The default category for questions shared in context 'MTH105'. Multiple Choice Questions (MCQs) MCQ1 Given these propositions I. Garri is from yam and 8+1= 6 II. Garri is from maize and 2+4= 8 III. Garri from cassava and 3+4= 9 IV. Garri is from cassava and 4+5=9 The only proposition is i 0.0000000 ii 0.0000000 iii 0.0000000 iv 1.0000000 MCQ2 Given that p ? q this means the symbols speak about Conjunction p ? q 1.0000000 Disjunction p ? q 0.0000000 Conjunction p v q 0.0000000 Disjunction p/q 0.0000000 MCQ3 If P is a given negation, its negation is ____ ? p 0.0000000 v p 0.0000000 ~ p 1.0000000 / p 0.0000000 MCQ4 Conditional statement is of the form “if P then Q.” then the symbolical representation is p ? q 0.0000000 p ΰ q 1.0000000 p v q 0.0000000 p ~ q 0.0000000 MCQ5 Bi-conditional statement can be symbolically represented as ___ p ? q 0.0000000 p ΰ q 0.0000000 p σ q 1.0000000 p v q 0.0000000 MCQ6 Given that (p v q)v r = p v (q v r) Commutative 0.0000000 Idempotent 0.0000000 Associative 1.0000000 Distributive 0.0000000 MCQ7 If p v (q ? r) = (p v q) ? (p v r) then it is a(an) ____ Identity 0.0000000 Commutative 0.0000000 Distributive 1.0000000 Associative 0.0000000 MCQ8 If A= 200050001 then A is matrix Square 0.0000000 Diagonal 1.0000000 Transpose 0.0000000 Symmetric 0.0000000 MCQ9 Given A= 123242 and B= 104213find A+B 104212 0.0000000 126453 0.0000000 227455 1.0000000 217545 0.0000000 MCQ10 If A= 213312 and B= 212122 then 2A+B= 428433 0.0000000 638746 1.0000000 637556 0.0000000 638756 0.0000000 MCQ11 Given that A= 123457 and B= 124365 find AB 27236658 1.0000000 23662758 0.0000000 66582327 0.0000000 23276658 0.0000000 MCQ12 Find the determinant of A= 4365 20 0.0000000 18 0.0000000 5 0.0000000 2 1.0000000 MCQ13 Find the determinant of 12-47 15 1.0000000 12 0.0000000 9 0.0000000 6 0.0000000 MCQ14 Find det X, given that X= 123321411 15 0.0000000 12 0.0000000 -12 1.0000000 -15 0.0000000 MCQ15 Given that 32X1 is a singular matrix, find X. 21/2 0.0000000 11/2 1.0000000 1 0.0000000 ½ 0.0000000 MCQ16 Given that M= 221+62-X213 find X, for M to be singular 21/2 0.0000000 31/2 0.0000000 41/2 0.0000000 51/2 1.0000000 MCQ17 Solve for x and y in x+3y=4 and 3x+4y=6 2/5,6/5 1.0000000 6/5,2/5 0.0000000 -6/5,2/5 0.0000000 6/5,-2/5 0.0000000 MCQ18 Given that co-factor matrix M= 16-12-4-5-33-12-3find the Adj M 16-5-5-12-312-43-3 1.0000000 16-12-5-12-312-412-3 0.0000000 16-5-5-1212-3-43-3 0.0000000 16-3-5-121212-4-12-3 0.0000000 MCQ19 Find the magnitude of 3i – 4j 3 0.0000000 4 0.0000000 5 1.0000000 7 0.0000000 MCQ20 Let x, y, z be the heights assigned to A, B, C such that x+2y+3z= 11, 2x+4y+5z= 21 and x+2y+3z= 11 x= 2, y=3, z=2 0.0000000 x=2, y=-3, z=1 0.0000000 x=2, y=3, z=1 1.0000000 x=2, y=3, z=-2 0.0000000 MCQ21 Find the unit vector in the direction of the vector 4i - 3j 1/5(4i – 3j) 1.0000000 1/5(4i + 3j) 0.0000000 1/5(3i – 4j) 0.0000000 1/5(3i + 4j) 0.0000000 MCQ22 If Z1= 3+i and Z2= 4+3i, find Z1+Z2 12+3i 0.0000000 7+4i 1.0000000 12–3i 0.0000000 7–4i 0.0000000 MCQ23 Given that Z1= 3–2i and Z2= 5+3i, find Z1 – Z2 2+4i 0.0000000 2–4i 0.0000000 2+4i 0.0000000 -2–4i 1.0000000 MCQ24 If Z1= 2–2i and Z2= 5–3i, find Z1/ z2 .