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If x, y are rational numbers such that `(x+y)+(x-2y)sqrt(2)=2x-y+(x-y-1)sqrt(5)` then

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Assertion : One of the rational number between (1)/(5) and (1)/(4) is (9)/(2) . Reason : If x and y are any two rational numbers such that x lt y , then (1)/(2)(x+y) is a rational number between x and y such that x lt (1)/(2) (x+y) lt y .

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(sqrt(x)+sqrt(y))^(2)=x+y+2sqrt(xy) and sqrt(x)sqrt(y)=sqrt(xy) , where x and y are positive real numbers . If a=1+sqrt(2)+sqrt(3) and b=1+sqrt(2)-sqrt(3) , then a^(2)+b^(2)-2a-2b=

If x and y are rational numbers then show that the following are also rational numbers (i)x^(2)-y^(2)(ii)x-y(iii)(x)/(y),y!=0,(iv)x+y

sqrt(2)x + sqrt(3)y=0 sqrt(5)x - sqrt(2)y=0

RESONANCE DPP-JEE MAINS-All Questions
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  2. Which of the following is correct? (log)2 0.9 is negative b. (log)(0. ...

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  3. If x, y are rational numbers such that (x+y)+(x-2y)sqrt(2)=2x-y+(x-y-1...

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  4. If the difference of the roots of the equation, x^2+p x+q=0 be unity, ...

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  5. The multiplication of a rational number 'x' and an irrational numbe...

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  6. If ' a ' is a natural number and ' b ' a digit such that (3a+2007)^2...

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  7. If n^(2)-11n+24=0 is satisfied by n(1)&n(2) where n(2)gtn(1) then

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  8. The value of the sum 1/(3^2+1)+1/(4^2+2)+1/(5^2+3)+...oo is equal to

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  9. If n^2+2n-8 is a prime number where n in n , then n is a. also a p...

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  10. The quadratic equation x^2-9x+3=0 has roots alphaa n dbetadot If x^2-b...

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  11. Number of ordered pairs (a,b) for which sin^(-1)(1+b+b^2+..oo)+cos^(-1...

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  12. Make the following expressions free from modulus sign: (x in R) |2x-...

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  13. If m ,n in Na n dm^2-n^2=13 ,t h e n(m+1)(n+1) is equal to a. 42 b. 5...

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  14. Make the following expressions free from modulus sign: (x in R) |x+1...

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  15. The chance that the vowels are separated in an arrangement of the l...

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  16. The difference of the squares of two consecutive odd integers is di...

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  17. Evaluate/simplify the following: |2 3-3 4|

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  18. Make the following expressions free from modulus sign: (x in R) |x^2...

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  19. Identify the correct statement If a ,b ,c are odd integers (a) a+b+c c...

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  20. If relation R is defined as R={((x+1)/2,(x-1)/2): w h e r ex in Wa n...

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