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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.
| 901. |
If 1 is added to the denominator of a rational number, it becomes 1/2 where as, 1 is added to the numerator of the rational number, it becomes 1. What is the Rational Number?\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\) |
| A. | 4/7 |
| B. | 5/9 |
| C. | 2/3 |
| D. | 10/11 |
| Answer» D. 10/11 | |
| 902. |
Consider the following system of linear equations:3x + 2ky = -2Kx + 6y = 2Here x and y are the unknowns and k is a real constant. The value of k for which there are infinite number of solutions is |
| A. | 3 |
| B. | 1 |
| C. | -3 |
| D. | -6 |
| Answer» D. -6 | |
| 903. |
Let f :R→ R be defined by f(x) = x2 - 3x + 2. Then the value of f(f(5)) is |
| A. | 90 |
| B. | 100 |
| C. | 110 |
| D. | 80 |
| Answer» D. 80 | |
| 904. |
Let P = 12xy – 10y2 – 18x2, Q = 14x2 + 12y2 + 9xy, and R = 5y2 – x2 + xy then (P + Q) – R = |
| A. | 20xy – 7x2 – 3y2 |
| B. | 20xy – 3x2 – 3y2 |
| C. | 22xy – 3x2 + 3y2 |
| D. | 22xy + 3x2 + 3y2 |
| Answer» C. 22xy – 3x2 + 3y2 | |
| 905. |
If \(\vec{a} = 4\hat{j}\) and \(\vec{b} = 3\hat{j} + 4\hat{k}\), then the vector form of the component of \(\vec{a}\) along \(\vec{b}\) is |
| A. | \(\dfrac{12}{10\sqrt{3}}(3\hat{j}+4\hat{k})\) |
| B. | \(\dfrac{12}{5}(3\hat{j}+4\hat{k})\) |
| C. | \(\dfrac{12}{\sqrt{13}}(3\hat{j}+4\hat{k})\) |
| D. | \((3\hat{j}+4\hat{k})\) |
| Answer» C. \(\dfrac{12}{\sqrt{13}}(3\hat{j}+4\hat{k})\) | |
| 906. |
In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.I. 2x2 – 17x + 36 = 0II. 2y2 – 13y + 21 = 0 |
| A. | x > y |
| B. | x < y |
| C. | x ≥ y |
| D. | x ≤ y |
| E. | x = y or no relationship could be established |
| Answer» B. x < y | |
| 907. |
If \(a^{x+5}\times a^{2x-1} \div a^x = 1\), then x _____. |
| A. | 3 |
| B. | 2 |
| C. | -3 |
| D. | -2 |
| Answer» E. | |
| 908. |
If x = α and x = β satisfy the equations cos2 x + a cos x + b = 0, sin2 x + p sin x + q = 0 both, then the relation among a, b, p and q will be: |
| A. | a2 + b2 = p2 + q2 |
| B. | a + p = b + q |
| C. | 2(b + q) = a2 + p2 - 2 |
| D. | b + q = a2 + p2 - q2 |
| Answer» D. b + q = a2 + p2 - q2 | |
| 909. |
If x + 1/x = √5, then x3 + 1/x3 is equal to∶ |
| A. | 5√5 |
| B. | 2√5 |
| C. | 4√5 |
| D. | 3√5 |
| Answer» C. 4√5 | |
| 910. |
If xy = 16 and x2 + y2 = 32, then the value of (x + y) is: |
| A. | ±10 |
| B. | ±4 |
| C. | ±8 |
| D. | ±6 |
| Answer» D. ±6 | |
| 911. |
If 3x2 – 9x + 3 = 0, then what is the value of (x + 1/x)3? |
| A. | 9 |
| B. | 729 |
| C. | 81 |
| D. | 27 |
| Answer» E. | |
| 912. |
Factors of x2 – 6x + 8 are:A) (x – 4) (x – 2)B) (x + 4) (x + 2)C) (x + 8) (x – 2)D) (x – 4) (x + 2) |
| A. | A |
