Partial Fraction, Logarithms & Limits MCQ
1. Find the value of x; 3x2 algae = 348
(A) 7.1
(B) 4.5
(C) 6.2
(D) 4.8
2. Transform 54y = n+1 into an equivalent a Logarithmic expression
(A) log12 (n+1)
(B) log41 (n2)
(C) log63 (n)
(D) log63 (n)
3. Partial fraction of 2x2 -3x 4/(x-1)3 will Be of the form
(A) Ax+B/(X-1) +C/(x-1)2 +D/(x-1)3
(B) A/x-1) +bx + c/(x-1)2 +D/(x-1)3
(C) A/(x-1) +B/(x-1)2 +C/(x-1)3
(D) None of the Above
4. Partial fractions of x/(x-a)(x-b)(x-c) Will be of the form
(A) A/(x+a) +B/(x+b) +C/(x+c)
(B) A/(x-a) +B/(x-b) + C/(x-c)
(C) A/(X+a) +B/(x-b) + C/(x+c)
(D) None of the Above
5. The adjacent side of the parallelogram is Represented by vectors 2iA+3j^ and In+4j^. The area of the parallelogram is
(A) 5 units
(B) 3 units
(C) 8 units
(D) 11 units
6. The partial fractions of1/(x+1)(x2 – 1) Will be of the form
(A) A/(x-1)+ B/(x2 + 1)
(B) A/(X + 1) +B/(x + 1) +C/(x-1)
(C) A/(x+1) +B/(x+1)2 +C/(x-1)
(D) None of the above
7. Solve for x the equation 2x+3 = 5x+2.
(A) In (24/8)
(B) In (25/8)/ln (2/5)
(C) In (32/5)/ln (2/3)
(D) In (3/25))
8. The rational fraction P(x)/Q(x) is a Proper fraction if
(A) Degree of P(x) = degree of Q(x)
(B) Degree of P(x) < degree of Q(x)
(C) Both (a) and (b)
(D) None of above
9. A relation in which the equality is true Only for several unknowns is called an
(A) Identity
(B) Equation
(C) Algebraic equation
(D) Algebraic relation
10. The function of form f(x) = P(x)/q(x), q(x) = 0, where p(x) and q(x) Are polynomials in x is called the
(A) Identity
(B) Equation
(C) Fraction
(D) Algebraic relation
11. An improper fraction can be reduced to a proper fraction by
(A) Addition
(B) Subtraction
(C) Multiplication
(D) Division
12. 2/(x+6)(x+8) =
(A) 1/(x-6) +7/(x-8)
(B) 1/(x-6)-7/(x-8)
(C) 1/(x+6) +7/(x+8)
(D) 1/(x+6)-7/(x+8)
13. (x+2)2 = x2 + 4x + 4 is
(A) A linear equation
(B) Cubic equation
(C) An identity
(D) An equation
14. Partial fractions of 1/(x3 -1) will be of the form
(A) A/x-1) – B/(x2 +X +1)
(B) A/Cx+1) + B/(x2 +X +1)
(C) A/(x+1) + bx + c/(x2 +X +1)
(D) Ax+B/(x-1) + C/(x2 -x + 1)
15. Which of the following functions f: Z X Z –> Z is not onto
(A) f(a, b) = a +b
(B) f(a, b) = a
(C) f(a, b) = |b|
(D) f(a, b) = a-b
Matrics and Determinants MCQ
1.. Find x, if 
is singular
(A) 1
(B) 2
(C) 3
(D) 4
2. If the points (3, -2), (x, 2), (8, 8) are Collinear, then find the value of x
(A) 2
(B) 3
(C) 4
(D) 5
3. The value of the determinant 
(A) 9x2 (x + y)
(B) 9y2 (x +y)
(C) 3y2 (x + y)
(D) 7x2 (x+ y)
4. If a, ß, y are in A.P., then 
(A) 0
(B) (x-2)(X-3)(x-4)
(C) (x- a)(x -B)(x- y)
(D) aßy (a-)(B- y)2
5. If A= 
,then (A2– 3I)/2
(A) A-1
(B) 2A
(C) 2A-1
(D) 3/2 A-1
6. Solve 
(A) -(a-b) (b-c) (c a)(a2+b2 + c2)
(B) (a b) (b – c) (c – a)
(C) (a2+b2+ c2)
(D) (a– b) (b -c) (c- a)(a2 + b2 + c2)
7. Using determinants, find the equation Of the line joining the points (1, 2) and (3, 6)
(A) y = 2x
(B) X = 3y
(C) y = X
(D) 4x- y = 5
