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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.
| 801. |
In the given question, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answerI. a2 + 36a + 324 = 0II. b2 - 35b + 96 = 0 |
| A. | a < b |
| B. | a > b |
| C. | a ≤ b |
| D. | a ≥ b |
| E. | a = b or the relationship cannot be determined |
| Answer» B. a > b | |
| 802. |
If b/y + z/c = 1 and c/z + x/a = 1, then what is (ab + xy)/bx equal to? |
| A. | 1 |
| B. | 2 |
| C. | 0 |
| D. | -1 |
| Answer» B. 2 | |
| 803. |
If \({{\rm{x}}^2} - {\rm{x}}\sqrt {68} + 1 = 0\), then what is the value of \({\rm{x}} - \frac{1}{{\rm{x}}}\)? |
| A. | √66 |
| B. | 8 |
| C. | √62 |
| D. | 6 |
| Answer» C. √62 | |
| 804. |
If P = 99, then the value of P(P2 + 3P + 3) is: |
| A. | 9999 |
| B. | 999999 |
| C. | 99999 |
| D. | 9999999 |
| Answer» C. 99999 | |
| 805. |
If 12x = 192 - 112, what is the value of x? |
| A. | 20 |
| B. | 17 |
| C. | 13 |
| D. | 11 |
| Answer» B. 17 | |
| 806. |
A barrel has 4 L and 500 ML of acid. In how many containers, each of capacity 25 ML, can be filled? |
| A. | 175 |
| B. | 180 |
| C. | 200 |
| D. | 185 |
| Answer» C. 200 | |
| 807. |
If (x/y) + (y/x) = 1, then what is the value of x3 + y3? |
| A. | –1 |
| B. | 0 |
| C. | 1 |
| D. | 3 |
| Answer» C. 1 | |
| 808. |
If α and β are two real numbers such that \(\alpha + \beta = - \frac{q}{p}\) and \(\alpha \beta = \frac{r}{p},\) where 1 < p < q < r, then which one of the following is the greatest? |
| A. | \(\frac{1}{{\alpha + \beta }}\) |
| B. | \(\frac{1}{\alpha } + \frac{1}{\beta }\) |
| C. | \(- \frac{1}{{\alpha \beta }}\) |
| D. | \(\frac{{\alpha \beta }}{{\alpha + \beta }}\) |
| Answer» D. \(\frac{{\alpha \beta }}{{\alpha + \beta }}\) | |
| 809. |
For matrices of the same dimension M, N, and scalar c, which one of these properties DOES NOT ALWAYS hold? |
| A. | (MT)T = M |
| B. | (cM)T = c(M)T |
| C. | (M + N)T = MT + NT |
| D. | MN = NM |
| Answer» E. | |
| 810. |
If the polynomial 2x4 + kn3 - 75k is divided by x the remainder is 150, then the value of k will be: |
| A. | 2 |
| B. | -1 |
| C. | -2 |
| D. | 1 |
| Answer» D. 1 | |
| 811. |
If -3 is a zero of polynomialp (x) = 2x2 + 3x - 3a then value of a is |
| A. | 2 |
| B. | -1 |
| C. | 0 |
| D. | 3 |
| Answer» E. | |
| 812. |
If a + 1/a = 1, find the value of a3 + 1/a3. |
| A. | 2 |
| B. | -2 |
| C. | 0 |
| D. | 1.5 |
| Answer» C. 0 | |
| 813. |
If (3x - 7)3 + (3x - 8) 3 + (3x + 6)3 = 3 (3x - 7) (3x - 8) (3x + 6), then what is the value of x? |
| A. | 1 |
| B. | 4 |
| C. | 3 |
| D. | 2 |
| Answer» B. 4 | |
| 814. |
If x4 + x-4 = 1442, (x > 0) then the value of x + x-1 is: |
| A. | \(3\sqrt {10} \) |
| B. | \(2\sqrt {10} \) |
| C. | \(4\sqrt {10} \) |
| D. | 15 |
| Answer» C. \(4\sqrt {10} \) | |
| 815. |
Eigen values of a real symmetric matrix are always |
| A. | Positive |
| B. | Negative |
| C. | Real |
