CBSE > Class 10 > Mathematics | CBSE Board | Homework Help

Let a be any positive integer and b = 4
Then, by Euclid''s algorithm a = 4q + r for some integer q 0 and 0 r < 4
Since, r = 0, 1, 2, 3
Therefore, a = 4q or 4q + 1 or 4q + 2 or 4q + 3

Since, a is an odd integer, o a = 4q + 1 or 4q + 3

Case I: When a = 4q + 1

Squaring both sides, we have,
a2 = (4q + 1)2
a2 = 16q2 + 1 + 8q
= 4(4q2 + 2q) + 1
= 4m + 1 where m = 4q2 + 2q

Case II: When a = 4q + 3

Squaring both sides, we have,
a2 = (4q +3)2
    = 16q2 + 9 + 24q
    = 16 q2 + 24q + 8 + 1
    = 4(4q2 + 6q + 2) +1
    = 4m +1 where m = 4q2 +7q + 2

Hence, a is of the form 4m + 1 for some integer m.

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ANSWER

Sin (1+tan)+ cos(1+cot)=sec+cosec

Posted by Abhay Singh 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 6 years, 11 months ago

According to given sum,

sin (1+tan)+cos (1+cot)=sec+cosec

=> LHS= sin (1+tan)+cos (1+1/tan)

=> sin (1+tan)+cos (1+tan)/tan

=> (1+tan)(sin+cos/tan)

=> (1+tan)(sin.tan+cos)/tan

=> (1+tan)(sin²/cos+cos)/tan

=> (1+tan)(sin²+cos²)/tan.cos

=>(1+tan)/tan.cos

=>(1/tan.cos)+tan/tan.cos

=>( cot/cos)+(1/cos)

=> cosec +sec

LHS= RHS.

3Thank You

ANSWER

Show that 12th cannot end with digit 0 or 5 for any natural number 'n'

Posted by Neha Duggal 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Arohi . 6 years, 11 months ago

If 12n ends with 0 then it must have 5 as a factor. But, 12n=(2×2×3)n which shows that only 2 and 3 are the prime factors of 12n. Also, we know from the fundamental theory of arithmetic that the prime factorization of each number is unique. So, 5 is not a factor of 12n. Hence, 12n can never end with the digit 0.

2Thank You

ANSWER

Find the distance between two parallel tangent of a circle of radius 6 CM

Posted by Renu Kumari Kumari 5 years, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Parth Raii???? 6 years, 11 months ago

sb aap jaise faltu nhi baithe h

1Thank You

Gurjar Kabir (बैंसला) 6 years, 11 months ago

12 cm

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ANSWER

Annual profit earned by 30 shops of a Shopping Complex in a locality give rise to following distribution Profit (in l a k h s). No of Shops More than or equal to 5. 3 0 More than or equal to 10. 28 More than or equal to 15. 16 More than or equal to 20. 14 More than or equal to 25. 10 More than or equal to 30. 7 More than or equal to 35. 3 draw both ogive for the data above hence obtain the median profit

Posted by Ramanpreet Singh 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Chetna Pandey 6 years, 11 months ago

How can we draw here???or itna bdaaa question.. .....

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ANSWER

At present asha's age ( in years) is 2 more then the square of her daughter nisha's age. When nisha grows to her mother's present age, asha's age would be one year less than 10 times the present age of nisha. Find the present ages of both asha and nisha.

