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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.
| 951. |
If l and m are the roots of the equation x2 + px + q, then \(- \frac{1}{l}\) and \(- \frac{1}{m}\) are the roots of: |
| A. | qx2 + px + 1 = 0 |
| B. | qx2 – px + 1 = 0 |
| C. | x2 – px + q = 0 |
| D. | x2 + px + q = 0 |
| Answer» C. x2 – px + q = 0 | |
| 952. |
If 2x - 2(4 - x) < 2x - 3 < 3x + 3; then x can take which of the following values? |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 5 |
| Answer» B. 3 | |
| 953. |
If the difference of two numbers is 4 and the difference of their squares is 64, then which is the smaller of the two number? |
| A. | 10 |
| B. | 6 |
| C. | 4 |
| D. | 8 |
| Answer» C. 4 | |
| 954. |
Find the value of λ such that the vectors \(3\hat i - \hat j + 4\hat k\) and \(- \lambda \hat i + 3\hat j + 3\hat k\) are perpendicular ? |
| A. | 2 |
| B. | - 2 |
| C. | 3 |
| D. | - 3 |
| Answer» D. - 3 | |
| 955. |
Divide 27 into two parts in such a way that 5 times the first part and 11 times the second part both together are equal to 195, then the ratio of the first and second part is |
| A. | 3 : 2 |
| B. | 17 : 10 |
| C. | 2 : 7 |
| D. | 5 : 4 |
| Answer» C. 2 : 7 | |
| 956. |
If x – 5√x – 1 = 0, then x2 + 1/x2 is equal to∶ |
| A. | 729 |
| B. | 731 |
| C. | 625 |
| D. | 727 |
| Answer» E. | |
| 957. |
If a3 + b3 = 341 and ab = 30, then what is the value of a + b? |
| A. | 1 |
| B. | 9 |
| C. | 7 |
| D. | 11 |
| Answer» E. | |
| 958. |
In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.I. 3x2 – 11x + 6 = 0II. 2y2 – 7y + 6 = 0 |
| A. | x > y |
| B. | x < y |
| C. | x ≥ y |
| D. | x ≤ y |
| E. | x = y or no relationship could be established |
| Answer» F. | |
| 959. |
If a + b + c + d + e + \(\frac{1}{a+b+c+d+e}=2\) find the value of (a + b + c + d + e)5 + \(\frac{1}{(a+b+c+d+e)^5}\) |
| A. | 1 |
| B. | 1/2 |
| C. | 2 |
| D. | 0 |
| Answer» D. 0 | |
| 960. |
If a + 2b = 10 and 2ab = 9, then |a - 2b| is equal to: |
| A. | 4 |
| B. | 8 |
| C. | 2 |
| D. | 6 |
| Answer» C. 2 | |
| 961. |
If \(x^4+\dfrac{1}{x^4}=14\), then value of \(x^3+\dfrac{1}{x^3}\) isA. \(3\sqrt{6}\)B. \(\dfrac{18}{\sqrt{6}}\)C. \(9\sqrt{\dfrac{2}{3}}\)D. \(3\sqrt{2}\) |
| A. | D |
| B. | B |
| C. | A |
| D. | C |
| Answer» D. C | |
| 962. |
If a3 + b3 = 432 and a + b = 12, then (a + b)2 – 3ab is equal to∶ |
| A. | 42 |
| B. | 52 |
| C. | 36 |
| D. | 38 |
| Answer» D. 38 | |
| 963. |
In the following question, two equations are given in variables x and y. You have to solve these equations and determine the relation between x and y.I) x2 – 16x + 63 = 0II) y2 – 44y + 84 = 0 |
| A. | if x < y |
| B. | if x ≤ y |
| C. | if x > y |
| D. | if x ≥ y |
| E. | if x = y or the relationship can not be established |
