MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
This section includes 1894 Mcqs, each offering curated multiple-choice questions to sharpen your General Aptitude knowledge and support exam preparation. Choose a topic below to get started.
| 1051. |
(9m5 + 12m4 - 6m2) ÷ 3m2 = ___ |
| A. | 3m3 + 4m2 - 2 |
| B. | 3m3 + 12m4 - 6m2 |
| C. | 3m3 |
| D. | 3m5 + 4m4 - 2m2 |
| Answer» B. 3m3 + 12m4 - 6m2 | |
| 1052. |
Directions: Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers.In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.Quantity I: x2 - 39x + 378 = 0Quantity II: y2 - 24y + 108 = 0 |
| A. | Quantity I ≤ Quantity II |
| B. | Quantity I > Quantity II |
| C. | Quantity I ≥ Quantity II |
| D. | Quantity I < Quantity II |
| E. | Quantity I = Quantity II |
| Answer» D. Quantity I < Quantity II | |
| 1053. |
For the equation y = 7x - 2, which of the following statement is true? |
| A. | It has a unique solution. |
| B. | It has two solutions |
| C. | It has infinite number of solutions |
| D. | It has no solution |
| Answer» D. It has no solution | |
| 1054. |
If x = (7 – 4√3), then find the value of x + 1/x. |
| A. | 14 |
| B. | 8√3 |
| C. | 14 + 8√3 |
| D. | 3√3 |
| Answer» B. 8√3 | |
| 1055. |
If, the sum of Squares of 3 distinct numbers is 1, then the sum of their product taken two at a time, lies in between: |
| A. | \(- \dfrac{1}{2} \ and \ 1\) |
| B. | \(\dfrac{1}{2} \ and \ \dfrac{3}{4}\) |
| C. | \(\dfrac{1}{2} \ and \ 1\) |
| D. | \(- \dfrac{1}{2} \ and \ \dfrac{3}{2}\) |
| Answer» B. \(\dfrac{1}{2} \ and \ \dfrac{3}{4}\) | |
| 1056. |
Let f(x) and g(x) be two polynomials (with real coefficients) having degree 3 and 4 respectively. What is the degree of f(x) g(x) |
| A. | 12 |
| B. | 7 |
| C. | 4 |
| D. | 3 |
| Answer» C. 4 | |
| 1057. |
Let \(\vec a = 2\hat i + {\lambda _1}\hat j + 3\hat k\), \(\vec b = 4\hat i + \left( {3 - {\lambda _2}} \right)\hat j + 6\hat k,{\rm{\;and\;}}\vec c = 3\hat i + 6\hat j + \left( {{\lambda _3} - 1} \right)\hat k\) be three vectors such that \(\vec b = 2\vec a\;{\rm{and\;\vec a\;is\;perpendicular\;to\;}}\vec c\). Then a possible value of (λ1, λ2, λ3) is: |
| A. | (1, 3, 1) |
| B. | \(\left( { - \frac{1}{2},\;4,\;0} \right)\) |
| C. | \(\left( {\frac{1}{2},4, - 2} \right)\) |
| D. | (1, 5, 1) |
| Answer» C. \(\left( {\frac{1}{2},4, - 2} \right)\) | |
| 1058. |
If x is a real number, then \(\sqrt {log_e\frac{{4x - {x^2}}}{3}} \)is a real number if and only if |
| A. | - 3 ≤ x ≤ 3 |
| B. | 1 ≤ x ≤ 2 |
| C. | -1 ≤ x ≤ 3 |
| D. | 1 ≤ x ≤ 3 |
| Answer» E. | |
| 1059. |
If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1 + x)n are in A. P., then the value of n is |
| A. | 2 |
| B. | 7 |
| C. | 11 |
| D. | 14 |
| Answer» C. 11 | |
| 1060. |
If x + y + z = 19, xyz = 216 and xy + yz + zx = 114, then the value of √(x3 + y3 + z3 + xyz) is: |
| A. | 28 |
| B. | 35 |
| C. | 30 |