Posted by Mudit Thakur 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Let the present age of Nisha be x years.
Then, as per given condition
Asha's age (in years) is 2 more than the square of her daughter Nisha's age.
So, Asha's age = x² + 2
Difference in their ages = x² + 2 - x
And, Asha's age when Nisha's age will be (x² + 2) years = ( x² + 2) + (x² + 2 - x)
If Asha's age is one year less than 10 times the present age of Nisha = 10x - 1
So, As per given condition
(x² + 2 - x) + (x² + 2) = 10x - 1
{tex}\Rightarrow{/tex} 2x² - x + 4 = 10x - 1
{tex}\Rightarrow{/tex} 2x² - 11x + 5 = 0
{tex}\Rightarrow{/tex} 2x² - 10x - x + 5 = 0
{tex}\Rightarrow{/tex} 2x(x - 5) - 1(x - 5) = 0
{tex}\Rightarrow{/tex} (x - 5)(2x - 1) = 0
{tex}\Rightarrow{/tex} x - 5 = 0 or 2x - 1 = 0
{tex}\Rightarrow{/tex} x = 5 or {tex}x = \frac{1}{2}{/tex}
{tex}\Rightarrow{/tex} x = 5 [as age can't be a fraction]
{tex}\Rightarrow{/tex} x² + 2 = 5² + 2 = 27
Hence, Nisha's age is 5 years and Asha's age is 27 years.

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ANSWER

If p and q are co-prime, then find HCF of (p,q)

Posted by Mansi ??⚘?? 6 years, 11 months ago

CBSE > Class 10 > Mathematics

7 answers

Mansi ??⚘?? 6 years, 11 months ago

Thanks to all of you ????

0Thank You

Aashu Kumar 6 years, 11 months ago

Answer will be 1

2Thank You

Yogita Ingle 6 years, 11 months ago

Two integers p and q are said to be coprime if they have no common factor other than 1.
∴ HCF of coprime numbers p and q = 1

1Thank You

Dipti Singh 6 years, 11 months ago

2Thank You

@ Aashu 6 years, 11 months ago

Wlcm

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Mansi ??⚘?? 6 years, 11 months ago

Thanks

0Thank You

@ Aashu 6 years, 11 months ago

HCF is one ....becoz coprime nos are having 1 as the common factor

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ANSWER

The sum of first q terms of an A.P. is 162. The ratio of its 6th term to its 13th term is 1:2. Find the first and 15th term of the A.P.

Posted by Anurag Maheshwari 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Let us suppose that 'a' be the first term and 'd' be the common difference of the A.P.
Now according to question it is given that
S₉ = 162.
Using formula for sum to n terms of A.P, we have
{tex}\Rightarrow \frac{9}{2}\left[ {2a + (9 - 1)d} \right] = 162{/tex}
{tex} \Rightarrow \frac{9}{2}\left[ {2a + 8d} \right] = 162{/tex}
{tex}\Rightarrow{/tex} 9a + 36d = 162 ........................(i)
Let a₆ and a₁₃ be the 6^_th and 13^th term of the A.P. respectively.
Therefore, using general form of nth term, we have,a₆ = a + 5d and a₁₃ = a + 12d
Since, {tex}\frac{{{a_6}}}{{{a_{13}}}} = \frac{1}{2}{/tex}
{tex} \Rightarrow \frac{{a + 5d}}{{a + 12d}} = \frac{1}{2}{/tex}
{tex}\Rightarrow{/tex} 2a + 10d = a + 12d
{tex}\Rightarrow{/tex} a = 2d
Now,substituting the value of a = 2d in equation (i), we get,
9(2d) + 36d = 162
{tex}\Rightarrow{/tex} 18d + 36d = 162
{tex}\Rightarrow{/tex} 54d = 162
{tex}\Rightarrow{/tex} d = 3
{tex}\Rightarrow{/tex} a = 2d = 2 {tex}\times{/tex} 3 = 6 = First term

Therefore, 15th term=a+14d=6+14(3)=48

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a girl of height 90 centimetre is walking away from the base of a lamp post at a speed of 1.2 m per second if the length is 3.6 m above the ground find the length of her shadow after 4 seconds

Posted by Chanchal Sheoran 6 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Sohail Akhtar 6 years, 11 months ago

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Gurjar Kabir (बैंसला) 6 years, 11 months ago

Length of her shadow after 4 second is 160 cm

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ANSWER

Find the linear relation between x and y such that P(x,y) is equidistant from the point A(1,4) and B(-1,2).

