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 r = 0, 1, 2, 3
So, a = 4q or 4q + 1 or 4q + 2 or 4q + 3 because 0 ≤ r < 4
Now, 4q i.e., 2(2q) is an even number
∴4q + 1 is an odd number.
4q + 2 i.e., 2(2q + 1) which is also an even number.
∴ (4q + 2) + 1 = 4q + 3 is an odd number.
Thus, we can say that any odd integer can be written in the form 4q + 1 or 4q + 3 where q is some integer.

1Thank You

Shreedhar J 5 years, 1 month ago

By Euclid division lemma, a=4q+r r=0,1,2,3 Case(i).r=0, a=4q=2(2q)=2m[even] (ii). r=1,a=4q+1=2(2q)+1=2m+1[even]

1Thank You

ANSWER

if 1 and -1 are the zeros of the polynomial x to the power 4 + x cube + 10 X square + 6 X + P show that l + 7 + P is equal to M + r o r is equal to zero

Posted by Mahantesh Kajagar 5 years, 1 month ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

use Euclid's algorithms to find HCF of 1190 and 1445 . Express the HCF in the form of 1190m+1445n

Posted by A Mariyappan 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 5 years, 1 month ago

1445 = 1190*1 + 255
1190 = 255*4 + 170
255 = 170*1 + 85
170 = 85*2 + 0
So, now the remainder is 0, then HCF is 85
Now,
85 = 255 - 170
(1445 - 1190) - (1190 - 255*4)
⇒ 1445 - 1190 - 1190 + 255*4
⇒ 1445 - 1190*2 + (1445 - 1190)*4
⇒ 1445 - 1190*2 + 1445*4 - 1190*4
⇒ 1445*5 - 1190*6
⇒ 1190*(- 6) + 1445*5
1190m + 1445n , where m = - 6 and n = 5

0Thank You

ANSWER

Find the values of p so that the equation( p-4 )x²-2(p-4) x+4=0 has real roots

Posted by Lucky Sharma 5 years, 1 month ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

If an AP the sum of n term is equal to n time of first term then common difference is...

Posted by Geeta Jadav 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

आदित्य बड़गुर्जर 5 years, 1 month ago

0Thank You

ANSWER

Write the measure at adjacent , side opposite side and hypotenus of angle

Posted by P L 5 years, 1 month ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Solve for x and y 5/x+y + 1/x-y =2 15/x+y -5/x-y =-2

Posted by Arpita Pathak 5 years, 1 month ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

2(56+56)4

Posted by Rishabh Shukla 5 years, 1 month ago

CBSE > Class 10 > Mathematics

4 answers

Muskan Shekhawat 5 years, 1 month ago

896

0Thank You

Geeta Jadav 5 years, 1 month ago

2(112)4=224×4=896

0Thank You

Raghav Jangir 5 years, 1 month ago

Or koi questions

3Thank You

Raghav Jangir 5 years, 1 month ago

8(56+56) =448+448 =896

1Thank You

ANSWER

From the top of a 7 metre high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height?

Posted by Ashima Dua 5 years, 1 month ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

By using euclid's algorithm find the latgest number which divides 650 and 1170

Posted by Archana Kumari 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Saloni Pathak 5 years, 1 month ago

1170=650 multiply 1+520 650=520 multiply 1+130 520=130multiply 4+0 130 is the answer

1Thank You

ANSWER

Exercise 4.4 problem 5 .10th NCERT solution

Posted by Princess Of God 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Kashish . 5 years, 1 month ago

5. Is it possible to design a rectangular park of perimeter 80 metres and area 400 m2. If so, find its length and breadth. Ans. Let length of park = x metres We are given area of rectangular park = Therefore, breadth of park = metres{Area of rectangle = length × breadth} Perimeter of rectangular park = 2 (length + breath) = metres We are given perimeter of rectangle = 80 metres According to condition: => ⇒ ⇒ ⇒ ⇒ Comparing equation, with general quadratic equation , we get a = 1, b = −40 and c = 400 Discriminant = (1) (400) = 1600 – 1600 = 0 Discriminant is equal to 0. Therefore, two roots of equation are real and equal which means that it is possible to design a rectangular park of perimeter 80 metres and area . Using quadratic formula to solve equation, Here, both the roots are equal to 20. Therefore, length of rectangular park = 20 metres Breadth of rectangular park =

0Thank You

ANSWER

Exercise 6.3 Question no. 10

Posted by Siddhi Pateriya 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years, 1 month ago

10. CD and GH are respectively the bisectors of ∠ACB and ∠EGF such that D and H lie on sides AB and FE of ΔABC and ΔEFG respectively. If ΔABC ~ ΔFEG, Show that:

(i) CD/GH = AC/FG
(ii) ΔDCB ~ ΔHGE
(iii) ΔDCA ~ ΔHGF

Solution:

Given, CD and GH are respectively the bisectors of ∠ACB and ∠EGF such that D and H lie on sides AB and FE of ΔABC and ΔEFG respectively.

