorrect assumptions that 1/root 2 is a rational number. Hence 1/root 2 is a irrational number.

ANSWER

Tantheta/1-cottheta + cottheta/1-tantheta = 1 + secthetacosectheta

Posted by Swapnil Kamble 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Puja Rani 2 years, 8 months ago

LHS- tan A 1- cot A 1- tan A so A tan A(tan A-1) (tan A-1) (tan2 A+tan A+1) tan A(tan A-1) + + + + cot A 1 tan A 1- tan A 1 tan A(1- tan A) 1 1-. 1 tan A tan A tan A-1 tan A tan2 A tan A-1 tan A(1- tan A) tan³ A-1 tan² A+tan A+1 tan A =tan A+ 1+ cot A sin A cos A cos A + +1 sin A sin² A+cos² A sin A cos A 1 +1 +1 sin A cos A = sec A cosec A+ 1 =RHS [a3- b3- (a- b) (a2+ab+b²)]

ANSWER

(Cotx-cosecx)²

Posted by Ishan Srivastava 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Aastha Vats 2 years, 8 months ago

Cotx^2 + cosecx^2 - 2cotx cosecx

ANSWER

325 can be expressed as a product of it's primes as :

Posted by Divyanshu Kumar 2 years, 8 months ago

CBSE > Class 10 > Mathematics

4 answers

Ambika Venkat 2 years, 8 months ago

5×5×13

Rithika S 2 years, 8 months ago

(5×5×13) =325 Where all numbers (13, 5) are prime numbers

Rajat Kumar 2 years, 8 months ago

325=5 x 5 x 13 where all are prime numbers

Divyanshu Kumar 2 years, 8 months ago

325 = 5x5x13 = 5^5x13

ANSWER

Two circular cylinders of equal volume have their heights in the ratio 1:2 . The ratio of their radii is

Posted by Sharma Sharma 2 years, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Lakshaya Swarnareka 2 years, 8 months ago

Let r1 and h1 be the radius and height of the first cylinder, then Volume = πr21h1 Similarly r2 and h2 are the radius and height of the second cylinder ∴Volume=πr2h2 But their volumes are equal, ∴πr21h1=πr22h2 =r21r22=h2h1 ⇒h2h1=r22r21 But h1h2=12 ∴r22r21=12⇒r21=2r22 ∴r21r21=21⇒r1r2=√21 ∴ Ration in radii = √2 : 1 Hence the correct answer is √2 : 1

Aastha Vats 2 years, 8 months ago

Let the height be h and 2h and radii be r and R. 22/7 × r^2 × h = 22/7 × R^2 × 2h r^2 × h = R^2 × 2h r^2/R^2 = 2h / h r^2 / R^2 = 2/1 r/R = root 2 / 1 r:R = root 2 : 1

ANSWER

If tanA =√2-1, show that sinA*cosA=√3/4

Posted by Sharma Sharma 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Vivek Prajapati 2 years, 8 months ago

Hlo sach mein nahi aata ki bas enjoy ke liye send Kari ho

ANSWER

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