| D. | 32 |
| Answer» C. 30 | |
| 1061. |
Factors of x2 + 3x - 40 are : |
| A. | (x - 5) and (x + 8) |
| B. | (x + 4) and (x - 10) |
| C. | (x + 5) and (x - 8) |
| D. | (x + 5) and (x + 8) |
| Answer» B. (x + 4) and (x - 10) | |
| 1062. |
For what value of λ, do the simultaneous equation 2x + 3y = 1, 4x + 6y = λ have infinite solutions? |
| A. | λ = 0 |
| B. | λ = 1 |
| C. | λ ≠ 2 |
| D. | λ = 2 |
| Answer» E. | |
| 1063. |
Find the value of y(y4 - y2 - y) when y = 5. |
| A. | 2900 |
| B. | 2975 |
| C. | 2925 |
| D. | 2995 |
| Answer» C. 2925 | |
| 1064. |
Find the sum of zeros for the quadratic polynomial 3x2 + 5x - 2 |
| A. | -3 / 5 |
| B. | 5 / 3 |
| C. | 3 / 5 |
| D. | -5 / 3 |
| Answer» E. | |
| 1065. |
If (6x + 4y) / (6x - 4y) = 8/6 then what is the value of x2 / y2? |
| A. | 78/9 |
| B. | 64/13 |
| C. | 196/9 |
| D. | 125/9 |
| Answer» D. 125/9 | |
| 1066. |
In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.I. 6x2 – 13x + 2 = 0II. 2y2 – 19y + 30 = 0 |
| A. | x > y |
| B. | x < y |
| C. | x ≥ y |
| D. | x ≤ y |
| E. | x = y or no relationship could be established |
| Answer» E. x = y or no relationship could be established | |
| 1067. |
Every open set of real numbers is the union of |
| A. | Countable collection of disjoint open intervals |
| B. | Uncountable collection of disjoint closed intervals |
| C. | Countable collection of disjoint closed intervals |
| D. | Uncountable collection of disjoint open intervals |
| Answer» B. Uncountable collection of disjoint closed intervals | |
| 1068. |
If a + b + c = 0, then (a3 + b3 + c3)2 = ? |
| A. | 3a2b2c2 |
| B. | 9a2b2c2 |
| C. | 9abc |
| D. | 27abc |
| Answer» C. 9abc | |
| 1069. |
If a + b = 4 and ab = 3, then what is the value of a3 + b3? |
| A. | 21 |
| B. | 17 |
| C. | 28 |
| D. | 31 |
| Answer» D. 31 | |
| 1070. |
Find the value of \(\sqrt {{{\left( {2x - 5} \right)}^2}} + 2\sqrt {{{\left( {x - 1} \right)}^2}} \), if 1 < x < 2 |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» D. 4 | |
| 1071. |
If T is an idempotent linear operator then T is diagonalisable and only Eigen values of T are |
| A. | 0 and 1 |
| B. | 1 and 2 |
| C. | 1 and -1 |
| D. | 0 and -1 |
| Answer» B. 1 and 2 | |
| 1072. |
If \(\rm \vec{a},\vec{b},\vec{c}\) are three non-coplanar vectors, then\(\rm (\vec{a}+\vec{b}+\vec{c}) \cdot[(\vec{a}+\vec{b}) \times( \vec{a}+\vec{c})]=\) |
| A. | 0 |
| B. | \(\rm [\vec{a}\; \vec{b} \;\vec{c}]\) |
| C. | 2\(\rm [\vec{a}\; \vec{b} \;\vec{c}]\) |
| D. | -\(\rm [\vec{a}\; \vec{b} \;\vec{c}]\) |
| Answer» E. | |
| 1073. |
If \(\frac a 3=\frac b 2=\frac c 1\), then \(\frac {a+b+2c}{b}\) is |
| A. | 3.8 |
| B. | 4 |
| C. | 3.5 |
| D. | 5 |
| Answer» D. 5 | |
| 1074. |
If a + b + c = 19, ab + bc + ca = 120, then what is the value of a3 + b3 + c3 – 3abc? |
| A. | 31 |
| B. | 23 |
| C. | 19 |
| D. | 18 |
| Answer» D. 18 | |
| 1075. |
