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Let the range of the function f: R→ R f(x) = | x-1| + |x - a| + | x| + |x+1| + |x+ 2a - 21 | a being a real parameter given by [α,∞).Then find the no. of integral values of a for which there is exactly one x0ε R such th ...
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If a,b,c ε R are distinct then the condition on a,b,c for which the equation 1/x-a + 1/x-b + 1/x-c + 1/x-b-c-a =0 has real roots is (a)a+b+c≠0,a≠0 (b)a-b-c≠0,a≠0 (c)2a=b+c (d) none of these ...
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√(3x2+6x+7) + √(5x2+10x+14) = 4-2x-x2 Find the no of real roots... ...
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The number of irrational roots of the equation ?? (x2-3x+1)(x2+3x+2)(x2-9x+20)= -30 ...
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(x2-x+1)4 - 6 x2(x2-x+1)2 +5x4= 0 of multiplicity (a)2 (b)3 (c)4 (d)6 ...
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limx→0 {(1+3x)1/3-1-x} / {(1+x)101- 1-101x} has the value equal to? ...
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limx→0 {(1+3x)1/3-1-x} / {(1+x)101- 1-101x} has the value equal to? ...
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Let f(x) = ax2+bx+c where a,b,c ε R. Suppose |f(x)| ≤ 1 for all x ε [0,1],then (a) |a|≤8 (b) |b|≤8 (C) |c|≤1 (d) |a|+|b|+|c|≤17 ...
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Suppose a,b,c are positive integers and f(x) = ax2-bx+c =0 has two distinct roots in (0,1) m then (a) a≥5 (b) b≥5 (c) abc≥25 (d) abc≥5 2 ...
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Let a,b,c be three distinct real numbers such that the expression ax2+bx+c, bx2+cx+a, and cx2+ ax+b is positive for each x belongs to R and let α =(bc+ca+ab)/(a2+b2+c2) Then (a) α<4 (b) α<1 (c) α>1/4 (d) α>1 ...
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Let α be a repeated root of p(x) = X3+ 3ax2 +3bx+c =0 , then (a) α is a root of x2+2ax+b=0 (b) α =(c-ab)/2(a2-b) (c) α=(ab-c)/(a2 -b) (d) α is a root of ax2+2bx+c =0 ...
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Let a,b,c,d be four integers such that ad is odd and bc is even,then ax3+bx2+cx+d = 0 has (a) at least one irrational roots (b) all three rational roots (c) all three integral roots (d) none of these ...
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What is the product? Please show mechanism too PhCOMe + ClCH2COOC2H5 --NaNH2→ ?? ...
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For what compound A stands in the following equation? MeCOMe + CH≡CH -NaNH2→ A ...
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3 CH2O + CH3CHO → Dil.Na2 Co3→ ? What is the product at a temperature of 400 C? ...
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Let a,b,p,q ε Q and suppose that f(x) = x2 +ax+b=0 and g(x)= x3 + px + q = 0 have a common irrational root , then (a) f(x) divides g(x) (b) g(x) ≡ x f(x) (c) g(x) ≡ (x-b-q)f(x) (d) none ...
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If three distinct real numbers a,b,c satisfy a2(a+p)=b2(b+p)=c2(c+p) where pεR,then the value of bc+ca+ab is? ...
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If three distinct real numbers a,b,c satisfy a2(a+p)=b2(b+p)=c2(c+p) where pεR,then the value of bc+ca+ab is? ...
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If three distinct real numbers a,b,c satisfy a2(a+p)=b2(b+p)=c2(c+p) where pεR,then the value of bc+ca+ab is? ...
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Let f(x)= ax2+bx+c ,a,b,c ε R.If f(x)takes real values for real values of x and non real values for non real of x,then (a) a=0 (b) b=0 (c) c=0 (d) nothing can be said about a,b,c ...
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What factor determines the difference in solubility of n-propyl alcohol and iso propyl alcohol? Which one is more soluble in water? ...
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In YDSE the angular width of a fringe formed on distant screen is 10 the wavelength of light used is 6000Λ . What is the spacing between the slits? ...
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A parallel beam of sodium light of wavelength 6000 Λ is incident on a thin glass plate of μ= 1.5 such that angle of incidence in the plate is 600.The smallest thickness of the plate which will make it appear dark by reflect ...
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Let a,b,c be non-zero real numbers such that 0 ∫ 1 (e-x +ex )(ax2+bx+c)dx = 0 ∫ 2 (e-x+ex)(ax2+bx+c)dx Then the quadratic equation ax2 +bx+c = 0 has (a) no root in (0,1) (b)at least one root in (1,2) (c) a double root in ...