(i) From the given condition,

ΔABC ~ ΔFEG.

∴ ∠A = ∠F, ∠B = ∠E, and ∠ACB = ∠FGE

Since, ∠ACB = ∠FGE

∴ ∠ACD = ∠FGH (Angle bisector)

And, ∠DCB = ∠HGE (Angle bisector)

In ΔACD and ΔFGH,

∠A = ∠F

∠ACD = ∠FGH

∴ ΔACD ~ ΔFGH (AA similarity criterion)

⇒CD/GH = AC/FG

(ii) In ΔDCB and ΔHGE,

∠DCB = ∠HGE (Already proved)

∠B = ∠E (Already proved)

∴ ΔDCB ~ ΔHGE (AA similarity criterion)

(iii) In ΔDCA and ΔHGF,

∠ACD = ∠FGH (Already proved)

∠A = ∠F (Already proved)

∴ ΔDCA ~ ΔHGF (AA similarity criterion)

2Thank You

ANSWER

Prove that 3+root 2 is a irrational number

Posted by Jahnavi Velagapudi 5 years, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

Yangzee Sherpa 5 years, 1 month ago

Let us consider that 3√2 is a rational number. It can be written in the form p/q (p and q are co-primes). →p/q = 3√2. →p/3q = √2. Now, p/3q = integer/integer = rational number. But, this contradicts the fact that √2 is irrational. Therefore, our assumption that 3√2 is rational is WRONG. Hence, 3√2 is an irrational number. HoPe It HeLpS yOu??

0Thank You

Gaurav Seth 5 years, 1 month ago

Let us consider that 3root2 is a rational number. It can be written in the form p/q (p and q are co primes)

p/q = 3root2

p/3q = root2

Now,

p/3q = integer/interger

= rational number

But, this contradicts the fact that root2 is irrational.

Therefore, our assumption that 3root2 is rational is WRONG.

Hence, 3root2 is an irrational number.

0Thank You

ANSWER

The roots of the quadratic equation x2 - 0.04 = 0 are

Posted by Rajesh Singh 5 years, 1 month ago

CBSE > Class 10 > Mathematics

3 answers

Mortal Combat 5 years, 1 month ago

0.04 or 0

1Thank You

Mortal Combat 5 years, 1 month ago

hope it will help you

1Thank You

Mortal Combat 5 years, 1 month ago

0.04and 0

1Thank You

ANSWER

The list of numbers-10,-6,-2,2,..... which is AP or not

Posted by Mrunal Keote 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Abhinav Chahar 5 years, 1 month ago

a=-10 Common difference=4

1Thank You

ANSWER

Find all other trigonometrical ratios in triangle PQR, angle Q=90degree and tan=3/4

Posted by Prãvëëñ Yâdåv 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years, 1 month ago

If Tan A = 3/4, then find the other trigonometric ratio of angle A.

sol) Tan A = Opposite side = 3
Adjacent side 4

.^., opposite side : adjacent side = 3:4

For angle A,

opposite side = BC=3k

Adjacent side =AB=4k(where k is any +ve no)

Now, we have in triangle ABC( by Pythagoras theorem)

AC^2 = AB^2 + BC^2

=>(3k)^2 + (4k)^2 = 25k^2

AC = √25k^2

=> 5k = Hypotenuse

Now,we can easily write the other ratios of trigonometry

sin A = 3k = 3
   5k    5

cos A = 4k = 4
   5k    5

cosec A =   1    =  5
   sin A 3

sec A =   1     =   5
   cos A 4

cot A =   1      =  4
   tan A 3

0Thank You

ANSWER

Places A and B are 100 km apart on highway .one car stars fro A and another from B at the same time. If the cars travel in same sites direction at different speeds they meet in 5 hours. If thy travel towards each other,they meet in 1 hour. What are the speeds of two cars?

Posted by Divyanshu Yadav 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years, 1 month ago

Let the speed of car at A be x kmph

and the speed of car at B be y kmph

As per the question,

5x - 5y = 100

x - y = 20 ... (1)

and x + y = 100 ... (2)

Solving (1) and (2), we get,

x = 60 and y = 40

Speed of the car at A = 60 kmph

Speed of the car at B = 40 kmph

0Thank You

ANSWER

Write five Indian mathematician names and their contribution

Posted by Ritika Ritika 5 years, 1 month ago

CBSE > Class 10 > Mathematics

3 answers

Ritika Ritika 4 years, 10 months ago

Thanks

0Thank You

Ritika Ritika 5 years, 1 month ago

And please tell their contribution

0Thank You

Prabhat Mishra 5 years, 1 month ago

Aryabhata. ... Brahmagupta. ... Srinivasa Ramanujan. ... P.C. Mahalanobis. ... C.R. Rao. ... D. R. ... Harish Chandra. ...

