Advertisements
Advertisements
Question
Find the values of following determinant.
`|(7/3,5/3), (3/2, 1/2)|`
Solution
APPEARS IN
RELATED QUESTIONS
Solve `\frac { 2 }{ x } + \frac { 1 }{ 3y } = \frac { 1}{ 5 }; \frac { 3 }{ x } + \frac { 2 }{ 3y } = 2` and also find ‘a’ for which y = ax – 2
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
`5/(x-1) + 1/y-2 = 2`
`6/(x-1) - 3/(y-2) = 1`
Solve the following pairs of equations by reducing them to a pair of linear equations
`(7x-2y)/(xy) = 5`
`(8x + 7y)/(xy) = 15`
Solve the following pairs of equations by reducing them to a pair of linear equations
`10/(x+y) + 2/(x-y) = 4`
`15/(x+y) - 5/(x-y) = -2`
Formulate the following problems as a pair of equations, and hence find their solutions:
Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current
Formulate the following problems as a pair of equations, and hence find their solutions:
2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.
The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju
A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.
In a ΔABC, ∠C = 3 ∠B = 2 (∠A + ∠B). Find the three angles.
Solve the following pair of linear equations.
(a − b) x + (a + b) y = a2− 2ab − b2
(a + b) (x + y) = a2 + b2
ABCD is a cyclic quadrilateral finds the angles of the cyclic quadrilateral.
In Fig. 1, ABCD is a rectangle. Find the value of x and y.
Solve the following for x:
`1/(2a+b+2x)=1/(2a)+1/b+1/(2x)`
The sum of two numbers is 1000 and the difference between their squares is 256000. Find the numbers.
The sum of a two digit number and the number obtained by reversing the order of its digits is 99. If the digits differ by 3, find the number.
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 a numerator and denominator of a fraction is 18. If the denominator is increased by 2, the fraction reduces to 1/3. Find the fraction.
Ten years later, A will be twice as old as B and five years ago, A was three times as old as B. What are the present ages of A and B?