8. The area of a triangle with vertices (-3, 0), (3, 0), and (0, k) is 9 sq. units. The Value of k will be
(A) 9
(B) 3
(C) -9
(D) 6
Calculus MCQ with Answers
1. Which of the following functions are NOT everywhere continuous
(A) f (x)= (x2-4)/(x+2)
(B) f (x)= (x+3)4
(C) f(x)= 1066
(D) f(x)= mx +b
2. Which of the following functions are Continuous
(A) f (x) = |x|
(B) f (x) = {3 x<4; x/2+3 x>4}
(C) f (x) = 1/x
(D) f (x) = {lnx <0, 0 x~0}
3. Find lim f(x);x->€ : f(x) = 9 / (4x2-7)
(A) + Infinity
(B) 2
(C) – Infinity
(D) 0
4. What is the limit of sin(¢)/¢ when 0 Approaches zero
(A) 1
(B) sin¢
(C) 0
(D) None of these
5. What will be the condition for L’Hôpital’s Rule to work
(A) The function must possess at least three non-zero derivatives
(B) The function must be Determinate
(C) The function must be Indeterminate.
(D) The function must be inconsistent
6. What is meant by the differential
(A) A word used a lot on a popular medical television series.
(B) A method of directly relating how Changes in a dependent variable Affect changes in an independent Variable.
(C) A gearbox on the back end of Your car.
(D) None of the above
7. The number of solutions of equations 3x2 +Xsinx + COSX = 0
(A) 3
(B) 2
(C) 1
(D) 0
8. Find the derivative of the following Function f (x)= 1963
(A) + Infinity
(B) 1963
(C) – Infinity
(D) 0
9. Find lim f(x); x->3 : f (x) = (x2-9)/(x-3)
(A) + Infinity
(B) +6
(C) -6
(D) None of the above
10. Find lim f(x); x->0 : f(x) = (x2+7x-120)/(x-7)
(A) + Infinity
(B) 1
(C) 0
(D) All of the above
11. Find the derivative of the following Function: f(x) = x2+6x+9
(A) F(x) = 2x+6+9
(B) F(x) = x2+6
(C) F(x) = 2x+6
(D) f'(x) = 2x
12. Which of the following functions are NOT differentiable
(A) f(x) = |x|
(B) f(x) = (x+3)4
(C) f(x) = 1066
(D) f(x) = 4
13. The equation of the tangent to the curve y= 4+sin2x , at x= 0 is
(A) y= 2
(B) y= 3
(C) y= 4
(D) y= 6
Analytical Geometry MCQ with Answers
1. If the distance between the points (2, – 2) and (-1, x) is 5, one of the values of x is
(A) -2
(B) 2
(C) -1
(D) 1
2. What is the acute angle between the lines y= 3x + 2 and y= 4x +9
(A) 4.4°
(B) 28.3°
(C) 5.2°
(D) 18.6°
3. Find the equation of the line passing Through the origin with a slope of 6
(A) y-6x = 0
(B) y= -6
(C) X +y= -6
(D) 6x+y= 0
4. Find the angle between the lines 3x+2y = 6 and x + y =6
(A) 12°20’
(B) 11°19’
(C) 14°25’
(D) 13°06’
5. The mid-point of the line segment joining the points-2, 8) and B (-6, 4) is
(A) (-4, -6)
(B) (2, 6)
(C) (-4, 2)
(D) (4, 2)
6. What is the equation of the line that passes thru (4, 0) and is parallel to the Line x-y-2 = 0
(A) X-y+4 = 0
(B) X+y+4 = 0
(C) X-y-4 = 0
(D) X-y = 0
7. Find the angle formed by the lines 2x+y-8 = 0 and x + 3y +4 = 0
(A) 30°
(B) 35°
(C) 45°
(D) 60°
8. Which of the following lines is parallel To the line 3x –2y + 6 = 0
(A) 3X +2y-12 = 0
(B) 4x-9y = 6
(C) 12x+18y = 15
(D) 15x-10y-9 = 0
9. Find the equation of the line through Point (3, 1) and is perpendicular to the Line x + 5y +5 0