5Thank You

ANSWER

2(sin⁶ &+cos⁶&)-3(sin⁴&+cos⁴&)+1=0

Posted by Pragya Bharti 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years, 1 month ago

2(sin⁶θ + cos⁶θ) - 3 (sin⁴θ + cos⁴θ) + 1
=2[(sin²θ)3 + (cos²θ)3] -3[(sin²θ)2 + (cos²θ)2]+1
=2[(sin²θ + cos²θ)3 -3sin²θcos²θ (sin²θ + cos²θ)] -3[(sin²θ + cos²θ)2
-2sin²θcos²θ]+1
The algebraic identity
a³ + b³ = (a+b)³ - 3ab(a+b) and
a²+ b²= (a+b)² - 2ab
are used in the above step where
a = sin²θ and b = cos²θ.
writing sin²θ + cos²θ = 1, we have
= 2[1-3 sin²θ cos²θ] -3[-2 sin²θcos²θ] + 1
= 2-6 sin²θcos²θ -3 + 6 sin²θcos²θ + 1
= -3+3=0

0Thank You

ANSWER

The area of rectangular plot is 528 m^2 .The length of the plot is one more than twice its breadth.We need to find the length and breadth of the plot. Length (in meters)

Posted by Sudha Sudha 5 years, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

Priyanshu Kumar 5 years, 1 month ago

So breadth =16 & length =33

0Thank You

Priyanshu Kumar 5 years, 1 month ago

Let the breadth be x Therefore length = 2x+1 (2x+1)x= 2x² +x= 528 m² {Since area of rect■ is l×b} 2x²+x= 528 2x²+x-528=0 2x²-32x+33x-528=0 2x(x-16)+33(x-16)=0 (x-16)(2x+33)=0 Therefore, x=16 Neglecting x=-33/2 {as a side can't be negative}

1Thank You

ANSWER

PT is the tangent at T while PA cuts the circle at A and B .The radius of the circle is 7cm if length of arc A*T =24cm and angle BYT = 6cm , then find angle APt

Posted by Prashant Kumar 5 years, 1 month ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Siddh Kijiye ki Bindu (1 - 1) ,(5,2),(9,5)

Posted by Neha Ramesh 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Himanshu Nagaich 5 years, 1 month ago

Let A(1,-1),B(5,2) and C(9,5) Area of Triangle=1/2[X1(Y2-Y3)+X2(Y3-Y1)+X3(Y1-Y2)] =1/2[1(2-5)+5(5+1)+9(-1-3)] =1/2[-3+30-36] =1/2*(-9) =4.5 unit sq.(AREA CANNOT BE NEGATIVE)

0Thank You

ANSWER

(Sin 30°+cos 30 °) - (sin 60 °+cos60 °)

Posted by Khusbhoo Kumari 5 years, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

Harini Reddy 5 years, 1 month ago

answer is 1

0Thank You

Gaurav Seth 5 years, 1 month ago

A n s w e r :

=> (sin30+cos30) - (sin60+cos60)

sin30 = 1/2

sin60= √3/2

cos30= √3/2

cos60= 1/2

=> (1/2+√3/2) - (√3/2+1/2)

=> 1+√3/2 - √3+1/2

=> 1+1+√3-√3 /2

=> 2/2

=>1

1Thank You

ANSWER

Three numbers in A.P. have sum 24. The middle term is- (a) 6 (b) 8 (c) 3 (d) 2

Posted by Chetan Soni 5 years, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

Harini Reddy 5 years, 1 month ago

how can we consider 8 as a middle term can please give step by step explanation

0Thank You

Tanu Man 5 years, 1 month ago

We will consider 8 as a middle term

1Thank You

ANSWER

Is it possible to design a rectangular park of perimeter 80 metres and area 400 m2. If so, find its length and breadth.

Posted by Vashu Tyagi 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Geeta Jadav 5 years, 1 month ago

Let length of rectangular park = x Breadth of rectangular park=y Now, Area of rectangal=l×b 400=x×y.......(1) Perimeter of rectangal=2(l+b) 80=2(x+y) 40=x+y X=40-y.........(2) Now, 400=xy 400=(40-y)y 400=40y-y^2 -y^2+40y-400=0 y^2-40y+400=0 y^2-20y-20y+400=0 y(y-20)-20(y-20)=0 (y-20)(y-20)=0 y=20m Now,put the value of y in eq(2), X=40-20 x=2m Hence, value of length =20m Value of breadth=20m

0Thank You

ANSWER

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined). Values of the trigonometric ratios of 30 , 45 and 60 ..... what does it means for which proof they said trigonometric identies or trigonometric ratios

Posted by Ayu No 5 years, 1 month ago

CBSE > Class 10 > Mathematics