MTH301 GRAND QUIZ SOLVED 100% VERIFIED BY ADMIN (MID TERM SYLLABUS)
Q1: Parametric equations for the straight through the point A(1,2,3) and parallel to the vector c=4i+5j
A) x=4+t, y=5+2t, z=0+3t
B) x=t, y=3t, z=3t
C) x=1+4t, y=2+5t, z=3+0t. (page70) (100% Sure)
D) x=4t, y=5t, z=0t
Q2: The product of continuous functions is continuous
A) True (Page 34) (100% Sure)
B) False
Q3: The function z=f(x,y) represents a surface in/on ___.
A) Plane (confirm) (100% Sure)
B) Space
C) Line
D) Vector space in plane
Q4: A plane can be completely determined if we know:
A) Two parallel lines passing through that plane
B) a point and a line passing through that point
C) a point and direction of perpendicular to it (page 71) (100% Sure)
D) two points anywhere on the plane
Q5: Cylindrical coordinate 'r' is related to the Cartesian coordinate as:
A) r= cos0
B) r= (z+y)
C) r = underroot(x2+y2) (page19) (100% Sure)
D) r=(x2+y2)
Q6: y = underroot 9-x2 , -3 ≤ x ≤ 3, in a ___ form of a curve in the plane.
A) implict
B) explict (page70) (100% Sure)
C) parametric
D) parametric vector
Q7: The surface z=f(x,y) falls (decreases) most rapidly at any point in the ___ of Gradient(z).
A) Direction
B) Opposit to the direction (confirm) (100% Sure)
C) Direction perpendicular to
D) Arbitary direction
Q8: If a firm's long-run average cost of production decreases as a result of increase in production, then the firm is experiencing.
A) Economies of scale (page58) (100% Sure)
B) Diseconomies of scale
C) Diminishing returns to scale
D) Diminishing returns to factors
Q9: To determine a point in plane (in 2 dimension) how many axes are required:
A) 1
B) 2 (page17) (100% Sure)
C) 3
D) None
Q10: All continuous functions have a minimum and maximum value.
A) True (page93) (100% Sure)
B) False
Q11: Sperical coordinate 'z' is related to the cylindrical coordinate as:
A) z=z
B) z=p
C) z=p cosp
D) z=p cosφ (page19) (100% Sure)
Q12: A function is not continuous at a point if its graph has a hole or break at that point.
A) True (page31)(100% Sure)
B) False
Q13: If a vertical of magnitude '4' is making angle 30-degree with Y-axis then its component vector along x-axis is ___.
A) 2
B) 2*sqrt(3) (confirm) (100% Sure)
C) -2
D) -2*sqrt(3)
Q14: For each fixed y, c ≤ y ≤ d, then function f(x,y) in a function of x alone, then A(y) the area of this function on the interval a ≤ x ≤ b, then the volume is:
A) V(S)= d,c∫(b,a∫f(x,y)dx)dy
B) V(S)= a,b∫(d,c∫f(x,y)dy)dx (page111) (100% Sure)
C) V(S)= d,c∫(b,a∫f(x,y)dx)dy
D) V(S)= a,b∫(d,c∫f(x,y)dx)dy
Q15: Value of the function f(x,y,z)=xy+z at the point (1,1,1) is:
A) 2 (confirm) (100% Sure)
B) 3
C) 1
D) 4
Q16: Face of the parabola (y-ax+bx+c) is openening downward when:
A) a > 0
B) a < 0 (page9) (100% Sure)
C) b > 0
D) b < 0
Q17: The mixed 2nd order partial derivatives of x=xy is equal to:
A) x^2
B) y^2
C) xy
D) 1 (page39) (100% Sure)
Q18: A ___ need not be the highest point on the entire graph.
A) relative minimum
B) relative maximum (page83) (100% Sure)
C) absolute minimum
D) absolute maximum
Q19: If we approach a point say (a,b) along different paths and get different values then it means:
A) Limit cannot be found using this technique
B) Limit does not exist (page28) (100% Sure)
C) Limit exist
D) None of these
Q20: Length or magnitude of a unit vector is ___.
A) 0
B) 1 (page53) (100% Sure)
Q21: If f(x,y)= x3 y2 +5 then df/dx=
A) 3x2 y2+5
B) 3x2 y2 (confirm) (100% Sure)
C) 2x3 y+5
D) 2x3 y
Q22: YZ-plane consists of all points where
A) yz=0
B) yz=1
C) x=0 (page14) (100% Sure)
D) z=0
Q23: The function f(x,y) grow most rapidly in the direction of:
A) gradient vector (page67) (100% Sure)
B) unit vector
C) x-axis
D) y-axis
Q24: 0∫2 0∫410dxdy= _____.
A) 20
B) 40
C) 60
D) 80 (confirm) (100% Sure)
Q25: 0∫11∫2dxdy
A) 0
B) 1 (confirm) (100% Sure)
C) 2
D) 3
Q26: The partial derivative of f(x,y)=x2 e-9 with respect to x is ____.
A) x2 e-9
B) 2x e-9 (confirm) (100% Sure)
C) -x2 e-9
D) x-2 e-9
Q27: To express the location of any object on earth which coordinate system is used:
A) rectangular coordiante system
B) polar coordinate system
C) spherical coordinate system (page22) (100% Sure)
D) cylindrical coordinate system
Q28: f(x,y,z) = √(x2+y2+z2)
A) (-∞, +∞)
B) (-∞, 0)
C) (0, +∞) (Page 24) (100% Sure)
D) (0, +∞)
Q29: Let be a function of two variables at a critical point (1,0),fxx (1,0)=4,fyy(1,0)=2 and fxy(1,0)=0
so D=fxx(1,0)fyy(1,0)-f2xy(1,0)=8
A) Then f has a relative maximum at (1,0)
B) Then no conclusoin can be drawn
C) Then f has a relative minimum at (1,0) (page89) (100% Sure)
D) Then f has a relative maximum at (1,0)
Q30: Value of the function f(x,y,z)=xyz at point (2,2,2) is ___.
A) 2
B) 6
C) 8 (confirm) (100% Sure)
D) 16
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