(2-2i)(5+3i)34 1.0000000 (2-2i)(5-3i)34 0.0000000 (2+2i)(5+3i)34 0.0000000 (2+2i)(5-3i)34 0.0000000 MCQ25 Find the distance between A (5, -3) and B (-1, 3) -63 0.0000000 -62 0.0000000 63 0.0000000 62 1.0000000 MCQ26 Find the angle of inclination if A (2, -3) and B (4, 5) 90o 0.0000000 60o 0.0000000 45o 1.0000000 30o 0.0000000 MCQ27 Find the distance between A (0, 1) and B (9, 6) 104 0.0000000 105 0.0000000 106 1.0000000 107 0.0000000 MCQ28 Find the distance between A (6, 3) and (6, 9) 8 0.0000000 6 1.0000000 4 0.0000000 2 0.0000000 MCQ29 Find the gradient of the straight line A (-2, 0) and B (6, -4) 2/3 0.0000000 3/2 0.0000000 1/2 1.0000000 2/2 0.0000000 MCQ30 Find the distance between A (6, 9) and B (11, 15) 36 0.0000000 25 0.0000000 61 1.0000000 51 0.0000000 MCQ31 Find the equation of a line with A (2, 3) and B (6, 8) 5x+4y= -2 0.0000000 5x-4y= -2 1.0000000 5x+4y= 2 0.0000000 5x-4y= 2 0.0000000 MCQ32 Find the equation of a line, which passes through the points A (0, 3) and (6, 0) x+2y= 6 0.0000000 x-2y= 6 0.0000000 y-2x= 6 0.0000000 y+2x= 6 1.0000000 MCQ33 Find the coordinate of the point of intercept of the equations 2x+3y= 5 and x+2y= 3. 1, 1 1.0000000 1, -1 0.0000000 -1, 1 0.0000000 -1, -1 0.0000000 MCQ34 Find the gradients of these equations x+y= 5 and x+2y= 6 respectively -1 and -1/2 1.0000000 1 and 1/2 0.0000000 -1 and 1/2 0.0000000 1 and -1/2 0.0000000 MCQ35 Find the coordinate of the meeting points of equations x+y= 3 and x+2y= 5 -1, -2 0.0000000 1, -1 0.0000000 -1, 2 0.0000000 1, 2 1.0000000 MCQ36 Find the equation of a line that is perpendicular to 2x+5y= 10 5x-2y=4 0.0000000 5x-2y= -4 1.0000000 2x-5y= -10 0.0000000 2x+5y =10 0.0000000 MCQ37 Given that two (2) lines with gradients M1 and M2 are parallel, then_____ M1 ? M2 0.0000000 M1 < M2 0.0000000 M2 < M1 0.0000000 M1 = M2 1.0000000 MCQ38 Find the equation of the line which is parallel to 3x+2y= 5 and passes through the point (3, -6). 3x+2y= 3 0.0000000 3y+2x= 3 0.0000000 3x+2y= -3 1.0000000 3y+2x= -3 0.0000000 MCQ39 Find the equation of the line which is perpendicular to 2x+3y= 6 and passes through the point (2, -4) 2x–3y= 8 0.0000000 2x+3y= -8 1.0000000 2x–3y= -8 0.0000000 2x+3y= 8 0.0000000 MCQ40 Given x2+y2–24x–10+60= 0, find the coordinate of the centre. 12, 5 1.0000000 5, 12 0.0000000 -12, -5 0.0000000 -5, -12 0.0000000 MCQ41 Find the coordinate of the centre and radius of circle of the equation x2+y2–24x–6y+86= 0 (-12, -3), r= 7 0.0000000 (12, -3), r= 7 0.0000000 (12, 3), r= 7 1.0000000 (-12, 3), r= 7 0.0000000 MCQ42 Given that nth term of a Sequence 4, 6, 8…….is a­n = a + (n-1) d, find the 7th term 10 0.0000000 12 0.0000000 14 0.0000000 16 1.0000000 MCQ43 Given the two (2) sequences 1, 3, 5 …..and 2, 4, 6……..the 8th terms of the two (2) sequences are …….. 11 and 12 0.0000000 13 and 14 0.0000000 15 and 16 1.0000000 17 and 18 0.0000000 MCQ44 Find the 16th term of an A.P whose first term is 102 and common difference -3. 