| Answer» F. | |
| 964. |
Find the values of x for the given equation 3x2 + 5x – 2 = 0 |
| A. | –3 and –2 |
| B. | 2 and –3 |
| C. | 3 and \(- \dfrac{1}{2}\) |
| D. | –2 and \(\dfrac{1}{3}\) |
| Answer» E. | |
| 965. |
For what values of m the equations 2x + 3y = 2 and (m + 2)x + (2m + 1)y = 2(m - 1) have infinitely many solutions: |
| A. | 4 |
| B. | 2 |
| C. | 5 |
| D. | 3 |
| Answer» B. 2 | |
| 966. |
If doubling a number and adding 16 to the result gives the same number as multiplying the number by 6 and taking away 4 from the product, then find the number. |
| A. | 4 |
| B. | 5 |
| C. | 6 |
| D. | 7 |
| Answer» C. 6 | |
| 967. |
In class VIII of an upper primary school at the beginning of the year, for every 2 boys, there were 3 girls. From the same class 5 girls left the school and 3 boys joined the class. As a result, boys and girls became equal in number. What was the total strength of the same class at the beginning of the year? |
| A. | 36 |
| B. | 40 |
| C. | 45 |
| D. | 52 |
| Answer» C. 45 | |
| 968. |
If 2x + 3y - 5z = 18, 3x + 2y + z = 29 and x + y + 3z = 17, then what is the value of xy + yz + zx? |
| A. | 32 |
| B. | 52 |
| C. | 64 |
| D. | 46 |
| Answer» C. 64 | |
| 969. |
If the roots of the equation a(b - c)x2 + b(c - a)x + c(a - b) = 0 are equal, then which of the following is true? |
| A. | b = (a + c)/ac |
| B. | 2/b = (1/a) + (1/c) |
| C. | 2b = (1/a) + (1/c) |
| D. | abc = ab + bc + ca |
| Answer» C. 2b = (1/a) + (1/c) | |
| 970. |
If 2x2 + y2 +8z2– 2√2xy + 4√2yz – 8zx = (Ax + y + Bz)2, then the value of (A2 + B2– AB)is: |
| A. | 18 |
| B. | 16 |
| C. | 6 |
| D. | 14 |
| Answer» E. | |
| 971. |
If ax + by = 1 and bx + ay \(= \frac{{2ab}}{{{a^2}\; + \;{b^2}}}\) then (x2 + y2)(a2 + b2) is equal to |
| A. | 1 |
| B. | 2 |
| C. | 0.5 |
| D. | 0 |
| Answer» B. 2 | |
| 972. |
If \(\sqrt {86 - 60\sqrt 2 } \; = \;a - b\sqrt 2 ,\) then what will be the value of √(a2 + b2), correct to one decimal place? |
| A. | 7.2 |
| B. | 8.2 |
| C. | 8.4 |
| D. | 7.8 |
| Answer» E. | |
| 973. |
In the following question, two equations numbered I and II are given. You have to solve both the equations and give answer:I. 2x2 – 14x + 24 = 0II. y2 + 30y + 224 = 0 |
| A. | x > y |
| B. | x ≥ y |
| C. | x < y |
| D. | x ≤ y |
| E. | x = y or the relation cannot be determined |
| Answer» B. x ≥ y | |
| 974. |
Let F4, F8 and F16 be finite fields of 4, 8 and 16 elements respectively then |
| A. | F4 is isomorphic to a subfield of F16 |
| B. | F4 is isomorphic to a subfield of F8 |
| C. | F8 is isomorphic to a subfield of F16 |
| D. | F16 is isomorphic to a subfield of F16 |
| Answer» B. F4 is isomorphic to a subfield of F8 | |
| 975. |
