MCQOPTIONS
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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.
| 601. |
If 16x2 + 9y2 + 4z2 = 24(x – y + z) – 61, then the value of (xy + 2z) is: |
| A. | 5 |
| B. | 1 |
| C. | 3 |
| D. | 2 |
| Answer» B. 1 | |
| 602. |
If (a + b) = 6 and ab = 16/3, then (a3 + b3) is equal to: |
| A. | 190 |
| B. | 220 |
| C. | 120 |
| D. | 150 |
| Answer» D. 150 | |
| 603. |
In a right angled triangle ABC, if the hypotenuse AC = p, then what is \(\overrightarrow {{\rm{AB}}} \cdot \overrightarrow {{\rm{AC}}} + \overrightarrow {{\rm{BC}}} \cdot \overrightarrow {{\rm{BA}}} + \overrightarrow {{\rm{CA}}} \cdot \overrightarrow {{\rm{CB}}} \) equal to? |
| A. | p |
| B. | p2 |
| C. | 2p2 |
| D. | \(\frac{{{{\rm{p}}^2}}}{2}\) |
| Answer» C. 2p2 | |
| 604. |
If \(x+\frac{1}{x}=4,\) then \({{x}^{3}}+\frac{1}{{{x}^{3}}}\) is equal to: |
| A. | 50 |
| B. | 52 |
| C. | 64 |
| D. | 40 |
| Answer» C. 64 | |
| 605. |
In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.I. x2 + 9x + 20 = 0II. 8y2 – 15y + 7 = 0 |
| A. | x > y |
| B. | x < y |
| C. | x ≥ y |
| D. | x ≤ y |
| E. | x = y or the relationship between x and y cannot be established. |
| Answer» C. x ≥ y | |
| 606. |
If 2x2 + 2x + 9 = 0, then (2x + 1)2 is equal to______. |
| A. | 18 |
| B. | 17 |
| C. | -17 |
| D. | 2 |
| Answer» D. 2 | |
| 607. |
If 1 + 9r2 + 81r4 = 256 and 1 + 3r + 9r2 = 32, then find the value of 1 - 3r + 9r2. |
| A. | 4 |
| B. | 12 |
| C. | 16 |
| D. | 8 |
| Answer» E. | |
| 608. |
In a company 2/3 of the workers are girls, 1/2 of the girls are married and 1/3 of the married girls live in hostel. If 3/4 of the boys are married and 2/3 of married boys live in hostel. Calculate the part of workers who don’t live in hostel. |
| A. | 11/18 |
| B. | 15/18 |
| C. | 17/18 |
| D. | 13/18 |
| Answer» E. | |
| 609. |
If \(\vec a, \vec b, \vec c\) are vectors such that \(\vec a + \vec b + \vec c = 0\) and \(|\vec a| = 10, |\vec b| = 4, |\vec c| = 6\), then the angle between the vectors \(\vec b\) and \(\vec c\) is? |
| A. | 0° |
| B. | 30° |
| C. | 45° |
| D. | 90° |
| Answer» B. 30° | |
| 610. |
If x = 1.1, then what is the value of \(\sqrt {4{{\rm{x}}^2} - 4{\rm{x}} + 1}\)? |
| A. | 1.21 |
| B. | 1.331 |
| C. | 2.21 |
| D. | 1.2 |
| Answer» E. | |
| 611. |
If √[(1 – p2) × (1 – q2)] = √3/2 and q = 0, then what is the value of √[2p2 + 2q2 + 2pq] + √[2p2 + 2q2 – 2pq]. |
| A. | 2 |
| B. | √2 |
| C. | 1 |
| D. | None of these |
| Answer» C. 1 | |
| 612. |
If x2 +y2 + z2 - 8x + 6y - 4z + 29 = 0, then find the value of z (x + y). |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 613. |
If a = 4 and b = 3, then the value of ab + ba = ? |
| A. | 127 |
| B. | 137 |
| C. | 145 |
| D. | 136 |
| Answer» D. 136 | |
| 614. |
If \(x + y + z = 3\) and \(xy + yz + zx=-11\), then what is the value of \({x^3} + {y^3} + {z^3} - 3xyz\)? |
| A. | 126 |
| B. | 145 |
| C. | 121 |
| D. | 154 |
| Answer» B. 145 | |
| 615. |
If \(a + \frac{1}{a} = - \sqrt {3,} \) find the value of \({a^3} + \frac{1}{{{a^3}}}\) |