(A) 5x-2y = 14
(B) 5x-y = 14
(C) 2x- 5y = 14
(D) 2x +5y = 14
10. Find the inclination of the line passing Through (-5, 3) and (10, 7)
(A) 14.73
(B) 14.93
(C) 14.83
(D) 14.63
11. What is the equation of the line joining the points (3, -2) and (-7, 6)
(A) 2x+3y= 0
(B) 4x-5y = 22
(C) 4x + 5y = 2
(D) 5x + 4y = 7
12. The line segment connecting (x, 6) and (9, y) is bisected by points (7, 3). Find the values of x and y
(A) 14, 6
(B) 33, 12
(C) 5, 0
(D) 14, 6
13. The points A (9, 0), B (9, 6), C (-9, 6), and D(-9, 0) are the vertices of a
(A) Square
(B) Rectangle
(C) Rhombus
(D) Trapezium
14. If the distance between the points (4, p) and (1, 0) is 5, then the value of p is
(A) 4 only
(B) +_4
(C) -4 only
(D) 0
Differential Equations & Laplace Transform MCQ
1. Solve xy’ (2y -1) = y (1-X)
(A) In (xy) = 2 (x- y) + C
(B) In (xy) = X- 2y + C
(C) In (xy) = 2y – X + C
(D) ln (xy) = X + 2y + C
2. Find the differential equation whose General solution is y = C1X + C2ex
(A) (x-1) y” – xy’ + y= 0
(B) (x+ 1) y” – xy + y = 0
(C) (x-1) y” + xy’ + y = 0
(D) (x +1) y” + xy’ + y = 0
3. The equation y2 = cx is general solution of
(A) y’ = 2y/x
(B) y’ = 2x/y
(C) y’ = y/2x
(D) y’ = x/2y
4. Solve (cos x cos y – cot x) dx – sin x siny dy = 0
(A) sin x cos y = ln (c cos x)
(B) sin x cos y = ln (c sin x)
(C) sin x cos y = -ln (c sin x)
(D) Sin x cos y = -In (c cos x)
5. Solve the Ordinary Differential Equation y’’ + 2y’ +5y = et sin(t) when y (0) = 0 and y’ (0) = 1. (Without solving For the constants, we get in the partial Fractions).
(A) et [Acost+A1sint+Bcos(2t) + B1)/2sin(2t)]
(B) e-t [Acost+A1sint+Bcos(2t)+B1sin(2t)]
(C) e-t [Acost+A1sint+Bcos(2t) + (B1)/2sin(2t)]
(D) et [Acost+A1sint+Bcos(2t) +(B1) sin(2t)]
6. Solve the differential equation: x(y -1) Dx +(x + 1) dy = 0. If y = 2 when x = 1
(A) 1.80
(B) 1.48
(C) 1.55
(D) 1.63
7. What is the differential equation of the Family of parabolas having their Vertices at the origin and their foci on The x-axis?
(A) 2x dy – y dx = 0
(B) x dy + y dx = 0
(C) 2y dx – x dy = 0
(D) dy/dx – x = 0
8. Solve (x+ y) dy = (x- y) dx
(A) x2+y2 = C
(B) x2 +2xy+ y2 = C
(C) x2-2xy- y2 = C
(D) x2-2xy + y2 = C
9. Which of the following equations is an Exact DE
(A) (x2+ 1) dx -xy dy = 0
(B) x dy +(3x – 2y) dx = 0
(C) 2xy dx+ (2+x2) dy = 0
(D) x2y dy- y dx = 0
10. Find the general solution of y’ =y sec x
(A) y = C (sec x + tan x)
(B) y = C (sec x -tan x)
(C) y = C (sec x tan x)
(D) y = C (sec2 x + tanx)
11. With the help of. Mr Melin gave an inverse Laplace Transformation formula
(A) Theory of calculus
(B) Theory of probability
(C) Theory of Statistics
(D) Theory of residues
12. Which of the following equations is a Variable separable DE
(A) (x+x2y) dy = (2x + xy2) dx
(B) (x+ y) dx-2y dy = 0
(C) 2y = (x2 + 1) dy
(D) y2 dx + (2x -3y) dy = 0
13. If dy x dx; what is the equation of y In terms of x if the curve passes through (1, 1)
(A) x2 -3y+3 = 0
(B) x3 -3y+2 = 0
(C) x3 +3y2+2 = 0
(D) 2y +x3+2 = 0