Posted by Simran Raj 6 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Raj Tomar 6 years, 11 months ago

Hii

1Thank You

Vikram Singh 6 years, 11 months ago

X-Y=5

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ANSWER

SinA+tanA=p then find value of cosecA

Posted by Soham Nirhali 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Raj Tomar 6 years, 11 months ago

1+sin

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ANSWER

If D,E and F are the mid-points of sides BC,CA and AB respectively of a △ABC , whose vertices are A(-4,1) , B(6,7) , and C(2,-9) , then prove that : ar (△DEF)=1/4 ar (△ABC).

Posted by Janhvi Bora 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Janhvi Bora 6 years, 11 months ago

Arrey koi to jawab do!

1Thank You

ANSWER

A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 2 3 . Find the number of blue marbles in the jar

Posted by Shriya ?? 6 years, 11 months ago

CBSE > Class 10 > Mathematics

3 answers

Manoj . 6 years, 11 months ago

1Thank You

Vishakha Singh? 6 years, 11 months ago

8 blue marbles?

3Thank You

Shriya ?? 6 years, 11 months ago

any one answer me

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ANSWER

The sum of the first nth term of an AP is 4n2 + 2n. Find the nth terms of an AP

Posted by Aashna Salam 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Janhvi Bora 6 years, 11 months ago

It's a difficult question??

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ANSWER

The radius of the circle is increasing at the rate of 0.7cm/sec. What is the rate of increasing of its circumference?

Posted by Sumit Kumar 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Ria Trivedi?? 6 years, 11 months ago

7/5pi cm per sec

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ANSWER

What is the relationship between opposite angle of rhombus

Posted by Harsh Tripathi 6 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Anushka Jugran ? 6 years, 11 months ago

Opposite angles r equal in a rhombus

1Thank You

Ria Trivedi?? 6 years, 11 months ago

Opposite angles of rhombus are equal

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ANSWER

Ayush starts walking from his house to office. Instead of going to his office directly,he goes to a bank first, from there his daughter 's school and reach the office. What is extra distance travelled by ayush in office? If the house is situated at (2,4) bank at (5,8) school at (13,14) and office at (13,26) and the coordinates are in km.

Posted by Kiran Yadav 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 6 years, 11 months ago

Solution:

So, extra distance travelled by Ayush in reaching his office = 27 – 24.6 = 2.4 km Hence, the required extra distance travelled by Ayush is 2.4 km.

2Thank You

ANSWER

If m times the m th term of an AP is equal to n times its n th term, show that the (m+n) th term of the AP is 0.

Posted by Robin Andrews Chacko 6 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Sachin Kori 6 years, 11 months ago

Let, "a" be the first term and "d" be the common difference ; Sm =Sn; m/2 { 2a + (m -1)d } = n/2 { 2a + (n-1)d } ; 2am + ( m2 - m )d = 2an + ( n2 - n )d ; 2am - 2an + ( m2 -m )d - ( n2 + n )d = 0 ; 2a (m - n) + ( m2 - m - n2 + n )d = 0 ; 2a (m - n) + ( m2 - n2 - ( m -n )d = 0 ; 2a (m - n) + [( m+n ) (m - n ) - (m - n)]d = 0 ; 2a (m - n) + (m - n) [ m+n - 1]d = 0 ; (m - n) [ 2a + (m+n - 1)d] = 0; since,,, m - n is not equal to zero [therefore m is not equal to n] ; therefore, 2a + ( m+n-1)d = 0 _____ eq.1 ; Sm+n = (m+n)/2 [ 2a + (m+n-1)d] ; Sm+n = m+n/2 × 0 [ from eq. 1] ; Sm+n = 0;; hence proved....