| D. | Complex |
| Answer» D. Complex | |
| 816. |
If 2(a2 + b2) = (a + b)2 then, |
| A. | a = b |
| B. | b = 2a |
| C. | a = 2b |
| D. | a = -b |
| Answer» B. b = 2a | |
| 817. |
Let V be a 3-dimensional vector space with A and B its subspaces of dimension 2 and 1 respectively.If A ∩ B = {0} then |
| A. | V = A - B |
| B. | V = A + B |
| C. | V = AB |
| D. | V = A/B |
| Answer» C. V = AB | |
| 818. |
If one of the zeroes of the polynomial 3x2 + 8x + k is the reciprocal of the other, then what is the value of k? |
| A. | 3 |
| B. | -3 |
| C. | \(-\frac{1}{3}\) |
| D. | \(\frac{1}{3}\) |
| Answer» B. -3 | |
| 819. |
For what value of k do the equations 3(k - 1)x + 4y = 24 and 15x + 20y = 8(k + 13) have infinite solutions? |
| A. | 3 |
| B. | 4 |
| C. | 2 |
| D. | 1 |
| Answer» D. 1 | |
| 820. |
If \(\vec{a}\) and \(\vec{b}\) are vectors such that \(|\vec{a}|=13, |\vec{b}|=5\) and \(\vec{a}\cdot \vec{b}=60\) then the value of \(|\vec{a}\times \vec{b}|\) is |
| A. | 625 |
| B. | 225 |
| C. | 45 |
| D. | 25 |
| Answer» E. | |
| 821. |
If ab(a + b) = 1, then what is the value of \(\frac{1}{{{a^3}{b^3}}} - {a^3} - {b^3}?\) |
| A. | -1 |
| B. | 1 |
| C. | 3 |
| D. | -3 |
| Answer» D. -3 | |
| 822. |
If \(a + \frac{1}{a} + 2 = 0\) , then the value of \({a^{15}} - \frac{1}{{{a^{100}}}}\) is: |
| A. | - 2 |
| B. | 2 |
| C. | 1 |
| D. | 0 |
| Answer» B. 2 | |
| 823. |
If x - y = 4 and xy = 45, then the value of x3 - y3 is: |
| A. | 82 |
| B. | 604 |
| C. | 822 |
| D. | 151 |
| Answer» C. 822 | |
| 824. |
if a + b + c = 0, then the value of \(\rm \dfrac{a^2}{bc} + \dfrac{b^2}{ca} + \dfrac{c^2}{ab}\) is: |
| A. | 1 |
| B. | 0 |
| C. | 3 |
| D. | -1 |
| Answer» D. -1 | |
| 825. |
Factories x2 - y2 - 9z2 + 6yz |
| A. | (x + y - 3z) (x + y + 3z) |
| B. | (x - y - 3z) (x - y + 2z) |
| C. | (x + y - 3z) (x - y + 3z) |
| D. | None of these |
| Answer» D. None of these | |
| 826. |
Find the value of x2 - y21. If x + y = 22. If x - y = 6 |
| A. | Only 1 is sufficient |
| B. | Neither 1 nor 2 is sufficient |
| C. | Only 2 is sufficient |
| D. | Both 1 and 2 together are sufficient |
| Answer» E. | |
| 827. |
Let \(y = \frac{1}{{10}}x\) and x + 50y = 120. What is the value of x and y? |
| A. | x = 2 and y = 20 |
| B. | x = 20 and y = 2 |
| C. | x = 10 and y = 2 |
| D. | x = 60 and y = 6 |
| Answer» C. x = 10 and y = 2 | |
| 828. |
If (G, ⋅) is a group such that (ab)-1 = a-1 b-1, ∀ a, b ∈ G, then G is a/an |
| A. | Commutative semi group |
| B. | Abelian group |
| C. | Non-abelian group |
| D. | None of these |
| Answer» C. Non-abelian group | |
| 829. |
If 3x - 4y + 5 = 0 and 6x - 8y + k = 0 represent the same line then the value of k is |
| A. | 5 |
| B. | 15 |
| C. | 10 |
| D. | none of these |
| Answer» D. none of these | |
| 830. |
One of the roots of the equation x2 – 6x + k = 0 is x = 2. The other root is: |
| A. | x = 4 |
| B. | x = -1 |
| C. | x = -4 |