| A. | 0 |
| B. | -6√3 |
| C. | -3√3 |
| D. | 6√3 |
| Answer» B. -6√3 | |
| 616. |
Form the quadratic equation whose roots are 3 and 4 |
| A. | x2 + 3x + 4 = 0 |
| B. | x2 - 3x + 4 = 0 |
| C. | 2x2 - 7x - 12 = 0 |
| D. | x2 - 7x + 12 = 0 |
| Answer» E. | |
| 617. |
Consider the 5 × 5 matrix\(A = \left[ {\begin{array}{*{20}{c}} 1&2&3&4&5\\ 5&1&2&3&4\\ 4&5&1&2&3\\ 3&4&5&1&2\\ 2&3&4&5&1 \end{array}} \right]\).It is given that A has only one real eigenvalue. Then the real eigenvalue of A is |
| A. | -2.5 |
| B. | 0 |
| C. | 15 |
| D. | 25 |
| Answer» D. 25 | |
| 618. |
If x2 + y2 + 6x + 5 = 4(x – y) then x – y is: |
| A. | 1 |
| B. | -1 |
| C. | 0 |
| D. | 4 |
| Answer» B. -1 | |
| 619. |
In the following question, two equations numbered I and II are given. You have to solve both the equations and give the answer:I. 4x2 – 3x - 1 = 0II. 2y2 - 7y - 9 = 0 |
| A. | x > y |
| B. | x ≥ y |
| C. | x < y |
| D. | x ≤ y |
| E. | x = y or the relation cannot be determined |
| Answer» F. | |
| 620. |
If x + 2y = 27 and x – 2y = -1, find the value of y? |
| A. | 13 |
| B. | 14 |
| C. | 7 |
| D. | 26 |
| Answer» D. 26 | |
| 621. |
If a - b = 5 and a2 + b2 = 31 then find the value of ab?A. 4B. 5C. 2D. 3 |
| A. | C |
| B. | A |
| C. | B |
| D. | D |
| Answer» E. | |
| 622. |
If \(\frac{{1\; + \;px}}{{1\; -\; px}}\sqrt {\frac{{1\; - \; qx}}{{1\; + \;qx}}} = 1,\;\)then what are the non-zero solutions of x? |
| A. | \(\pm \frac{1}{p}\sqrt {\frac{{2p - q}}{q}} ,\;2p \ne q\) |
| B. | \(\pm \frac{1}{{pq}}\sqrt {p - q} ,\;p \ne q\) |
| C. | \(\pm \frac{p}{p}\sqrt {p - q} ,\;p \ne q\) |
| D. | \(\pm \frac{q}{p}\sqrt {2p - q} ,\;2p \ne q\) |
| Answer» B. \(\pm \frac{1}{{pq}}\sqrt {p - q} ,\;p \ne q\) | |
| 623. |
If \(\frac{x}{y} + \frac{y}{x} = 1\) then the value of \(x^3 + y^3\) will be |
| A. | 0 |
| B. | 1 |
| C. | x |
| D. | y |
| Answer» B. 1 | |
| 624. |
If a – 1/a = 7 then a2 + 1/a2 = ? |
| A. | 54 |
| B. | 51 |
| C. | 53 |
| D. | 52 |
| Answer» C. 53 | |
| 625. |
If 20 x2 – 30x + 1 = 0, then what is the value of \({25x^2}\; + \;\frac{1}{{16{x^2}}}?\) |
| A. | \(58\frac{3}{4}\) |
| B. | \(58\frac{1}{2}\) |
| C. | \(53\frac{3}{4}\) |
| D. | \(53\frac{1}{2}\) |
| Answer» D. \(53\frac{1}{2}\) | |
| 626. |
A man travels 434 km, partly by rail and partly by steamer, He spends 8 hours more time on steamer, If the velocity of the steamer is 25 km/hr and the velocity of rail is 65 km/hr, how much distance does he cover by steamer? |
| A. | 318 km |
| B. | 398 km |
| C. | 265 km |
| D. | 477 km |
| Answer» D. 477 km | |
| 627. |
If x2 - 2√5x + 1 = 0, then which of the following is the value of \(x^3 + \frac{1}{x^3}\)? |
| A. | 34 |
| B. | 144√5 |
| C. | 46 |
| D. | 34√5 |
| Answer» E. | |
| 628. |
If \(\frac{{\sqrt {5 + x} + \sqrt {5 - x} }}{{\sqrt {5 + x} - \sqrt {5 - x} }} = 3\), then what is the value of x? |
| A. | 5/2 |
| B. | 25/3 |
| C. | 4 |
| D. | 3 |
| Answer» E. | |
| 629. |
If x8 - 1442x4 +1 = 0, then a possible value of x - 1/x is∶ |
| A. | 4 |
| B. | 6 |
| C. | 5 |