| B. | D |
| C. | C |
| D. | B |
| Answer» B. D | |
| 913. |
A worker may claim Rs. 1.5 for each km which he travels by taxi and 50 paise for each km he drives his own car. In one week he claimed Rs. 50 for travelling 80 km. how many km did he travel by taxi? |
| A. | 20 km |
| B. | 14 km |
| C. | 12 km |
| D. | 10 km |
| Answer» E. | |
| 914. |
For what value of μ do the simultaneous equations 5x + 7y = 2, 15x + 21y = μ have no solution? |
| A. | μ = 0 |
| B. | μ ≠ 6 |
| C. | μ ≠ 0 |
| D. | μ = 6 |
| Answer» C. μ ≠ 0 | |
| 915. |
In the following questions, two equations numbered I and II are given. You have to solve both the equations.I) 2x2 + 15x + 13 = 0II) y2 - 7y + 12 = 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» D. If x ≤ y | |
| 916. |
If (a + b + 4)(ab + 4(a + b)) - 4ab = 0, and a ≠ -4, b ≠ -4, then, 1/(a + b + 4)117 - 2-234 is equal to: |
| A. | 0 |
| B. | 14117 |
| C. | -12234 |
| D. | 12117 |
| Answer» B. 14117 | |
| 917. |
If \(a = \dfrac{1}{3 - 2 \sqrt 2}\), \(b= \dfrac{1}{3 + 2 \sqrt 2}\)then the value of a2 + b2 is: |
| A. | 36 |
| B. | 37 |
| C. | 34 |
| D. | 35 |
| Answer» D. 35 | |
| 918. |
If 92x – 1 – 81x-1 = 1944, then x is? |
| A. | 3 |
| B. | 9/4 |
| C. | 4/9 |
| D. | 1/3 |
| Answer» C. 4/9 | |
| 919. |
If (a + b) = 6 and ab = 8, then (a3 + b3) is equal to: |
| A. | 216 |
| B. | 144 |
| C. | 108 |
| D. | 72 |
| Answer» E. | |
| 920. |
If x3 + y3 = 35 and xy = 6, x > y, then value of (x - y) will be |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | None of the above |
| Answer» B. 2 | |
| 921. |
If p/x + q/y = m and q/x + p/y = n, then what is x/y equal to? |
| A. | (np + mq) / (mp + nq) |
| B. | (np + mq) / (mp - nq) |
| C. | (np - mq) / (mp - nq) |
| D. | (np - mq) / (mp + nq) |
| Answer» D. (np - mq) / (mp + nq) | |
| 922. |
If \(\dfrac{y}{x} = 2 - \dfrac{x}{y}\), then the value of \(\dfrac{x^3 + xy^2}{x^3 + y^3}\) is equal to |
| A. | 0 |
| B. | \(\dfrac{2}{3}\) |
| C. | \(\dfrac{3}{4}\) |
| D. | 1 |
| Answer» E. | |
| 923. |
A (- 3, 4), B (5, 4), C and D form a rectangle. If x – 4y + 7 = 0 is a diameter of circum-circle of the rectangle ABCD then the area of rectangle ABCD is |
| A. | 8 |
| B. | 16 |
| C. | 32 |
| D. | 64 |
| Answer» D. 64 | |
| 924. |
If the value of \(\frac{{3x\sqrt y + 2y\sqrt x }}{{3x\sqrt y - 2y\sqrt x }} - \frac{{3x\sqrt y - 2y\sqrt x }}{{3x\sqrt y + 2y\sqrt x }}\) is same as that of \(\sqrt x\sqrt y\), then which of the following relations between x and y is correct? |
| A. | 9x - 4y = 24 |
| B. | 9x + 4y = 24 |
| C. | 9x + 4y = 36 |
| D. | 9x - 4y = 36 |
| Answer» B. 9x + 4y = 24 | |
| 925. |
\(\frac{{5.75 \times 5.75 \times 5.75 + 3.25 \times 3.25 \times 3.25}}{{57.5 \times 57.5 + 32.5 \times 32.5 - 57.5 \times 32.5}} = ?\) |