| D. | x = 1 |
| Answer» B. x = -1 | |
| 831. |
If a - b = 5 and ab = 14, then find a2 + b2. |
| A. | 53 |
| B. | 27 |
| C. | 5 |
| D. | 19 |
| Answer» B. 27 | |
| 832. |
If \({x^2} + \frac{1}{{{x^2}}} = 6\), then find the value of \(\frac{{2x\left( {x - 1} \right)}}{{{x^3} - {x^2} - x + 1}}\) |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» C. 2 | |
| 833. |
One of the roots of the equation x2 – 4x + 2k = 0 is x = 1. The other root is: |
| A. | x = -3 |
| B. | x = -2 |
| C. | x = 3 |
| D. | x = 1 |
| Answer» D. x = 1 | |
| 834. |
If x4 + x2y2 + y4 = 133 and x2 - xy + y2 =7, then what is the value of xy? |
| A. | 8 |
| B. | 12 |
| C. | 4 |
| D. | 6 |
| Answer» E. | |
| 835. |
For the given orthogonal matrix Q,\(Q = \left[ {\begin{array}{*{20}{c}} {\frac{3}{7}}&{\frac{2}{7}}&{\frac{6}{7}}\\ { - \frac{6}{7}}&{\frac{3}{7}}&{\frac{2}{7}}\\ {\frac{2}{7}}&{\frac{6}{7}}&{ - \frac{3}{7}} \end{array}} \right]\)The inverse is __________ |
| A. | \(\left[ {\begin{array}{*{20}{c}} {\frac{3}{7}}&{\frac{2}{7}}&{\frac{6}{7}}\\ { - \frac{6}{7}}&{\frac{3}{7}}&{\frac{2}{7}}\\ {\frac{2}{7}}&{\frac{6}{7}}&{ - \frac{3}{7}\;} \end{array}} \right]\) |
| B. | \(\left[ {\begin{array}{*{20}{c}} { - \frac{3}{7}}&{ - \frac{2}{7}}&{ - \frac{6}{7}}\\ {\frac{6}{7}}&{ - \frac{3}{7}}&{ - \frac{2}{7}}\\ { - \frac{2}{7}}&{ - \frac{6}{7}}&{\frac{3}{7}} \end{array}} \right]\) |
| C. | \(\left[ {\begin{array}{*{20}{c}} {\frac{3}{7}}&{ - \frac{6}{7}}&{\frac{2}{7}}\\ {\frac{2}{7}}&{\frac{3}{7}}&{\frac{6}{7}}\\ {\frac{6}{7}}&{\frac{2}{7}}&{ - \frac{3}{7}} \end{array}} \right]\) |
| D. | \(\left[ {\begin{array}{*{20}{c}} { - \frac{3}{7}}&{\frac{6}{7}}&{ - \frac{2}{7}}\\ { - \frac{2}{7}}&{ - \frac{3}{7}}&{ - \frac{6}{7}}\\ { - \frac{6}{7}}&{ - \frac{2}{7}}&{\frac{3}{7}} \end{array}} \right]\) |
| Answer» D. \(\left[ {\begin{array}{*{20}{c}} { - \frac{3}{7}}&{\frac{6}{7}}&{ - \frac{2}{7}}\\ { - \frac{2}{7}}&{ - \frac{3}{7}}&{ - \frac{6}{7}}\\ { - \frac{6}{7}}&{ - \frac{2}{7}}&{\frac{3}{7}} \end{array}} \right]\) | |
| 836. |
If \(a + b = \frac 7 3\) and \(a^2 + b^2 = \frac {31} 9,\) find 27 (a3 + b3). |
| A. | 154 |
| B. | 156 |
| C. | 152 |
| D. | 164 |
| Answer» B. 156 | |
| 837. |
Match List I with List IIList IList IINumbersSquare roots A. 41209 I. 9 B. 841 II. 29 C. 81 III. 232 D. 53824 IV. 203 Choose the correct answer from the options given below: |
| A. | A - IV, B - III, C - I, D - II |
| B. | A - II, B - IV, C - I, D - III |
| C. | A - II, B - III, C - I, D - IV |
| D. | A - IV, B - II, C - I, D - III |
| Answer» E. | |
| 838. |
If (a – 1/a) = 3/4, find the value of (a3 – 1/a3). |
| A. | 164/31 |
| B. | 171/64 |
| C. | 171/32 |
| D. | 164/37 |
| Answer» C. 171/32 | |
| 839. |
4x2 + kx + 5 is divisible by x + 1. The same expression is also divisible by: |
| A. | 4x + 5 |
| B. | 4x – 1 |
| C. | 4x – 5 |
| D. | x – 5 |
| Answer» B. 4x – 1 | |
| 840. |
