IIT JEE –Past papers<br />MATHEMATICS- UNSOLVED PAPER - 2000<br />
SECTION – I<br />Single Correct Answer Type<br />There are  35 items in this question. For each item four alternative answ...
01<br />Problem<br />Let<br /> <br />    0 only when θ    0<br />    0 for all real θ<br />     0 for all real θ<br />    ...
Problem<br />02<br />If x + y = k is normal to y2 = 12x, then k is<br /> <br />3<br />9<br />-9<br />-3<br />
Problem<br />03<br />For  <br />a.<br />b.   <br />c.<br />d.<br />
Problem<br />04<br />If		 , are the roots of the equation x2 + bx + c = 0, where c < 0 < b, then  <br /> a. 0 <  α<  β<br ...
Problem<br />05<br />Let f :              be any function. Define g :            by g (x) = |f(x)| for all x. Then g is <b...
Problem<br />06<br />The domain of definition of the function y(x) given by the equation 2x + 2y = 2 is<br />a.<br />0  x ...
Problem<br />07<br />If x2 + y2 = 1, then<br />  <br />yy" – 2(y’)2 + 1 = 0<br />yy” + (y’)2 + 1 = 0<br />yy” + (y’)2 – 1 ...
Problem<br />08<br />If a, b, c, d are positive real numbers such that a + b + c + d = 2, then M = (a + b) c + d) satisfie...
Problem<br />09<br />If the system of equations x – ky – z = 0, kx – y – z = 0, x + y –z = 0 has a nonzero solution, then ...
Problem<br />10<br />The triangle PQR is inscribed in the circle   x2 + y2 = 25. If    Q and R have co-ordinates (3, 4) an...
Problem<br />11<br />In a triangle ABC, 2ac<br />a2 + b2 – c2<br />c2 + a2 – b2<br />b2 – c2 – a2<br />c2 – a2 – b2<br />
Problem<br />12<br />For <br />e<br />e-1<br />e-5<br />e5<br />
Problem<br />13<br />Consider an infinite geometric series with first term a and common ratio r. If its sum is 4 and the s...
Problem<br />14<br />Let 		      where f is such that .<br /> 				       Then g(2) satisfies the<br /> inequality<br />  a...
Problem<br />15<br />In a triangle ABC, let 	        . If r is the inradius and R is thcircumradius of the triangle, then ...
Problem<br />16<br />How many different nine digit numbers can be formed from the number 223355888 by rearranging the digi...
Problem<br />17<br />If arg (z) < 0, then arg (-z) –arg(z) = <br /> <br />a.   π<br />b.  - π<br />c.   - π/2<br /> d.  π/...
Problem<br />18<br />Let PS be the median of the triangle with vertices P(2, 2), Q(6,-1) and R(7, 3). The equation of the ...
Problem<br />19<br />A pole stands vertically, inside a triangular  park ABC. If the angle of elevation of the top of the ...
Problem<br />20<br />If  		                       then <br />0<br />1<br />2<br />3<br />
Problem<br />21<br />The incentre of the triangle with vertices (1,       ), (0, 0) and (2, 0) is <br /> <br />a.<br />b.<...
Problem<br />22<br />Consider the following statements S and R: <br />S: both sin x and cos x are decreasing functions in ...
Problem<br />23<br />Let f(x)			       then f decreases in the interval<br />( - ∞ , -2)<br />(-2, -1)<br />(1, 2)<br />(2...
Problem<br />24<br />In the circles x2 + y2 + 2x + 2ky + 6 = 0 and x2 + y2 + 2ky + k = 0 intersect orthogonally, then k is...
Problem<br />25<br />If the vectors a, b and c form the sides BC, CA and AB respectively, of a triangle ABC, then  <br />a...
Problem<br />26<br />If the normal to the curve y = f(x) at the point (3, 4) makes an angle 3π/4 with the positive x-axis,...
27<br />Problem<br />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 ...
Problem<br />28<br />Let			      then at x = 0, f has<br />A local maximum <br />No local maximum <br />A local minimum <b...
