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IIT JEE –Past papers,[object Object],MATHEMATICS- UNSOLVED PAPER - 2000,[object Object]
SECTION – I,[object Object],Single Correct Answer Type,[object Object],There are  35 items in this question. For each item four alternative answers   are provided.  Indicate  the choice  of the  alternative   that you  think to be the  correct answer by writing the corresponding letter from (a), (b), (c), (d), whichever is appropriate,  in the  answer book, strictly  according   to the   order in which  these  items  appear  below.,[object Object]
01,[object Object],Problem,[object Object],Let,[object Object], ,[object Object],    0 only when θ    0,[object Object],    0 for all real θ,[object Object],     0 for all real θ,[object Object],    0 only when θ        0 ,[object Object]
Problem,[object Object],02,[object Object],If x + y = k is normal to y2 = 12x, then k is,[object Object], ,[object Object],3,[object Object],9,[object Object],-9,[object Object],-3,[object Object]
Problem,[object Object],03,[object Object],For  ,[object Object],a.,[object Object],b.   ,[object Object],c.,[object Object],d.,[object Object]
Problem,[object Object],04,[object Object],If		 , are the roots of the equation x2 + bx + c = 0, where c < 0 < b, then  ,[object Object], a. 0 <  α<  β,[object Object],b. α< 0 <  β<| α|,[object Object],c. α< β < 0,[object Object],d. α< 0 <α| < ,[object Object]
Problem,[object Object],05,[object Object],Let f :              be any function. Define g :            by g (x) = |f(x)| for all x. Then g is ,[object Object],Onto if f is onto.,[object Object],One-one if f is one-one.,[object Object],Continuous if f is continuous.,[object Object],Differentiable if f is differentiable. ,[object Object]
Problem,[object Object],06,[object Object],The domain of definition of the function y(x) given by the equation 2x + 2y = 2 is,[object Object],a.,[object Object],0  x      1,[object Object],-  <  x  0,[object Object],d.     -    < x < 1,[object Object]
Problem,[object Object],07,[object Object],If x2 + y2 = 1, then,[object Object],  ,[object Object],yy" – 2(y’)2 + 1 = 0,[object Object],yy” + (y’)2 + 1 = 0,[object Object],yy” + (y’)2 – 1 = 0,[object Object],yy” + 2(y’)2 + 1 = 0,[object Object]
Problem,[object Object],08,[object Object],If a, b, c, d are positive real numbers such that a + b + c + d = 2, then M = (a + b) c + d) satisfies the relation,[object Object],  ,[object Object],0      M       1,[object Object],1       M       2,[object Object],2       M       3,[object Object],3        M       4,[object Object]
Problem,[object Object],09,[object Object],If the system of equations x – ky – z = 0, kx – y – z = 0, x + y –z = 0 has a nonzero solution, then the possible value of k are,[object Object],-1, 2,[object Object],1, 2,[object Object],0, 1,[object Object],-1, 1,[object Object]
Problem,[object Object],10,[object Object],The triangle PQR is inscribed in the circle   x2 + y2 = 25. If    Q and R have co-ordinates (3, 4) and (-4, 3) respectively, then is	              equal  ,[object Object],π/2,[object Object],π/3,[object Object],π/4,[object Object],π/6,[object Object]
Problem,[object Object],11,[object Object],In a triangle ABC, 2ac,[object Object],a2 + b2 – c2,[object Object],c2 + a2 – b2,[object Object],b2 – c2 – a2,[object Object],c2 – a2 – b2,[object Object]
Problem,[object Object],12,[object Object],For ,[object Object],e,[object Object],e-1,[object Object],e-5,[object Object],e5,[object Object]
Problem,[object Object],13,[object Object],Consider an infinite geometric series with first term a and common ratio r. If its sum is 4 and the second term is  3/4 then,[object Object],  ,[object Object],a.,[object Object],b.,[object Object],c.,[object Object],d.,[object Object]
Problem,[object Object],14,[object Object],Let 		      where f is such that .,[object Object], 				       Then g(2) satisfies the,[object Object], inequality,[object Object],  a.    ,[object Object],  b. 0 ≤ g(2)<2,[object Object],   c. 3/2<g(2) < 5/2,[object Object],   d.,[object Object],2 < g (2) < 4 ,[object Object]
Problem,[object Object],15,[object Object],In a triangle ABC, let 	        . If r is the inradius and R is thcircumradius of the triangle, then 2(r + R) is equal to  ,[object Object],a  + b,[object Object],b + c,[object Object],c + a,[object Object],a + b + c,[object Object]
Problem,[object Object],16,[object Object],How many different nine digit numbers can be formed from the number 223355888 by rearranging the digits so that the odd digits occupy even positions?  ,[object Object],16,[object Object],36,[object Object],60,[object Object],180,[object Object]
Problem,[object Object],17,[object Object],If arg (z) < 0, then arg (-z) –arg(z) = ,[object Object], ,[object Object],a.   π,[object Object],b.  - π,[object Object],c.   - π/2,[object Object], d.  π/2,[object Object]