If a1/3 + b1/3+ c1/3 = 0, then (a + b + c)6 is equal to: |
| A. | 729 a2b2c2 |
| B. | 729 abc |
| C. | 81 a2b2c2 |
| D. | 81 abcm |
| Answer» B. 729 abc | |
| 1076. |
If a3 + 3a2 + 9a = 1, then what is the value of a3 + (3/a)? |
| A. | 31 |
| B. | 26 |
| C. | 28 |
| D. | 24 |
| Answer» D. 24 | |
| 1077. |
If a + b = 1 and ab = -6, then what is the value of a3 + b3? |
| A. | 17 |
| B. | 15 |
| C. | 19 |
| D. | 13 |
| Answer» D. 13 | |
| 1078. |
Directions: In the following questions two equations numbered I and II are given. You have to solve both the equations and Give answer:I. 3y + 18 = 50 – 5yII. x2 = 16 |
| A. | If x > y |
| B. | If x ≥ y |
| C. | If x < y |
| D. | If x ≤ y |
| E. | If x = y or the relationship cannot be established |
| Answer» E. If x = y or the relationship cannot be established | |
| 1079. |
For any vector a, the value of (a × i)2 + (a × j)2 is equal to |
| A. | 3a2 |
| B. | a2 |
| C. | 2a2 |
| D. | 4a2 |
| Answer» C. 2a2 | |
| 1080. |
If 2x2 + y2 + 6x – 2xy + 9 = 0, then the value of (4x3 – y3 + x2y2) is: |
| A. | 0 |
| B. | -9 |
| C. | -3 |
| D. | 9 |
| Answer» B. -9 | |
| 1081. |
A sack of mathematics textbooks weighs 2 kg 400 g. If the weight of one mathematics textbook is 300 g, then how many textbooks are there in the sack? |
| A. | 10 |
| B. | 8 |
| C. | 26 |
| D. | 12 |
| Answer» C. 26 | |
| 1082. |
If a + b = 4 and ab = -5, then what is the value of a3 + b3? |
| A. | 34 |
| B. | 36 |
| C. | 124 |
| D. | 126 |
| Answer» D. 126 | |
| 1083. |
In the following question, two equations numbered I and II are given. You have to solve both the equations and give answer:I. 11x2 + 18x + 7 = 0II. 3y2 + 2y - 1 = 0 |
| A. | x > y |
| B. | x ≥ y |
| C. | x < y |
| D. | x ≤ y |
| E. | x = y or the relation cannot be determined |
| Answer» F. | |
| 1084. |
If x4 + x2y2 + y4 = 29 and x2– xy + y2 = 5, then what is the value of 5xy? |
| A. | –1 |
| B. | 2 |
| C. | –2 |
| D. | 0 |
| Answer» C. –2 | |
| 1085. |
If x + 1/x = 5, then x3 + 1/x3 is equal to∶ |
| A. | 110 |
| B. | 130 |
| C. | 145 |
| D. | 125 |
| Answer» B. 130 | |
| 1086. |
If x6 – 512y6 = (x2 + Ay2)(x4 – Bx2y2 + Cy4), then what is the value of (A + B - C)? |
| A. | -72 |
| B. | 72 |
| C. | -80 |
| D. | 48 |
| Answer» D. 48 | |
| 1087. |
If x + y + z = 0, then what is the value of x2/yz + y2/xz + z2/xy? |
| A. | 0 |
| B. | 1/3 |
| C. | 1 |
| D. | 3 |
| Answer» E. | |
| 1088. |
Eigen values of \(\left[ {\begin{array}{*{20}{c}} 2&2&1\\ 1&3&1\\ 1&2&2 \end{array}} \right]\) are |
| A. | 1, 2, 3 |
| B. | 1, 1, 2 |
| C. | 1, 1, 5 |
| D. | 2, 2, 5 |
| Answer» D. 2, 2, 5 | |
| 1089. |
On simplification, \(\frac{{{x^3} - {y^3}}}{{x[{{\left( {x + y} \right)}^2} - 3xy]}} \div \frac{{y\left[ {{{\left( {x - y} \right)}^2} + 3xy} \right]}}{{{x^3} + {y^3}}} \times \frac{{{{\left( {x + y} \right)}^2} - {{\left( {x - y} \right)}^2}}}{{{x^2} - {y^2}}}\) is equal to: |