Problem<br />29<br />If a, b and c are nit coplanar vectors, then the scalar triple product [2a – b, 2b – c, 2c - a] =  <b...
Problem<br />30<br />If b > a, then the equation (x –a) (x -b) – 1 = 0,m has<br />Both roots in [a, b]<br />Both roots in ...
Problem<br />31<br />If z1, z2, z3 are complex number such that | z1| = |z2| = | z3|                                      ...
Problem<br />32<br />For the equation 3x2 + px + 3 = 0, p > 0, if one of the roots is square of the other, then p is equal...
Problem<br />33<br />If the line x – 1 = 0 is the directrix of the parabola y2 – kx + 8 = 0, then one of the value of k is...
Problem<br />34<br />For all  <br />ex  < 1 + x<br />loge (1 + x) < x<br />sin x > x<br />loge x > x<br />
Problem<br />35<br />The value of the integral<br /> <br />3/2<br />5/2<br />3<br />5<br />
FOR SOLUTION VISIT WWW.VASISTA.NET<br />
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  • Transcript of "IIT JEE Maths 2000"

    1. 1. IIT JEE –Past papers<br />MATHEMATICS- UNSOLVED PAPER - 2000<br />
    2. 2. SECTION – I<br />Single Correct Answer Type<br />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.<br />
    3. 3. 01<br />Problem<br />Let<br /> <br /> 0 only when θ 0<br /> 0 for all real θ<br /> 0 for all real θ<br /> 0 only when θ 0 <br />
    4. 4. Problem<br />02<br />If x + y = k is normal to y2 = 12x, then k is<br /> <br />3<br />9<br />-9<br />-3<br />
    5. 5. Problem<br />03<br />For  <br />a.<br />b. <br />c.<br />d.<br />
    6. 6. Problem<br />04<br />If , are the roots of the equation x2 + bx + c = 0, where c < 0 < b, then  <br /> a. 0 < α< β<br />b. α< 0 < β<| α|<br />c. α< β < 0<br />d. α< 0 <α| < <br />
    7. 7. Problem<br />05<br />Let f : be any function. Define g : by g (x) = |f(x)| for all x. Then g is <br />Onto if f is onto.<br />One-one if f is one-one.<br />Continuous if f is continuous.<br />Differentiable if f is differentiable. <br />
    8. 8. Problem<br />06<br />The domain of definition of the function y(x) given by the equation 2x + 2y = 2 is<br />a.<br />0 x 1<br />- < x 0<br />d. - < x < 1<br />
    9. 9. Problem<br />07<br />If x2 + y2 = 1, then<br />  <br />yy" – 2(y’)2 + 1 = 0<br />yy” + (y’)2 + 1 = 0<br />yy” + (y’)2 – 1 = 0<br />yy” + 2(y’)2 + 1 = 0<br />
    10. 10. Problem<br />08<br />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<br />  <br />0 M 1<br />1 M 2<br />2 M 3<br />3 M 4<br />
    11. 11. Problem<br />09<br />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<br />-1, 2<br />1, 2<br />0, 1<br />-1, 1<br />
    12. 12. Problem<br />10<br />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  <br />π/2<br />π/3<br />π/4<br />π/6<br />
    13. 13. Problem<br />11<br />In a triangle ABC, 2ac<br />a2 + b2 – c2<br />c2 + a2 – b2<br />b2 – c2 – a2<br />c2 – a2 – b2<br />
    14. 14. Problem<br />12<br />For <br />e<br />e-1<br />e-5<br />e5<br />
    15. 15. Problem<br />13<br />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<br />  <br />a.<br />b.<br />c.<br />d.<br />
    16. 16. Problem<br />14<br />Let where f is such that .<br /> Then g(2) satisfies the<br /> inequality<br /> a. <br /> b. 0 ≤ g(2)<2<br /> c. 3/2<g(2) < 5/2<br /> d.<br />2 < g (2) < 4 <br />
    17. 17. Problem<br />15<br />In a triangle ABC, let . If r is the inradius and R is thcircumradius of the triangle, then 2(r + R) is equal to  <br />a + b<br />b + c<br />c + a<br />a + b + c<br />
