Advertisements
Advertisements
प्रश्न
Find the value of following determinant.
`|(5,3), (-7,0)|`
उत्तर
`|(5,3), (-7,0)|`
= (5 × 0) − (3 × (−7))
= 0 − (−21)
= 0 + 21
= 21
APPEARS IN
संबंधित प्रश्न
Solve `\frac{2}{x+2y}+\frac{6}{2x-y}=4\text{ ;}\frac{5}{2( x+2y)}+\frac{1}{3( 2x-y)}=1` where, x + 2y ≠ 0 and 2x – y ≠ 0
Solve `\frac{1}{x+y}+\frac{2}{x-y}=2\text{ and }\frac{2}{x+y}-\frac{1}{x-y}=3` where, x + y ≠ 0 and x – y ≠ 0
Solve the following pairs of equations by reducing them to a pair of linear equations
`1/(2x) + 1/(3y) = 2`
`1/(3x) + 1/(2y) = 13/6`
Formulate the following problems as a pair of equations, and hence find their solutions:
Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.
One says, "Give me a hundred, friend! I shall then become twice as rich as you". The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II)
[Hint: x + 100 = 2 (y − 100), y + 10 = 6(x − 10)]
Solve the following pair of linear equations: px + qy = p − q, qx − py = p + q
Solve the following pair of linear equations.
`x/a-y/b = 0`
ax + by = a2 + b2
Solve the following for x:
`1/(2a+b+2x)=1/(2a)+1/b+1/(2x)`
A and B each have a certain number of mangoes. A says to B, "if you give 30 of your mangoes, I will have twice as many as left with you." B replies, "if you give me 10, I will have thrice as many as left with you." How many mangoes does each have?
The sum of two numbers is 8. If their sum is four times their difference, find the numbers.
A two-digit number is 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.
A two-digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number, the digits are reversed. Find the number.
A two-digit number is such that the product of its digits is 20. If 9 is added to the number, the digits interchange their places. Find the number.
Let the numerator and denominator of the fraction be x and y respectively. Then the fraction is `x/y`
If the numerator is multiplied by 2 and the denominator is reduced by 5, the fraction becomes `6/5`. Thus, we have
`(2x)/(y-5)=6/5`
`⇒ 10x=6(y-5)`
`⇒ 10x=6y-30`
`⇒ 10x-6y+30 =0`
`⇒ 2(5x-3y+15)=0`
`⇒ 5x - 3y+15=0`
If the denominator is doubled and the numerator is increased by 8, the fraction becomes `2/5`. Thus, we have
`(x+8)/(2y)=2/5`
`⇒ 5(x+8)=4y`
`⇒ 5x+40=4y`
`⇒ 5x-4y+40=0`
So, we have two equations
`5x-3y+15=0`
`5x-4y+40=0`
Here x and y are unknowns. We have to solve the above equations for x and y.
By using cross-multiplication, we have
`x/((-3)xx40-(-4)xx15)=-y/(5xx40-5xx15)=1/(5xx(-4)-5xx(-3))`
`⇒ x/(-120+60)=(-y)/(200-75)=1/(-20+15)`
`⇒x/(-60)=-y/125``=1/-5`
`⇒ x= 60/5,y=125/5`
`⇒ x=12,y=25`
Hence, the fraction is `12/25`
Let the numerator and denominator of the fraction be x and y respectively. Then the fraction is `x/y`
If 3 is added to the denominator and 2 is subtracted from the numerator, the fraction becomes `1/4`. Thus, we have
`(x-2)/(y+3)=1/4`
`⇒ 4(x-2)=y+3`
`⇒ 4x-8=y+3`
`⇒ 4x-y-11=0`
If 6 is added to the numerator and the denominator is multiplied by 3, the fraction becomes `2/3`. Thus, we have
`(x+6)/(3y)=2/3`
`⇒ 3(x+6)=6y`
`⇒ 3x +18 =6y`
`⇒ 3x-6y+18=0`
`⇒ 3(x-2y+6)=0`
`⇒ x-3y+6=0`
Here x and y are unknowns. We have to solve the above equations for x and y.
By using cross-multiplication, we have
`x/((-1)xx6-(-2)xx(-11))=(-y)/(4xx6-1xx(-11))=1/(4xx(-2)-1xx(-1))`
`⇒ x/(-6-22)=-y/(24+11)=1/(-8+1)`
`⇒ x/-28=-y/35=1/-7`
`⇒ x= 28/7,y=35/7`
`⇒ x= 4,y=5`
Hence, the fraction is`4/5`
The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.
The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.
A father is three times as old as his son. After twelve years, his age will be twice as that of his son then. Find the their present ages.
Ten years ago, a father was twelve times as old as his son and ten years hence, he will be twice as old as his son will be then. Find their present ages.
Asha has only ₹1 and ₹2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is ₹75, then the number of ₹1 and ₹2 coins are, respectively.
