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When x ^(100) is divided by x ^(2) -3x +...

When `x ^(100)` is divided by `x ^(2) -3x +2,` the remainder is `(2 ^(k +1) -1) x -2 (2 ^(k)-1),` then `k =`

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VK JAISWAL ENGLISH-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. The curve y=(lambda=1)x^2+2 intersects the curve y=lambdax+3 in exactl...

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  2. Find the number of integral vaues of 'a' for which the range of functi...

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  3. When x ^(100) is divided by x ^(2) -3x +2, the remainder is (2 ^(k +1)...

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  4. Let p(x)=0 be a polynomial equation of the least possible degree, with...

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  5. The range of value's of k for which the equation 2 cos^(4) x - sin^(4...

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  6. Let p (x) be a polynomial with real coefficient and p (x)-p'(x) =x^(2)...

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  7. Find the smallest positive integral value of a for which the greater r...

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  8. If the equation x ^(4)+kx ^(2) +k=0 has exactly two distinct real root...

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  9. Let a,b,c, d be the roots of x ^(4) -x ^(3)-x ^(2) -1=0. Also consider...

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  10. The number of integral value of a,a, in [-5, 5] for which the equation...

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  11. The number of non-negative integral vlaues of n, n le 10 so that a roo...

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  12. If and y ar real numbers connected by the equation 9x ^(2)+2xy+y^(2) -...

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  13. Consider two numbers a,b, sum of which is 3 and the sum of their cubes...

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  14. If y ^(2)(y^(2) -6) + x ^(2) -8x +24 =0 and the minimum value of x ^(...

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  15. Consider the equation x ^(3) -ax ^(2) +bx-c=0, where a,b,c are ration...

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  16. Let alpha satisfy the equation x ^(3) +3x ^(2) +4x+5=0 and beta satisf...

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  17. The number of ordered pairs (a,b) where a,b are integers satisfying th...

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  18. The real value of x satisfying ""^(3)sqrt(20x +^(3)sqrt(20x+13))=13 c...

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  19. If the range of the values of a for which the roots of the equation x ...

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  20. Find the number of positive integers satisfying the inequality x^(2) -...

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