Organisation : IIT Delhi
Exam : Joint Admission Test – JAM
Document Type : Model Question Paper
Category or Subject : Mathematical Statistics
Year : 2016
Website : http://jam.iitd.ac.in/
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Download Question Paper 2016 : https://www.pdfquestion.in/uploads/9720-MSQP2016.pdf
JAM Mathematical Statistics Model Paper
Section – A :
Multiple Choice Questions (Mcq)
Q. 1 – Q.10 Carry One Mark Each.
Q.1 Let P [1 2 0 2 ] Then rank of P equals
(A) 4
(B) 3
(C) 2
(D) 1
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Q.2 Let B ,Y be real numbers such that B=0 0 and Y=0. Suppose P [B,Y] and P-1, P. Then
(A) 1
(B) 0
(C) 2
(D) 3
Q.3 Let m<1. The volume of the solid generated by revolving the region between the y-axis and the curve xy > 4, 1< y < m, about the y-axis is 15 . The value of m is
(A) 14
(B) 15
(C) 16
(D) 17
Q.4 Consider the region S enclosed by the surface z ? y2 and the planes z = 1, x= 0, x =1, y =-1 and y =1. The volume of S is
(A) 1/3
(B) 2/3
(C) 1
(D) 4/3
Q.5 An institute purchases laptops from either vendor 1 V or vendor 2 V with equal probability. The lifetimes (in years) of laptops from vendor 1 V have a U (0,4) distribution, and the lifetimes (in years) of laptops from vendor 2 V have an Exp(1/2) distribution. If a randomly selected laptop in the institute has lifetime more than two years, then the probability that it was supplied by vendor V2 is
(A) 2 /2 + e
(B) 1/1+ e
(C) 1 /1 1+ e
(D) 1
Q.5 Let y (x) be the solution to the differential equation
A) 10
(B) 12
(C) 14
(D) 16
Q.6 Let f x x =sinX2-1 Then
(A) f is differentiable at 0 but g is NOT differentiable at 0
(B) g is differentiable at 0 but f is NOT differentiable at 0
(C) f and g are both differentiable at 0
(D) NEITHER f NOR g is differentiable at 0
Q.7 Let f (x, y) = x2 – 400 x y2 for all ( x, y) = 2. Then f attains its
(A) local minimum at (0,0) but NOT at (1,1)
(B) local minimum at (1,1) but NOT at (0,0)
(C) local minimum both at (0,0) and (1,1)
(D) local minimum NEITHER at (0,0) NOR at (1,1)
Physics :
Section – A :
Multiple Choice Questions (Mcq) :
Q. 1 – Q.10 carry one mark each.
Q.1 For an infinitely long wire with uniform line-charge density, y, along the z-axis, the electric field at a point (a,b,0) away from the origin is (e^x,e^y,and e^z are unit vectors in Cartesian-coordinate system.)
Q.2 A 1 W point source at origin emits light uniformly in all the directions. If the units for both the axes are measured in centimetre, then the Poynting vector at the point (1,1,0) in W/cm2 is (e^x,e^y,and e^z are unit vectors in Cartesian-coordinate system.)
Q.3 A charged particle in a uniform magnetic field B= B0 e^z starts moving from the origin with velocity v=(3e^x+ 2x) 2/ey. The trajectory of the particle and the time at which it reaches 2 meters above the xy- plane are (e^x,e^y,and e^z are unit vectors in Cartesian-coordinate system.)
Q.4 The eigenvalues of the matrix representing the following pair of linear equations x+iy = 0 & ix+y = 0 are
(A) 1+i, 1+i
(B) 1- i, 1- i
(C) 1, i
(D) 1+ i, 1- i
Q.5 The solution of the Boolean equation y= A+B+ AB is
(A) 1
(B) A+B
(C) A-B
(D) AB
Q.6 A spherical closed container with smooth inner wall contains a monoatomic ideal gas. If the collisions between the wall and the atoms are elastic, then the Maxwell speed-distribution function for the atoms is best represented by
Q.7 Two sinusoidal signals of frequencies x- and y-having same amplitude are applied to x- and y- channels of a cathode ray oscilloscope (CRO), respectively. The following stationary figure will be observed when
Q.8 The phase difference (d) between input and output voltage for the following circuits (i) and (ii) will be
(A) 0 and 0.
(B) p/2 and 0 < d = p/2 respectively.
(C) p/2 and p/2.
(D) 0 and 0 < d = p/2 respectively.
Q. 11 – Q. 30 carry two marks each.
Q.11 For the given set of equations: x?+y=1 y+z=1 z+x=1, which one of the following statements is correct?
(A) Equations are inconsistent.
(B) Equations are consistent and a single non-trivial solution exists.
(C) Equations are consistent and many solutions exist.
(D) Equations are consistent and only a trivial solution exists.
Q.12 The tangent line to the curve x2+ xy +5=0 at (1, 1) is represented by
(A) y=3x-2.
(B) y= -3x+4.
(C) x=3x-2.
(D) x= -3y+4.
Q.13 In the following RC circuit, the capacitor was charged in two different ways.
(i) The capacitor was first charged to 5V by moving the toggle switch to position P and then it was charged to 10V by moving the toggle switch to position Q.
(ii) The capacitor was directly charged to 10V, by keeping the toggle switch at position Q.
(A) The energy dissipation in cases (i) and (ii) will be equal and non-zero.
(B) The energy dissipation for case (i) will be more than that for case (ii).
(C) The energy dissipation for case (i) will be less than that for case (ii).
(D) The energy will not be dissipated in either case.
Q.14 If a constant voltage +V is applied to the input of the following OPAMP circuit for a time t, then the output voltage Vo will approach
(A) +V exponentially.
(B) -V exponentially.
(C) +V linearly.
(D) -V linearly
Q.15 Light travelling between two points takes a path for which
(A) time of flight is always minimum.
(B) distance is always minimum.
(C) time of flight is extremum.
(D) distance is extremum.