| A. | 1 |
| B. | 4 |
| C. | 1/4 |
| D. | 1/2 |
| Answer» C. 1/4 | |
| 1090. |
If \(\frac{x}{b+c}=\frac{y}{c+a}=\frac{z}{b-a}\), then which one of the following is correct? |
| A. | x + y + z = 0 |
| B. | x - y - z = 0 |
| C. | x + y - z = 0 |
| D. | x + 2y + 3z = 0 |
| Answer» C. x + y - z = 0 | |
| 1091. |
If \(\frac{{61}}{{19}}{\rm{}} = {\rm{}}3{\rm{\;}} + {\rm{\;}}\frac{1}{{x\; + \;\frac{1}{{y\; + \;\frac{1}{z}}}}}\) where x, y and z are natural numbers, then what is z equal to? |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» D. 4 | |
| 1092. |
Find the degree of the polynomial 8x4 + 2x2y3 + 4. |
| A. | 4 |
| B. | 5 |
| C. | 0 |
| D. | 1 |
| Answer» C. 0 | |
| 1093. |
If \(x + \frac{4}{x}-4=0,\) then the value of x2 – 4 is equal to: |
| A. | 4 |
| B. | 1 |
| C. | 2 |
| D. | 0 |
| Answer» E. | |
| 1094. |
If \(x - \frac 3 x = 6,\; x \ne 0,\) then the value of \(\frac {x^4 - \frac {27}{x^2}}{x^2 - 3x - 3}\) is: |
| A. | 54 |
| B. | 270 |
| C. | 80 |
| D. | 90 |
| Answer» E. | |
| 1095. |
If (1/x) + (1/y) + (1/z) = 0 and x + y + z = 9, then what is the value of x3 + y3 + z3 – 3xyz? |
| A. | 81 |
| B. | 361 |
| C. | 729 |
| D. | 6561 |
| Answer» D. 6561 | |
| 1096. |
Expand \({\left( {\frac{x}{3} + \frac{y}{5}} \right)^3}\) |
| A. | \(\frac{{{x^3}}}{{25}} + \frac{{{x^2}y}}{{15}} + \frac{{x{y^2}}}{{25}} + \frac{{{y^3}}}{{125}}\) |
| B. | \(\frac{{{x^3}}}{{27}} + \frac{{{x^2}y}}{{25}} + \frac{{x{y^2}}}{{25}} + \frac{{{y^3}}}{{125}}\) |
| C. | \(\frac{{{x^3}}}{{27}} + \frac{{{x^2}y}}{{15}} + \frac{{x{y^2}}}{{25}} + \frac{{{y^3}}}{{125}}\) |
| D. | \(\frac{{{x^3}}}{{27}} + \frac{{xy}}{{15}} + \frac{{x{y^2}}}{{25}} + \frac{{{y^3}}}{{125}}\) |
| Answer» D. \(\frac{{{x^3}}}{{27}} + \frac{{xy}}{{15}} + \frac{{x{y^2}}}{{25}} + \frac{{{y^3}}}{{125}}\) | |
| 1097. |
Let X be a square matrix. Consider the following two statements on X.I. X is invertible.II. Determinant of X is non-zero.Which one of the following is TRUE? |
| A. | I implies II; II does not imply I. |
| B. | II implies I; I does not imply II. |
| C. | I does not imply II; II does not imply I. |
| D. | I and II are equivalent statements. |
| Answer» E. | |
| 1098. |
If 9a2 + 4b2 + c2 + 21 = 4(3a + b – 2c), then the value of (9a + 4b – c) is∶ |
| A. | 2 |
| B. | 6 |
| C. | 16 |
| D. | 12 |
| Answer» E. | |
| 1099. |
If \(\rm |\vec{a}\times \vec{b}|^2 + |\vec{a}\cdot \vec{b}|^2=144\) and \(\rm |\vec{a}|=4\), then what is \(\rm |\vec{b}|\) equal to? |
| A. | 3 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» B. 4 | |
| 1100. |
Consider the following statements in respect of a vector \(\vec c=\vec a+\vec b\), where \(|\vec a|=|\vec b|\ne0\):1. \(\vec c\) is perpendicular to \((\vec a-\vec b).\)2. \(\vec c\) is perpendicular to \(\vec a \times \vec b.\)Which of the above statement is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» D. Neither 1 nor 2 | |