37 0.0000000 47 0.0000000 57 1.0000000 67 0.0000000 MCQ45 The 4th and 9th terms of an A.P are 10 and 20 respectively; find the first term and the common difference. 4, 2 1.0000000 4, 3 0.0000000 4, 5 0.0000000 4, 7 0.0000000 MCQ46 Find the common ratio of the following 6, 18, 54…………………………………… 2 0.0000000 3 1.0000000 4 0.0000000 5 0.0000000 MCQ47 Find the common ratio of 1/32, 1/16, 1/8……………………………………………………… 4 0.0000000 2 1.0000000 1/2 0.0000000 1/4 0.0000000 MCQ48 Find the limit of 5xx+1as X ΰ 8 0 0.0000000 1 0.0000000 5 1.0000000 6 0.0000000 MCQ49 The derivative of 5x3+3x+2/x 15x2+3+2/x2 0.0000000 15x2-3+2/x2 0.0000000 15x2+3-2/x2 1.0000000 15x2-3-2/x2 0.0000000 MCQ50 If y=sin-1x, find dy/dx 1/1-x2 0.0000000 1/1+x2 0.0000000 1/1-x2 1.0000000 1/1+x2 0.0000000 Fill in the Blank (FBQs) FBQ1 A matrix, which has the same number of rows and columns is called _____ square matrix 1.0000000 0.0000000 FBQ2 ___ is a matrix in which all its diagonal elements are one identify matrix 1.0000000 FBQ3 The disjunction of X and Y is denoted by ____ X V Y 1.0000000 0.0000000 FBQ4 ____ is the conjunction of X and Y (X ^ Y) 1.0000000 0.0000000 FBQ5 The statement of the form ‘m’ If and only If ‘n’ or ‘m’ If ‘n’ is denoted by ___ m <-> n 1.0000000 FBQ6 Let ‘a’ be she is tall and ‘b’ be she is nice. The state in symbolic is written as ___ (a ^ b) 1.0000000 FBQ7 Let ‘a’ be she is fair or ‘b’ be she is beautiful. The statement in symbolic form is ( a ? b) 1.0000000 FBQ8 If ‘p’ is she is tall and ‘q’ is she is beautiful. The statement that she is tall or short and beautiful can be symbolically represented as ____ (p ? (~ p ^ q)) 1.0000000 0.0000000 FBQ9 If p and q stand for he is tall and handsome respectively, then (~ p ^ - q) is ___ ? He is neither tall nor handsome 1.0000000 0.0000000 FBQ10 The equilibrium prices and quantities for two commodity market models Xdj = -2 – p + q and Xsi = -2 – q is ___ (2, 4) 1.0000000 FBQ11 The equation of the line passing through the points A (2,3) and B (4, 6) is ___? 2y = 3x 1.0000000 FBQ12 ____ is defined to be the matrix obtained by replacing every number aij of the given matrix A by its cofactor in the determinant of A. cofactor 1.0000000 FBQ13 Given that A = 1425 , the determinant of A is ___ -3 1.0000000 0.0000000 FBQ14 The determinant of A2 – 2A is ___, Given that A = 1221 15 1.0000000 FBQ15 If A = 200010203 it is called _____? diagonal matrix 1.0000000 FBQ16 The determent of 1-11-223-121 is -3 1.0000000 FBQ17 The conditional statement of the form if ‘a’ then ‘b’ is ___ (a->b) 1.0000000 FBQ18 ____ are the vectors with the same magnitude and directions. equal vectors 1.0000000 FBQ19 Equal directions and magnitude means the vectors are ____ Parallel 1.0000000 0.0000000 FBQ20 If three or more points lie on a straight line, they are said to be __ Collinear 1.0000000 FBQ21 The modulus |.a| is the same thing as ____ Magnitude 1.0000000 FBQ22 A complex variable Z is of the form a + bi where a and b are called ____ real number 1.0000000 0.0000000 FBQ23 In a complex variable Z of the form a + bi, i is called ___ imaginary number 1.0000000 FBQ24 Two or more complex numbers Z1, Z2 and Z3…… are said