Sample Paper II for IIT-Mathematics

Apr 11 • Engineering Sample Papers • 1414 Views • 1 Comment on Sample Paper II for IIT-Mathematics

  IIT SAMPLE PAPER

This is the sample paper for the maths section of IIT exam.

Ques 1:- which of the following is a contradiction?

a)pv(~p^q)        b) (p^q) ~(pvq)    c) (p=>q)=>p  d) none of these

Ques 2:- Let f(x) satisfy the requirements of Lagrange’s Mean Value theorem in [0,2]. If f(0)=0 and {f(x)<=1/2 for all x in [0,2],then

a)f(x)<=2       b) {f(x)}<=1    c) f(x)=2x    d) f(x)=3 for at least one x in [0,2]

Ques 3:- The ends A and B of a rod of length √5 are sliding along the curve y= 2x2   .Let  Xa  and X b be the x-coordinate of the ends. At the moment when A is at (0,0) and B is at (1,2) the derivative dxb /dxa has the value equal to

a)1/3                 b) 1/5           c) 1/8            d) 1/9

Ques 4:- The value of f{0} so that f{x}=(4x-1)3/sin(x/4)log(1+x2 /3) is continuous  everywhere ,is equal to

a)3(log 4)3         b) (log  4)3     c) 12(log 4)  d) 15(log 4)3

Ques 5:- the area of the region bounded by the curves   y=│x-1│ and y=3-│x│is

a)6sq unit          b) 2 sq unit    c) 3  sq unit   d) 4 sq unit

Ques 6:-The equation of the curve ,whose slope at any point different from origin is y+y/x, is

a)y=xe             b) xy=ex        c) y+xex =c        d) y=c  xe , c≠0

Ques 7:- The value of ∫ex .x2 +1/(x+1)2 dx is

a)ex (x-1)/(x+1)+c      b) ex (x+1)/(x-1)+c     c) none of these

d) ex .x+c

Ques 8:- The sum of three terms of a strictly increasing GP is (a)S and sum of the squares of these terms is S2  so where thus a2 lies

a)(1/3,2)      b) (1/3,3)        c) (1,2)   d) none of these

Ques 9:- The sum of three terms of a strictly increasing GP is (a)S and sum of the squares of these terms is S2  then if S=10√3 then the greatest value of the middle term is

a)5               b) 5√3              c) 10          d) 10√3

Ques 10:- The focal chord to y2=16x is tangent to (x-6)2 +y2 =2,then the possible values of the slope of this chord are

a){-2,2}        b) 2,1/2}      c {-1,1}        d) {2,-1/2}

Ques 11:-The number of ordered pairs (α,β)where α,βϵ(-∏,∏) satisfying cos(α-β) =1 and cos( α+,β)=1/e is

a)0           b) 1           c) 2          d) 4

Ques12:- If y ≠ y(x) and 2+sin x/y+1(dx/dy)=-cos x y(0)=1,then y(∏/2)equals

a)1/3           b) 2/3      c) -1/3      d) 1

Ques 13:-The Cartesian equation of plane r=(1+∏-β)i +(2-∏)j+(3-2∏=2 β)k is

a)2x+y=5       b) 2x-y=5    c) 2x+z=5    d) 2x-z=5

Ques 14:-If α, β are the roots of the equation  x2=p(x+1)-q=0 then the value of (α2+2 α+1/ α2+2 α+q)+( (β2+2V+1/ β2+2V+q) is

a)2            b) 0          c) 1            d) none of these

Ques 15:- let a relation R be defined by B={(4,5).(1,4),(4,6),(7,6),(3,7)} then R-1 OR is

a){(1,5),(1,6),(3,6)}           b {(1,1),(4,4),(7,7),(3,3)}    c) none of these    d) {(1,1),(4,4),(4,7),(7,4),(7,7),(3,3)}

Ques 16:-The sum of n terms of the following series  1+(1+x)+(1+x+x2)+…… will be

a)1-xn/1-x           b)x(1-xn)1-x

c)n(1-x)-x(1-xn)/(1-x)2

d)none of theses

Ques17:-if a>b then f(x)=√x-a/b-x is continuous on

a)(b,a)         b)[b,a]      c)[b,a)   d)(b,a]

Ques18:-Each of these questions contains two statement I (Assertion) and statement II (reason)thus Statement I is The line 2x+y =5 is a diameter of the circle x2+ y2 -6x+2y=0, Statement II normal of a circle always pass through center of circle.  Each of these question also has four alternatives choices , only one of which is the correct answer you have to select one of the codes a,b,c,d  given below:

A) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I

B) Statement I is true, Statement II is true; Statement II is a not correct explanation for Statement I

C) Statement I is true, Statement II is false

D) Statement I is false, Statement II is false

Ques19:- Each of these questions contains two statement I (Assertion) and staementII (reason)thus Statement I for a=-1/√3 the volume of the parallelepiped formed by vectors I+aj, ai+j+k and j+ak is maximum, Statement II the volume of the parallelepiped having three coterminous edges  vector a, vector b and vector c=│[a bc]│. Each of these question also has four alternatives choice, only one of which is the correct answer you have to select one of the codes a,b,c,d  given below:

A) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I

B) Statement I is true, Statement II is true; Statement II is a not correct explanation for Statement

C) Statement I is true, Statement II is false

D) Statement I is false, Statement II is false

Ques 20:- Each of these questions contains two statement I (Assertion) and statement II (reason) thus Statement I The domains of f(x)√cos(sin x) and g(x)=√sin (cos x) are same ,Statement II since ,-1<+cos(sin x)<=1 and -1<+sin (cos x)<=1. Each of these question also has four alternatives choice ,only one of which is the correct answer you have to select one of the codes a,b,c,d  given below:

A) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I

B) Statement I is true, Statement II is true; Statement II is a not correct explanation for Statement I

C) Statement I is true, Statement II is false;

D) Statement I is false, Statement II is false

Ques21:-If a,b,c  are sides of a triangle and matrices is  a2        b2       c2                                 

(a+1)(b+1)2(c+1)2

(a-1) 2  (b-1) 2  (c-1) 2

=0 is then

a)    ∆ABC  is equilateral

b)   ∆ABC   is right angled isosceles

c)    ∆ABC   is isosceles

d)   None of these

Ques 22:-The ends of a rod of length L move on two mutually perpendicular lines. The locus of the point on the rod which divides it  in the ratio 1:2 is

a)36x2+9y2=l 2             b)36x2+9y2=4l 2         c)9x2+36y2=4l 2      d)none of these

Ques 23:-The position vectors of points A and B are  i-j+3k and 3i+3j+3k respectively . The equation of a plane is vector r .(5i+2j-7k)+9=0 . The points A and B

a)lie on the plane           b)are on the same side of the plane

c)are on the opposite sides of the plane

d)none of these

Ques 24:- A die is tossed thrice .A success is getting 1 or 6 on a toss .The mean and the variance of number of successes is

a)a=1,b2=2/3                b)a=2/3, b2=1         c)a=2, b2=2/3          d)none of these

Ques25:- The integral ∫-1/21/2[[x]+log (1+x)/(1_x)]dx is equal to

a)-1/2               b)0              c)1            d)2log ½

Ques 26:- P and Q be two points on the upper half of the ellipse x2/a2+y2/b2=1 . The center of the ellipse is at the origin O and PQ is parallel to the x-axis such that the triangle OPQ has the maximum possible areas.Point is randomly selected from inside of the upper half of the ellipse . The probability the it lies outside the triangle is

a)∏-1/∏              b)2∏-1/2∏             c) ∏-1/2∏          d) ∏-1/4∏

Ques 27:- A square OABX is formed by line pairs xy=0 and xy+1=x+y, where O is the origin.A circle with center C inside the squire is drawn to touch the line pair xy =0 and another circle with center c2 and radius twice that of c2 and the radius twice the c1 is drawn to touch the circle c1 and the other line pair .The radius of the circle with center c1 is

a)√2/V3(√2+1)           b) 2√2/√2(√2+1)         c) √2/3(√2+1)         d) √2+1/3√2

Ques28:- Suppose the functioning(x)=x2n+1 +anx+bn; (n ϵ  N)satisfies the equation ∫11(px+q)ga(x)dx=0

For all linear functions (px+q) then

a)an=bn=0            b) bn=0;an=-3/2n+3       c) an =0; bn=-3/2n+3          d) an=3/2n+3;bn=-3/2n+3

Ques29:- A function y = f(x) has a second order derivatives f”(x)=6(x-1) if its graph passes through the point(2,1) and at that point the tangent to the graph is y=3x-5, then the function is

a)(x-1)3           b) (x+1)3        c) (x+1)2      d) (x-1)2

Ques30:-If a and d are two complex numbers , then the sum to (n+1) terms of the following series aC0-(a+d)C1+(a+2d)C2-…… is

a)a/2n          b) na          c) 0      d) none of these

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One Response to Sample Paper II for IIT-Mathematics

  1. Soubarna Biswas says:

    Here is another sample paper for IIT Mathematics section. Get well prepared so that in future you do not regret. ALL THE BEST once again!

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