Class XII Engineering

The coefficient of x99 in the polynomial (x-1)(x-2)..(x-100) isa) -5050(correct)b) 1 c) 0d) -1If the sum of n terms of a G.P. is S, their product is P and the sum of their reciprocals is R, then a) P2=R/Sb) P2=S/Rc) P2=(R/S)nd) P2=(S/R)n If a, b, c are in A.P., then the straight line ax+by+c=0 will pass through a fixed point whose coordinates are If x satisfies |x-1|+|x-2|+|x-3|≥6 then a)0 ≤ x ≤ 4b) x ≤ 0 or x ≥ 4 c) x ≤ -2 or x ≥ 4d) NoneBoth the roots of the eqn (x-b)(x-c) +(x-a)(x-c)+(x-b)(x-a)=0 are always a) positiveb) negativec)real d)noneThe number of ways in which we can post 5 letters in 8 letter boxes is a) 40b) 85 c) 58d)noneIf the cube roots of unity are 1, w, w2 then the roots of the eqn (x-1)3+8 =0 are a) -1, (1+2w), (1+2w2) b) -1, (1-2w), (1-2w2) c) -1, -1, -1d) NoneIf z= x + iy and w=(1-iz/z-i), then |w|=1 implies that, in the complex planea) z lies on the imaginary axis,b) z lies on the real axis,c) z lies on the unit circle d) none The locus of a point z which satisfies the equation arg. z =π/6 is a) a circle with centre at the origin b) a pair of straight lines passing through the origin c) a straight line through the origin d)noneThe number of common tangents to the circles x2+y2+2x+8y-23=0 and x2-y2-4x-10y+19=0 area)1b)2c)3d)4a)0b)∞c)1d)noneFor a real number y, let [y] be the greatest integer less than or equal to y; then f(x)=tanπ[x-π])/1+[x]2 is, a) discontinuous at some x,b) continuous at all x but the derivative f’(x) does not exist for some x.c) f’(x) exists for all x but second derivative f’’(x) does noe exist.d) f’(x) exists for all x. If x + |y| = 2y then y as function of x isa) defined for all real x,b) continuous for all x,c) differentiable for all x, d)such that dy/dx=1/3 for x<0 The function f(x)=log(1+ax)-log(1-bx) /x is not defined at x=0. The value which should be assigned to f at x=0 so that it is continous at x=0 is a) a-bb) a+bc)log a +log bd) None The value of 0 to π /8 ʃtan22x dx isa) ½ - π/8 b) π/8c) – π/8 + 1 d) None For what values of ‘c’ and ‘a’ is the following equation true?ʃ (sin 2x +cos 2x) dx = (1/√2) sin (2x –c) + aa) c = π/4, a = 0b) c = π/4, a arbitraryc) c = π/2 ; a = 0d) none ʃ (10 x9 + 10x loge 10) / (10x + x10) dx will be given by a) 10 x – x10 b) 10 x + x10c) (10 x – x10)-1d) log(10 x + x10)The value of 0 to π/2 ʃ ex sin x dx is a) (eπ/2 – 1)/2b) (eπ/2 + 1)/√2c) (eπ/2 + 1)/2d) NoneThe area bounded by the rectangular hyperbola xy = c2, the x- axis and the ordinates x = c and x = 2c is a) c2log 2b) c log 2c) log 2d)None The value of ʃ x2 (3-x)1/2 dx limits 0 to 3 is (144√3)/35 16√3/9 9√3/5 None of theseThe general solution of the differential equation (ydx – xdy)/y = 0 is a) xy = Cb) x= Cy2c) y= Cxd) y= Cx2The general solution of the differential equation is ex dy + (y ex + 2x) dx = 0 is a) x ey + x2 = Cb) x ey + y2 = Cc) y ex + x2 = Cd) y ey + x2 = CIf ɵ is the angle between any two vectors a-> and b-> then |a . b|= |a x b| when ɵ is equal to a) 0b) π/4c) π/2d)πTwo events A and B are will be independent, if a) A and B are mutually exclusive b) P(A’ B’) = [1 - P(A)][1- P(B)]c) P(A) = P(B)d) P(A) +P(B) = 1In a box containing 100 bulbs, 10 are defective. The probability that out of sample of 5 bulbs, none is defective is a) 10-1b) (1/2)5c) (9/10)5d)9/10