Find the value of ‘m’ if 2xm + x3 – 3x2 – 26 leaves a remainder of 994 when it is divided by x - 2 |
| A. | 8 |
| B. | 11 |
| C. | 10 |
| D. | 9 |
| Answer» E. | |
| 976. |
If \({a^2} + \frac{1}{{{a^2}}} = 38\), then find the value of \(\left( {a - \frac{1}{a}} \right)\) |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» D. 8 | |
| 977. |
If non - zero a, b, c are such that a + b + c = 0, then the value of \(\frac{a^2}{bc} + \frac{b^2}{ac} + \frac{c^2}{ab}\) is |
| A. | 3 |
| B. | 2 |
| C. | -3 |
| D. | 0 |
| Answer» B. 2 | |
| 978. |
If the system of equations 2x - 3y - 3 and -4x + qy - \(\dfrac{p}{2}\) is inconsistent which of the following cannot be the value of p ? |
| A. | -18 |
| B. | -24 |
| C. | -12 |
| D. | -36 |
| Answer» D. -36 | |
| 979. |
If x = 16 then what is the value of \(\sqrt x + \frac{1}{{\sqrt x }}?\) |
| A. | 4 |
| B. | 4.5 |
| C. | 4.25 |
| D. | 2√8 |
| Answer» D. 2√8 | |
| 980. |
Find the unit place digit in the expression \({\left( {159} \right)^{144}} + {\left( {114} \right)^{123}} - {\left( {110} \right)^{510}} + {\left( {213} \right)^{25}}\) |
| A. | 3 |
| B. | 4 |
| C. | 7 |
| D. | 8 |
| Answer» E. | |
| 981. |
If p = 101, then the value of \(\sqrt[3]{p(p^2 - 3p + 3)-1}\) is |
| A. | 100 |
| B. | 101 |
| C. | 1001 |
| D. | 1000 |
| Answer» B. 101 | |
| 982. |
How many perfect squares having digit 6 in the unit’s place are there between 1 and 600? |
| A. | 3 |
| B. | 6 |
| C. | 4 |
| D. | 5 |
| Answer» E. | |
| 983. |
If a + b + c = 11, ab + bc + ca = 3 and abc = -135, then what is the value of a3 + b3 + c3? |
| A. | 929 |
| B. | 925 |
| C. | 827 |
| D. | 823 |
| Answer» D. 823 | |
| 984. |
If x = (√5 + 1)/(√5 - 1) and y = (√5 - 1)/(√5 + 1), then find the value of x2 - y2. |
| A. | √5 |
| B. | 2√5 |
| C. | 3√5 |
| D. | 4√5 |
| Answer» D. 4√5 | |
| 985. |
Ram buys 4 chairs and 9 stools for Rs. 1340. If he sells chairs at 10% profit and stools at 20% profit, he earns a profit of Rs. 188. How much money did he have to pay for the chairs? |
| A. | Rs. 200 |
| B. | Rs. 400 |
| C. | Rs. 800 |
| D. | Rs. 1600 |
| Answer» D. Rs. 1600 | |
| 986. |
A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is |
| A. | 24 |
| B. | 81 |
| C. | 18 |
| D. | 32 |
| Answer» B. 81 | |
| 987. |
In a triangle ABC, if taken in order, consider the following statements;1) \(\overrightarrow {AB} + \overrightarrow {BC} + \overrightarrow {CA} = \vec 0\)2) \(\overrightarrow {AB} + \overrightarrow {BC} - \overrightarrow {CA} = \vec 0\)3) \(\overrightarrow {AB} - \overrightarrow {BC} + \overrightarrow {CA} = \vec 0\)4) \(\overrightarrow {BA} - \overrightarrow {BC} + \overrightarrow {CA} = \vec 0\)How many of the above statements are correct? |
| A. | One |
| B. | Two |
| C. | Three |
| D. | Four |
| Answer» B. Two | |
| 988. |
