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Questions
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Answers
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Q1) if f(x)={x2+3x+a, bx+2, x<=1, x>1, x e R, is everywhere differentiable then
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A)a=3, b=5
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Q2) Let p(x) be a real polynomial of the least degree that has a local maximum at x=1 and a local minimum at x=3. If p(1)=6 and p(3)=2, then p(0) is equal to
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C) 3
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Q 3) The function f(x)= 2x3-3x2-12x+4, x eR has
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C) one local maximum and one local minimum
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Q4) Let x=f(x)+ f(2a-x), x[0,2a] and f(x)>0 for all x9[0,a]. Then (x) is
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A)Decreasing on [0,a]
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Q5) if g(f(x))= sin x and f(g(x))= (sin √x)2, then
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- f(x)= sin2 x, g (x)=√x
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Q6) The expression 24n-15n-1, where n N is divisible by 24n-15n-
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- 225
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Q7) If z1, z2 are complex numbers such that 2z1/3z2 is a purely imaginary number, then the value of |z1-z2/z1+z2| is
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-
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Q8) The value of the integral ∫3√x/√9-x + x√x dx
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A) 3/2
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Q9) The line y-√3x+3=0 cuts the parabola y2=x+2 at the points P and Q. If the point X is (√3,0), then the value of XP XQ is
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A) 4(2+√3/3
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Q10) Let f(x)=|1-2x|, then
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A) f(x) is continuous but not differentiable at x=1/2
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Q11) if f is the inverse function of g and g(x)=1/1+xn, then value of f(x) is
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A) 1+{f(x)}n
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Q12) Let f be a function that is differentiable for all real x. If f(2) = -4 and f(x)>=6 for all x equivalent[2,4], then
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C) f(4)>=8
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Q13) If E and F are two independent events with P(E)= 0.3 and P(E u F0 = 0.5, then P(E/F)-P(F/E)
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C)1/70
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Q14) the set of points of discontinuity of the function f(x) = x-[x], x equivalent R is
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D) Z
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Q15) For what value of “a”, the sum of squares of the roots of the equation x2-(a-2)x-a+1=0 will have the least value
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D) 1
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Q16) ∫11 x3+|x|+1/x2+2|x|+1 dx is equal to
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A) 2 log 2
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Q17) If sum of n terms of an AP is 3n2+5n and its mth term is 164, then the value of m is
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B) 27
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Q18) If 9P5+5, 9P4=10Pr, then the value of r is
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C) 5
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Q19) An n×n matrix is formed using 0,1, and -1 as its elements. The number of such matrices that are skew-symmetric is
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D) 3n(n-1)/2
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Q20) Let f(x) be a second-degree polynomial. If f(1) and p. Q, r are in AP then f(P) f(q), f(r) are
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A) In AP
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Q21) A function f is defined by f(x)=2+(x-1)2/3 on|0,2|. Find correct statement.
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A), B), and C)
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Q22) The straight line x-3/3=y-2/1=z-1/0 is
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D) perpendicular to the z axis
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Q23) If the sum of squares of the roots of the equation x2-(a-2)x-(a+1)=0 is least for an appropriate value of the variable parameter the value of a is
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C) 1
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Q24) Let x-y=0 and x+y=1 be two perpendicular diameters of a circle of radius R. The circle will pass through the origin if R is equal to
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1/√2
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