If (x + y)2 = xy + 1 and x3 – y3 = 1, then what is the value of x – y? |
| A. | 1 |
| B. | 0 |
| C. | –1 |
| D. | 2 |
| Answer» B. 0 | |
| 841. |
If \(\overrightarrow{AC}=2\hat{i}+\hat{j}+\hat{k}\) and \(\overrightarrow{BD}=-\hat{i}+3\hat{j}+2\hat{k}\) then the area of the quadrilateral ABCD is |
| A. | \(\dfrac{5}{2}\sqrt{3}\) |
| B. | \(5\sqrt{3}\) |
| C. | \(\dfrac{15}{2}\sqrt{3}\) |
| D. | \(10\sqrt{3}\) |
| Answer» B. \(5\sqrt{3}\) | |
| 842. |
If \({x^2} - \sqrt 3 x + 1 = 0\), then \(\left( {{x^3} + {x^{ - 3}}} \right)\) is equal to: |
| A. | 0 |
| B. | \(4\sqrt {37}\) |
| C. | 1 |
| D. | \(3\sqrt {3}\) |
| Answer» B. \(4\sqrt {37}\) | |
| 843. |
If a + 1/a = 3, then a3 + 1/a3 = ? |
| A. | 6 |
| B. | 9 |
| C. | 18 |
| D. | 12 |
| Answer» D. 12 | |
| 844. |
Given a system of equations\(x\; + \;2y\; + \;2z\; = \;{b_1},\;\;\;\;\;5x\; + \;y\; + \;3z\; = \;{b_2}\)Which of the following is true about solutions? |
| A. | The system has a unique solution for any given \({b_1}\) and \({b_2}\) |
| B. | The system will have infinitely many solutions for any given \({b_1}\) and \({b_2}\) |
| C. | Whether or not a solution exists depends on the given \({b_1}\) and \({b_2}\) |
| D. | The system world have no solution for any value of \({b_1}\) and \({b_2}\) |
| Answer» C. Whether or not a solution exists depends on the given \({b_1}\) and \({b_2}\) | |
| 845. |
If a + b = 2c, then what is the value of a/(a - c) + c/(b - c)? |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 846. |
If \(\left( {a - \frac{1}{a}} \right) = 6\), then \(\left( {{a^4} + \frac{1}{{{a^4}}}} \right) = ?\) |
| A. | 1444 |
| B. | 34 |
| C. | 38 |
| D. | 1442 |
| Answer» E. | |
| 847. |
If x + y + z = 22 and xy + yz + zx = 35, then what is the value of (x – y)2 + (y – z)2 + (z – x)2? |
| A. | 793 |
| B. | 681 |
| C. | 758 |
| D. | 715 |
| Answer» D. 715 | |
| 848. |
If x/y = 4/9, then what is the value of (7x2 – 19xy + 11y2)/y2? |
| A. | 59/81 |
| B. | 100/27 |
| C. | 319/81 |
| D. | 913/81 |
| Answer» D. 913/81 | |
| 849. |
Consider the following equations for two vectors \(\vec{a}\) and \(\vec{b}\)1. \(\left( \vec{a}+\vec{b} \right)\cdot \left( \vec{a}-\vec{b} \right)={{\left| {\vec{a}} \right|}^{2}}-{{\left| {\vec{b}} \right|}^{2}}\)2. \(\left( \left| \vec{a}+\vec{b} \right| \right)\left( \left| \vec{a}-\vec{b} \right| \right)={{\left| {\vec{a}} \right|}^{2}}-{{\left| {\vec{b}} \right|}^{2}}\)3. \({{\left| \vec{a}\cdot \vec{b} \right|}^{2}}+{{\left| \vec{a}\times \vec{b} \right|}^{2}}={{\left| {\vec{a}} \right|}^{2}}{{\left| {\vec{b}} \right|}^{2}}\)Which of the above statement are correct? |
| A. | 1, 2 and 3 |
| B. | 1 and 2 only |
| C. | 1 and 3 only |
| D. | 2 and 3 only |
| Answer» D. 2 and 3 only | |
| 850. |
If 5x / 6 - (4 / 3)(2 - 3x / 2) = 1 / 3, then what is the value of x? |
| A. | 17 / 18 |
| B. | - 18 / 17 |
| C. | 18 / 17 |
| D. | - 17 / 18 |
| Answer» D. - 17 / 18 | |