Let y = x / 6 and 4x + 12y = 48. What is the value of x and y? |
| A. | x = 3 and \(y = \frac{2}{3}\) |
| B. | x = 3 and \(y = \frac{4}{3}\) |
| C. | x = 9 and y = 3 |
| D. | x = 8 and \(y = 1\frac{2}{3}\) |
| Answer» E. | |
| 989. |
Determine the value of \({\left( {{\rm{y}} - \frac{1}{{\rm{y}}}} \right)^2}\) when \({\rm{\;}}{{\rm{y}}^4}{\rm{}} + {\rm{}}\frac{1}{{{{\rm{y}}^4}}}{\rm{}} = {\rm{}}34\) |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» E. | |
| 990. |
Let \(\vec a = 3\hat i + 2\hat j + x\hat k{\rm{\;and\;}}\vec b = \hat i - \hat j + \hat k\), for some real x. Then \(\left| {\vec a \times \vec b} \right| = r\) is possible if: |
| A. | \(\sqrt {\frac{3}{2}} < r \le 3\sqrt {\frac{3}{2}}\) |
| B. | \(r \ge 5\sqrt {\frac{3}{2}}\) |
| C. | \(0 < r \le \sqrt {\frac{3}{2}}\) |
| D. | \(3\sqrt {\frac{3}{2}} < r < 5\sqrt {\frac{3}{2}}\) |
| Answer» C. \(0 < r \le \sqrt {\frac{3}{2}}\) | |
| 991. |
If \(p + \frac{1}{p}=112\), find \((p - 112)^{15}+\frac{1}{p^{15}}\) |
| A. | 1 |
| B. | 15 |
| C. | 10 |
| D. | 0 |
| Answer» E. | |
| 992. |
A real square matrix A is called skew-symmetric if |
| A. | AT = A |
| B. | AT = A-1 |
| C. | AT = -A |
| D. | AT = A + A-1 |
| Answer» D. AT = A + A-1 | |
| 993. |
If \({x^4} - 3{x^2} - 1 = 0\), then the value of \(\left( {{x^6} - 3{x^2} + \frac{3}{{{x^2}}} - \frac{1}{{{x^6}}} + 1} \right)\) is: |
| A. | 54 |
| B. | 51 |
| C. | 28 |
| D. | 26 |
| Answer» D. 26 | |
| 994. |
If (a + b + c) = 6 and a2 + b2 + c2 = 14, then (ab + bc + ca) = ? |
| A. | 22 |
| B. | 11 |
| C. | 33 |
| D. | 44 |
| Answer» C. 33 | |
| 995. |
A necessary condition for a series \(\sum {u_n}\) to converge is that |
| A. | un → 0, as n → ∞ |
| B. | un → 2, as n → ∞ |
| C. | un → ∞, as n → ∞ |
| D. | un → 1, as n → ∞ |
| Answer» B. un → 2, as n → ∞ | |
| 996. |
If \({x^4} + \frac{1}{{{x^4}}} = 98\) and x > 1, then what is the value of \(x - \frac{1}{x}?\) |
| A. | 2 |
| B. | 2√2 |
| C. | √5 |
| D. | √3 |
| Answer» C. √5 | |
| 997. |
If 24.2 kg of ghee cost Rs. 12525.92, how much would 8.5 kg of the same ghee cost? |
| A. | Rs. 5239.50 |
| B. | Rs. 4675.20 |
| C. | Rs. 4399.60 |
| D. | Rs. 4980.30 |
| Answer» D. Rs. 4980.30 | |
| 998. |
If a + b + c = 27, then what is the value of (a – 7)3 + (b – 9)3 + (c – 11)3 – 3(a – 7)(b – 9)(c – 11)? |
| A. | 0 |
| B. | 9 |
| C. | 27 |
| D. | 81 |
| Answer» B. 9 | |
| 999. |
Determine the value of \(\left( {\frac{1}{r} + \frac{1}{s}} \right)\) when r3 + s3 = 0 and r + s = 6. |
| A. | 0 |
| B. | 0.5 |
| C. | 1 |
| D. | 6 |
| Answer» C. 1 | |
| 1000. |
If (a + b - 1)2 + (b + c - 9)2 + (c + a - 4)2 ≤ 0, then the value \(\sqrt {{{\left( {a + b} \right)}^{c\;}} + {{\left( {c + a} \right)}^b} - 1} \) is∶ |
| A. | 9 |
| B. | 6 |
| C. | 7 |
| D. | 8 |
| Answer» E. | |