to be equal if their ___ are equal real parts 1.0000000 FBQ25 Given that a complex number Z= a+ bi, then its conjugate is written as ___ Z = a – bi 1.0000000 a-bi 1.0000000 FBQ26 If Zn = rn (cos ? + I sin ? ) = r (cos ? + I sin ?)n, it is called ____ De Moivre’s Theorem 1.0000000 FBQ27 The slope is the same thing as ___ of the line with x-axis tangent of an angle inclination 1.0000000 FBQ28 The gradient of a line is the same as the ___ of that line,, usually denoted by ‘m’. Slope 1.0000000 0.0000000 FBQ29 The gradient or slope of any line can be determined by the ____ in y and/over that of x. rate of change 1.0000000 0.0000000 FBQ30 The equation of a straight line y – mx – c = 0 has ___ and ___ as slope and the intercept on the y-axis. m and c 1.0000000 FBQ31 The equation of a line that passes through the origin is ____ y = mx 1.0000000 FBQ32 The equation of a line given one point and the slope is generally written as ___ y-y1 = m (x-x1) 1.0000000 FBQ33 ___ is the locus of curve equidistant from a point. Circle 1.0000000 FBQ34 Differentiation is the inverse process of ___ Integration 1.0000000 FBQ35 If the value of turning point in ____ is negative then it is a maximum point. second derivative 1.0000000 FBQ36 If the value of the turning point in the second derivation is positive, then it is a ____ minimum point 1.0000000 FBQ37 __ is the point at which curve is neither a maximum nor minimum. point of inflexion 1.0000000 FBQ38 At point of inflexion, the turning points are equal and can be referred to as ___ double stationary points 1.0000000 FBQ39 At the point of inflexion, the value of the stationary point at the second derivation is ___ Zero 1.0000000 FBQ40 If a die is rolled, the probability of getting odd and prime number is___ 14 1.0000000 FBQ41 ___ is the amount by which a resource is underutilized in optimization model. Slack 1.0000000 0.0000000 FBQ42 Comparing straight line equations with business that is demand function, we have y = mx + c and q = mp + c, where y=q stands for ___ function of goods demanded 1.0000000 FBQ43 Comparing straight line equations with business that is demand function, we have y = mx + c and q = mp + c, where mx = mp then m stands for gradient of x and p respectively 1.0000000 * coefficient of x and p respectively* 1.0000000 FBQ44 Comparing straight line equations with business that is demand function, we have y = mx + c and q = mp + c, where mx = mp then x and p stand for ___ variable price of the goods demanded 1.0000000 FBQ45 The equation of a line with two points and the slope is ___ m = y2-y1/x2-x1 = y-y1/x-x1 1.0000000 m = y1-y2/x2-x1 = y-y2/x-x2 1.0000000 FBQ46 Give that AB-=-BA- are vectors of the same magnitude but in _____ direction. Opposite 1.0000000 FBQ47 If AB-=1, then AB- and it is called a ___ vector Unit 1.0000000 FBQ48 Given AB-=-BA- are vectors of the ___ magnitude but in opposite direction. same 1.0000000 FBQ49 a-is equal to –a If “a” is less than ___ Zero 1.0000000 0 1.0000000 FBQ50 a- is equal to “a” If ‘a’ is greater than ___ Zero 1.0000000 0 1.0000000Zero* 1.0000000 0 1.0000000