| A. | 0.0009 |
| B. | 0.9 |
| C. | 0.009 |
| D. | 0.09 |
| Answer» E. | |
| 926. |
Find the unit place digit in (82)102 + (183)103. |
| A. | 1 |
| B. | 6 |
| C. | 8 |
| D. | 9 |
| Answer» B. 6 | |
| 927. |
If (9 - 3x) - (17x - 10) = - 1, then the value of x is |
| A. | 1 |
| B. | -1 |
| C. | 9/10 |
| D. | -9/10 |
| Answer» B. -1 | |
| 928. |
If A is a square matrix then orthogonality property mandates |
| A. | AAT = A-1 |
| B. | AAT = 0 |
| C. | AAT = A2 |
| D. | AAT = I |
| Answer» E. | |
| 929. |
A force \({\rm{\vec F}} = {\rm{\hat i}} + 3{\rm{\hat j}} + 2{\rm{\hat k}}\) acts on a particle to displace it from the point \({\rm{A}}\left( {{\rm{\hat i}} + 2{\rm{\hat j}} - 3{\rm{\hat k}}} \right)\) to the point \({\rm{B}}\left( {3{\rm{\hat i}} - {\rm{\hat j}} + 5{\rm{\hat k}}} \right)\).The work done by the force will be |
| A. | 5 units |
| B. | 7 units |
| C. | 9 units |
| D. | 10 units |
| Answer» D. 10 units | |
| 930. |
If [√(a2 + b2 + ab)] + [√(a2 + b2 - ab)] = 1, then what is the value of (1 - a2)(1 - b2)? |
| A. | 1/4 |
| B. | 4/7 |
| C. | 5/4 |
| D. | 3/4 |
| Answer» E. | |
| 931. |
If x2 – 4x + 1 = 0, then what is the value of x9 + x7 – 194x5 – 194x3? |
| A. | 4 |
| B. | -4 |
| C. | 1 |
| D. | -1 |
| Answer» C. 1 | |
| 932. |
Find the value of x.\(\frac{11}{4} =\frac{77}{x}\) |
| A. | 44 |
| B. | 77 |
| C. | 28 |
| D. | 308 |
| Answer» D. 308 | |
| 933. |
A whole number is added to 50 and the same number is subtracted from 50. The sum of the resulting numbers is |
| A. | 50 |
| B. | 0 |
| C. | 100 |
| D. | 25 |
| Answer» D. 25 | |
| 934. |
If x – 1/x = 8, then x3 – 1/x3 = ? |
| A. | 678 |
| B. | 536 |
| C. | 696 |
| D. | 512 |
| Answer» C. 696 | |
| 935. |
Given:-x + y = 0-x - 2y + 3z = 02x + y - 3z = 0then: |
| A. | x = z, y = 0 |
| B. | y = z, x = 0 |
| C. | x = y, 0 = z |
| D. | x = y = z |
| Answer» E. | |
| 936. |
If \(9 \frac{1}{4} = y - 1 \frac{1}{3}\), then the value of y is: |
| A. | \(\frac{41}{12}\) |
| B. | \(\frac{95}{12}\) |
| C. | \(\frac{41}{7}\) |
| D. | \(\frac{127}{12}\) |
| Answer» E. | |
| 937. |
Consider two subsets of R3 given as S1 = {[7, 7, 7]} and S2 = {[ 0, 0, 0]}. Which of the following statements is true? |
| A. | Both S2 and S2 are linearly independent |
| B. | S1 is linearly independent but S2 is linearly dependent |
| C. | S1 is linearly dependent but S2 is linearly independent |
| D. | Both S1 and S2 are linearly dependent |
| Answer» C. S1 is linearly dependent but S2 is linearly independent | |
| 938. |
\(\frac{(225)^{0.2}\times(225)^{0.3}}{(225)^{0.8}\times(225)^{0.2}}=?\) |
| A. | 15 |
| B. | 1.5 |
| C. | \(\frac{1}{15}\) |
| D. | \(\frac{1}{25}\) |
| Answer» D. \(\frac{1}{25}\) | |
| 939. |