    18. 18. Problem<br />16<br />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?  <br />16<br />36<br />60<br />180<br />
    19. 19. Problem<br />17<br />If arg (z) < 0, then arg (-z) –arg(z) = <br /> <br />a. π<br />b. - π<br />c. - π/2<br /> d. π/2<br />
    20. 20. Problem<br />18<br />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 <br /> <br />2x – 9y – 7 = 0<br />2x – 9y – 11 = 0<br />2x + 9y – 11 = 0<br />2x + 9y + 7 = 0<br />
    21. 21. Problem<br />19<br />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  <br />Centroid<br />Circumecentre<br />Incentre<br />Orthocentre<br />
    22. 22. Problem<br />20<br />If then <br />0<br />1<br />2<br />3<br />
    23. 23. Problem<br />21<br />The incentre of the triangle with vertices (1, ), (0, 0) and (2, 0) is <br /> <br />a.<br />b.<br />c.<br />d. <br />
    24. 24. Problem<br />22<br />Consider the following statements S and R: <br />S: both sin x and cos x are decreasing functions in the interval .<br />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? <br />Both S and R are wrong,<br />Both S and R are correct, but R is not the correct explanation for <br />S is correct and R is the correct explanation for S.<br />S is correct and R is wrong.<br />
    25. 25. Problem<br />23<br />Let f(x) then f decreases in the interval<br />( - ∞ , -2)<br />(-2, -1)<br />(1, 2)<br />(2, + ∞ )<br />
    26. 26. Problem<br />24<br />In the circles x2 + y2 + 2x + 2ky + 6 = 0 and x2 + y2 + 2ky + k = 0 intersect orthogonally, then k is <br /> <br />2 or – 3/2<br />2 or – 3/2<br />2 or 3/2<br />2 or 3/2<br />
    27. 27. Problem<br />25<br />If the vectors a, b and c form the sides BC, CA and AB respectively, of a triangle ABC, then  <br />a . b + b . c + c . a = 0<br />a x b = b x c = c x a<br />a . b = b . c = c . a<br />a x b + b x c + c x a = 0<br />
    28. 28. Problem<br />26<br />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) =  <br />-1<br />-3/4<br />4/3<br />1<br />
    29. 29. 27<br />Problem<br />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  <br />0<br />π/3<br />π/2<br />π/4<br />
    30. 30. Problem<br />28<br />Let then at x = 0, f has<br />A local maximum <br />No local maximum <br />A local minimum <br />No extremum<br />
    31. 31. Problem<br />29<br />If a, b and c are nit coplanar vectors, then the scalar triple product [2a – b, 2b – c, 2c - a] =  <br />0<br />1<br />-<br />+<br />
    32. 32. Problem<br />30<br />If b > a, then the equation (x –a) (x -b) – 1 = 0,m has<br />Both roots in [a, b]<br />Both roots in (-∞, a)<br />Both roots in (b, + ∞)<br />One root in (-∞, a) and other in (b, +∞)<br />
    33. 33. Problem<br />31<br />If z1, z2, z3 are complex number such that | z1| = |z2| = | z3| =1, then | z1, z2, z3| is <br />Equal to 1<br />Less than 1<br />Greater than 3<br />Equal to 3 <br />
    34. 34. Problem<br />32<br />For the equation 3x2 + px + 3 = 0, p > 0, if one of the roots is square of the other, then p is equal to  <br />1/3<br />1<br />3<br />2/3<br />
    35. 35. Problem<br />33<br />If the line x – 1 = 0 is the directrix of the parabola y2 – kx + 8 = 0, then one of the value of k is  <br />1/8<br />8<br />4<br />1/4<br />
    36. 36. Problem<br />34<br />For all <br />ex < 1 + x<br />loge (1 + x) < x<br />sin x > x<br />loge x > x<br />
    37. 37. Problem<br />35<br />The value of the integral<br /> <br />3/2<br />5/2<br />3<br />5<br />
    38. 38. FOR SOLUTION VISIT WWW.VASISTA.NET<br />

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