Problem,[object Object],18,[object Object],Let PS be the median of the triangle with vertices P(2, 2), Q(6,-1) and R(7, 3). The equation of the line passing through (1, -1) and parallel to PS is ,[object Object], ,[object Object],2x – 9y – 7 = 0,[object Object],2x – 9y – 11 = 0,[object Object],2x + 9y – 11 = 0,[object Object],2x + 9y + 7 = 0,[object Object]
Problem,[object Object],19,[object Object],A pole stands vertically, inside a triangular  park ABC. If the angle of elevation of the top of the pole from each corner of the park is same, then in ABC the foot of the pole is at the  ,[object Object],Centroid,[object Object],Circumecentre,[object Object],Incentre,[object Object],Orthocentre,[object Object]
Problem,[object Object],20,[object Object],If  		                       then ,[object Object],0,[object Object],1,[object Object],2,[object Object],3,[object Object]
Problem,[object Object],21,[object Object],The incentre of the triangle with vertices (1,       ), (0, 0) and (2, 0) is ,[object Object], ,[object Object],a.,[object Object],b.,[object Object],c.,[object Object],d. ,[object Object]
Problem,[object Object],22,[object Object],Consider the following statements S and R: ,[object Object],S: both sin x and cos x are decreasing functions in the interval 	        .,[object Object],R : If a differentiable function decreases in an interval (a, b), then its derivative also decreases in (a, b).                     Which of the following is true? ,[object Object],Both S and R are wrong,,[object Object],Both S and R are correct, but R is not the correct explanation for ,[object Object],S is correct and R is the correct explanation for S.,[object Object],S is correct and R is wrong.,[object Object]
Problem,[object Object],23,[object Object],Let f(x)			       then f decreases in the interval,[object Object],( - ∞ , -2),[object Object],(-2, -1),[object Object],(1, 2),[object Object],(2, + ∞ ),[object Object]
Problem,[object Object],24,[object Object],In the circles x2 + y2 + 2x + 2ky + 6 = 0 and x2 + y2 + 2ky + k = 0 intersect orthogonally, then k is ,[object Object], ,[object Object],2 or – 3/2,[object Object],2 or – 3/2,[object Object],2 or 3/2,[object Object],2 or 3/2,[object Object]
Problem,[object Object],25,[object Object],If the vectors a, b and c form the sides BC, CA and AB respectively, of a triangle ABC, then  ,[object Object],a . b + b . c + c . a = 0,[object Object],a x b = b x c = c x a,[object Object],a . b = b . c = c . a,[object Object],a x b + b x c + c x a = 0,[object Object]
Problem,[object Object],26,[object Object],If the normal to the curve y = f(x) at the point (3, 4) makes an angle 3π/4 with the positive x-axis, then f’(3) =  ,[object Object],-1,[object Object],-3/4,[object Object],4/3,[object Object],1,[object Object]
27,[object Object],Problem,[object Object],Let the vectors a, b, c and d be such that (a x b) x (c x d) = 0. Let P1 and P2 be planes determined by the pairs of vectors a, b and c, d respectively. Then the angle between P1 and P2 is  ,[object Object],0,[object Object],π/3,[object Object],π/2,[object Object],π/4,[object Object]
Problem,[object Object],28,[object Object],Let			      then at x = 0, f has,[object Object],A local maximum ,[object Object],No local maximum ,[object Object],A local minimum ,[object Object],No extremum,[object Object]
Problem,[object Object],29,[object Object],If a, b and c are nit coplanar vectors, then the scalar triple product [2a – b, 2b – c, 2c - a] =  ,[object Object],0,[object Object],1,[object Object],-,[object Object],+,[object Object]
Problem,[object Object],30,[object Object],If b > a, then the equation (x –a) (x -b) – 1 = 0,m has,[object Object],Both roots in [a, b],[object Object],Both roots in (-∞, a),[object Object],Both roots in (b, + ∞),[object Object],One root in (-∞, a) and other in (b, +∞),[object Object]
Problem,[object Object],31,[object Object],If z1, z2, z3 are complex number such that | z1| = |z2| = | z3|                                        =1, then | z1, z2, z3| is ,[object Object],Equal to 1,[object Object],Less than 1,[object Object],Greater than 3,[object Object],Equal to 3   ,[object Object]
Problem,[object Object],32,[object Object],For the equation 3x2 + px + 3 = 0, p > 0, if one of the roots is square of the other, then p is equal to  ,[object Object],1/3,[object Object],1,[object Object],3,[object Object],2/3,[object Object]
Problem,[object Object],33,[object Object],If the line x – 1 = 0 is the directrix of the parabola y2 – kx + 8 = 0, then one of the value of k is  ,[object Object],1/8,[object Object],8,[object Object],4,[object Object],1/4,[object Object]
Problem,[object Object],34,[object Object],For all  ,[object Object],ex  < 1 + x,[object Object],loge (1 + x) < x,[object Object],sin x > x,[object Object],loge x > x,[object Object]
Problem,[object Object],35,[object Object],The value of the integral,[object Object], ,[object Object],3/2,[object Object],5/2,[object Object],3,[object Object],5,[object Object]
FOR SOLUTION VISIT WWW.VASISTA.NET,[object Object]

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IIT JEE Maths 2000

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Editor's Notes

  1. aaa
  2. d
  3. d
  4. aaa