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25. The integer k for which the inequali...

25. The integer k for which the inequality `x2-2(4k-1)x +15k2- 2k-7 > 0 is valid for any real x is
(a) 2
(b) 3
(c) 4
(d) infinite

A

2

B

3

C

4

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let `f(x) = x^(2) - 2(4k -1)x+15k^(2) - 2k -7`. Then, `f(x) gt 0` for all x `in` R
`rArr" ""Disc" lt 0`
`rArr" "4(4k-1)^(2)-4(15k^(2)-2k-7) lt 0`
`rArr" "k^(2)-6k + 8 lt 0 rArr 2 lt k lt 4`
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OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Chapter Test
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  2. The set of values of a for which x^2+ax+sin^(-1)(x^2-4x+5)+cos^(-1)(x^...

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  3. The set of possible values of lambda for which x^2-(lambda^2-5 lambda...

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  4. The equation (a + 2)x^2 + (a-3)x = 2a - 1, a != -2 has roots rational ...

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  5. If cos alpha, sin beta, sin alpha are in increasing G.P. , then roots ...

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  6. If alpha,beta are roots of x^2-3x+a=0,a in Ra n dalpha<1<beta, then f...

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  7. If the equations ax^2+bx+c=0 and cx^2+bx+a=0, a!=c have a negative com...

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  8. If the roots of the equation x^3-12x^2 +39x -28 =0 are in AP, then the...

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  9. If the roots of a1x^2 + b1x+ c1 = 0 are alpha1 ,beta 1 and those o...

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  10. If the roots of the equation ax^(2)-4x+a^(2)=0 are imaginery and the s...

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  11. If a, b, c are positive real numbers, then the roots of the equation a...

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  12. If the absolute value of the difference of the roots of the equation x...

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  13. If alpha, beta be roots of the equation 375x ^(2) -25x-2=0 and s (n) =...

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  14. The quadratic equation x^(2) + (a^(2) - 2) x - 2a^(2) and x^(2) - 3x +...

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  15. The roots of ax^(2) +bx +c =0 " whose " a ne 0, b ,c in R , " are non...

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  16. The value of m for which the equation x^3-mx^2+3x-2=0 has two roots ...

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  17. If the equation formed by decreasing each root of the a x^2+b x+c=0 by...

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  18. If the roots of the equation ax^2-bx-c=0 are changed by same quantity ...

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  19. If x^2-2rprx+r=0; r=1, 2,3 are three quadratic equations of which each...

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  20. If x ^(2) + px +1 is a factor of ax ^(3) + bx +c, then:

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  21. If (x-1)^3 is a factor of x^4+ax^3+bx^2+cx-1=0 then the other factor ...

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