If \(x + \frac{1}{x}\; = \;6,x \ne 0,\) then the value of \(\frac{{{x^2} + \;3x\; + \;1}}{{{x^4}\; + \;{x^{ - 2}}}}\) is: |
| A. | \(\frac{1}{{12}}\) |
| B. | \(\frac{1}{{14}}\) |
| C. | \(\frac{1}{{24}}\) |
| D. | \(\frac{1}{{22}}\) |
| Answer» E. | |
| 940. |
If 3x - y = 27 and 3x + y = 243, then x is equal to |
| A. | 4 |
| B. | 6 |
| C. | 2 |
| D. | 0 |
| Answer» B. 6 | |
| 941. |
If A and B are the roots of the equation ax2 + bx + c = 0, then which equation will have roots (AB + A + B) and (AB – A – B)? |
| A. | a2x2 + 2acx + c2 + b2 = 0 |
| B. | a2x2 – 2acx + c2 – b2 = 0 |
| C. | a2x2 – 2acx + c2 + b2 = 0 |
| D. | a2x2 + 2acx + c2 – b2 = 0 |
| Answer» C. a2x2 – 2acx + c2 + b2 = 0 | |
| 942. |
If a + b + c = 0. Then \(\frac{{{a^2}}}{{bc}} + \frac{{{b^2}}}{{ca}} + \frac{{{c^2}}}{{ab}}= ?\) |
| A. | 2 |
| B. | 3 |
| C. | 0 |
| D. | 1 |
| Answer» C. 0 | |
| 943. |
If x = 255, y = 256, z = 257, then find the value of x3 + y3 + z3 - 3xyz |
| A. | 1378 |
| B. | 2304 |
| C. | 1876 |
| D. | 1984 |
| E. | 2105 |
| Answer» C. 1876 | |
| 944. |
If, \({\rm{a}} = \frac{{\sqrt 3 + \sqrt 2 }}{{\sqrt 3 - \sqrt 2 }}\:{\rm{and\;b}} = \frac{{\sqrt 3 - \sqrt 2 }}{{\sqrt 3 + \sqrt 2 }}\), then what is the value of a2 + b2 - ab? |
| A. | 97 |
| B. | (2√3) + 2 |
| C. | (4√6) + 1 |
| D. | 98 |
| Answer» B. (2√3) + 2 | |
| 945. |
Consider two functions y1 (x) = x and y2 (x) = |x|. Then: |
| A. | both functions are linearly dependent on the real line. |
| B. | y1(x) is linearly independent but y2(x) is linearly dependent on the real line. |
| C. | y1(x) is linearly dependent but y2(x) is linearly dependent on the real line. |
| D. | both functions are linearly independent on the real line. |
| Answer» B. y1(x) is linearly independent but y2(x) is linearly dependent on the real line. | |
| 946. |
If a number is as much more than 51 as it is lesser than 97, then what is that number? |
| A. | 21 |
| B. | 76 |
| C. | 441 |
| D. | 74 |
| Answer» E. | |
| 947. |
In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts in all 60 question and secure 130 marks, the number of question he attempts correctly, is- |
| A. | 35 |
| B. | 38 |
| C. | 39 |
| D. | 40 |
| Answer» C. 39 | |
| 948. |
Number of real roots of the quadratic equation 3x2 + 4x + 25 = 0 is |
| A. | one |
| B. | two |
| C. | nil |
| D. | infinite |
| Answer» D. infinite | |
| 949. |
If x + y + z = 19, xyz = 216 and xy + yz + zx = 114, then the value of x3 + y3 + z3 + xyz is: |
| A. | 1225 |
| B. | 1441 |
| C. | 577 |
| D. | 361 |
| Answer» B. 1441 | |
| 950. |
If \(\sqrt x - \frac{1}{{\sqrt x }} = 2\sqrt 2,\) then \({x^2} + \frac{1}{{{x^2}}}\) is equal to∶ |
| A. | 100 |
| B. | 102 |
| C. | 98 |
| D. | 104 |
| Answer» D. 104 | |