| Questions | Answers |
| Q1) if f(x)={x2+3x+a, bx+2, x<=1, x>1, x e R, is everywhere differentiable then | A)a=3, b=5 |
| 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 | C) 3 |
| Q 3) The function f(x)= 2x3-3x2-12x+4, x eR has | C) one local maximum and one local minimum |
| Q4) Let x=f(x)+ f(2a-x), x[0,2a] and f(x)>0 for all x9[0,a]. Then (x) is | A)Decreasing on [0,a] |
| Q5) if g(f(x))= sin x and f(g(x))= (sin √x)2, then | - 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- | - 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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| Q8) The value of the integral ∫3√x/√9-x + x√x dx | A) 3/2 |
| 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 | A) 4(2+√3/3 |
| Q10) Let f(x)=|1-2x|, then | A) f(x) is continuous but not differentiable at x=1/2 |
| Q11) if f is the inverse function of g and g(x)=1/1+xn, then value of f(x) is | A) 1+{f(x)}n |
| 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 | C) f(4)>=8 |
| 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) | C)1/70 |
| Q14) the set of points of discontinuity of the function f(x) = x-[x], x equivalent R is | D) Z |
| 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 | D) 1 |
| Q16) ∫11 x3+|x|+1/x2+2|x|+1 dx is equal to | A) 2 log 2 |
| Q17) If sum of n terms of an AP is 3n2+5n and its mth term is 164, then the value of m is | B) 27 |
| Q18) If 9P5+5, 9P4=10Pr, then the value of r is | C) 5 |
| 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 | D) 3n(n-1)/2 |
| 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 | A) In AP |
| Q21) A function f is defined by f(x)=2+(x-1)2/3 on|0,2|. Find correct statement. | A), B), and C) |
| Q22) The straight line x-3/3=y-2/1=z-1/0 is | D) perpendicular to the z axis |
| 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 | C) 1 |
| 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 | 1/√2 |
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