1Thank You

Gaurav Seth 6 years, 11 months ago

Let the first term of AP = a
common difference = d
We have to show that (m+n)th term is zero or a + (m+n-1)d = 0

mth term = a + (m-1)d
nth term = a + (n-1) d

Given that m{a +(m-1)d} = n{a + (n -1)d}
⇒ am + m²d -md = an + n²d - nd
⇒ am - an + m²d - n²d -md + nd = 0
⇒ a(m-n) + (m²-n²)d - (m-n)d = 0
⇒ a(m-n) + {(m-n)(m+n)}d -(m-n)d = 0
⇒ a(m-n) + {(m-n)(m+n) - (m-n)} d = 0
⇒ a(m-n) + (m-n)(m+n -1) d = 0
⇒ (m-n){a + (m+n-1)d} = 0
⇒ a + (m+n -1)d = 0/(m-n)
⇒ a + (m+n -1)d = 0

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ANSWER

Solve for x and y:99x+101y = 499 : 101x + 99y = 501

Posted by Parkil Goswami 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Vaishnavi Singh 6 years, 11 months ago

y=2,x=3

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ANSWER

What is the schedule of toppers for studies

Posted by Sharad Agarwal 6 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Anushka Jugran ? 6 years, 11 months ago

Ye to kisi topper se hi puchna padega.. Mujhe to koi idea nhi hai

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D.J Alok 6 years, 11 months ago

Search in YouTube ?✌?✌️

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Is it true to say that the pair of equations -x+2y +2=0 and x/2-y/4-1=0 has a unique solution.Justify your answer

Posted by Bhatra Pranuth 6 years, 11 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

How to get centum in board xam ?

Posted by Sg . 6 years, 11 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

finding hcf of69 and4 using Euclid, s division algorithms and represent in form of m+n.

Posted by Shristi Kumari 6 years, 11 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

For which values of 'p' does the pair of equation given below as unique solution 4x+py+8=0,2x+2y+2=0

Posted by Achar Sreevathsa 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Samridhi Yadav 6 years, 11 months ago

P should not be equal to 4 rather it can be of any value

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ANSWER

The internal and external diameters of a hollow hemispherical shell are 6cm and 10cm respectively.It is melted and recast into a solid cone of base diameter 14cm.Find the height of cone so formed......Ans is 4cm ... Please answer fast

Posted by Isha Saini 6 years, 11 months ago

CBSE > Class 10 > Mathematics

6 answers

Sachin Kori 6 years, 11 months ago

Given, Internal radius of hemispherical shell ( r ) = 3 cm ; External radius of hemispherical shell ( R ) = 5 cm ; Radius of cone = 7cm ; volume of hemispherical shell = volume of cone ; 2/3 × 22/7 × { (5×5×5) - (3×3×3) } = 1/3 × 22/7 × (7×7) × h ; 2 {(5×5×5) - (3×3×3)} = 49 × h ; 2 { 125 - 27 } = 49 × h ; 2 × 98 = 49 × h ; h = 196 ÷ 49 ; h = 4cm

0Thank You

Samridhi Yadav 6 years, 11 months ago

Ots answer is sixteen by fourty nine

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Sachin Kori 6 years, 11 months ago

Given, Internal radius of hemispherical shell (r) = 3 cm EXternal radius of hemispherical shell (R)= 5 cm Radius of cone = 7 cm volume of hemispherical shell = volume of cone 2/3 × 22/7 { (5×5×5) - (3×3×3) } = 1/3 × 22/7 (7×7) × h 2 { (5×5×5) - (3×3×3)} = 49× h 2 { 125 - 27 } = 49 × h 2 × 98 = 49 × h 196 = 49 × h h = 196 ÷ 49 h = 4 cm

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Isha Saini 6 years, 11 months ago

Lekin uska answer wrong h google pe book me alag answer h

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Isha Saini 6 years, 11 months ago

Uspe ni h ye question

1Thank You

Isha Saini 6 years, 11 months ago

Plzz koi to iska solution dedo

2Thank You

ANSWER

Formula for mid point..