| D. | 8 |
| Answer» C. 5 | |
| 630. |
If a + b + c = 8 and ab + bc + ca = 20, then a3 + b3 + c3 – 3abc is equal to∶ |
| A. | 36 |
| B. | 32 |
| C. | 24 |
| D. | 30 |
| Answer» C. 24 | |
| 631. |
If x/2 – [4(15/2 – x/3)]/3 = -x/18, then what is the value of x? |
| A. | -10 |
| B. | 9/8 |
| C. | 10 |
| D. | -9/8 |
| Answer» D. -9/8 | |
| 632. |
For what value of k is (x + 1) is a factor of x3 + kx2 – x + 2? |
| A. | 4 |
| B. | 3 |
| C. | 1 |
| D. | -2 |
| Answer» E. | |
| 633. |
A man buys 2 apples and 3 kiwi fruits for Rs. 37. If he buys 4 apples and 5 kiwi fruits for Rs. 67, then what will be the total cost of 1 apple and 1 kiwi fruit? |
| A. | Rs. 15 |
| B. | Rs. 28 |
| C. | Rs. 18 |
| D. | Rs. 20 |
| Answer» B. Rs. 28 | |
| 634. |
If \(\frac{3x - 8}{2x}\)=1, then x = _______. |
| A. | 6 |
| B. | 8 |
| C. | 4 |
| D. | -8 |
| Answer» C. 4 | |
| 635. |
If \(x + \frac{1}{x} = 8,\) then \(x^2 + \frac{1}{x^2} = \) |
| A. | 14 |
| B. | 58 |
| C. | 12 |
| D. | 62 |
| Answer» E. | |
| 636. |
If x and y are natural numbers such that x + y = 2017, then what is the value of (-1)x + (-1)y? |
| A. | 2 |
| B. | -2 |
| C. | 0 |
| D. | 1 |
| Answer» D. 1 | |
| 637. |
If \(\dfrac{5x-7}{3}+2=\dfrac{4x-3}{4}+4x\), then the value of (8x + 5) is |
| A. | 9 |
| B. | 13 |
| C. | 6 |
| D. | 7 |
| Answer» D. 7 | |
| 638. |
If x2 – 6x + 1 = 0, then the value of [{x4 + (1/x2)} ÷ (x2 + 1)] is: |
| A. | 35 |
| B. | 39 |
| C. | 33 |
| D. | 36 |
| Answer» D. 36 | |
| 639. |
If \(\sqrt x + \frac{1}{{\sqrt x }} = \sqrt 6 ,\)then \({x^2} + \frac{1}{{{x^2}}}\) is equal to: |
| A. | 16 |
| B. | 18 |
| C. | 12 |
| D. | 14 |
| Answer» E. | |
| 640. |
In the following question, two equations are given. You have to solve both the equations and find the relation between ‘x’ and ‘y’ and mark the correct answer.A. x2 – 10x + 25 = 0B. y2 = 25 |
| 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» C. if x < y | |
| 641. |
If xy = - 18 and x2 + y2 = 85, then find the value of (x + y). |
| A. | 8 |
| B. | 10 |
| C. | 9 |
| D. | 7 |
| Answer» E. | |
| 642. |
If x + y = 15 and xy = 14, then the value of x – y is : |
| A. | 12 |
| B. | 14 |
| C. | 13 |
| D. | 11 |
| Answer» D. 11 | |
| 643. |
If \(p + \left( {\frac{1}{p}} \right) = 2\) find the value of p × p × p |
| A. | 1 |
| B. | 2 |
| C. | 4 |
| D. | 8 |
| Answer» B. 2 | |
| 644. |
If the roots of the equation lx2 + mx + m = 0 are in the ratio p ∶ q, then \(\sqrt {\frac{p}{q}} + \sqrt {\frac{q}{p}} {\rm{\;}} + \sqrt {\frac{m}{l}} \) is equal to |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» B. 1 | |
| 645. |
If a3 - b3 = 56 and a - b = 2, then what is the value of ab? |
| A. | 8 |
| B. | 12 |
| C. | 6 |
| D. | 9 |
| Answer» B. 12 | |
| 646. |
Consider the system of equations: x + y = 2 and 2x + 2y = 5. This system has |
| A. | One solution |
| B. | No solution |
| C. | Infinite solution |
| D. | Four solutions |
| Answer» C. Infinite solution | |
| 647. |
Find sin θ if theta is the angle between the vectors \(\;\vec a = 3\hat j + 4\hat k\;and\;\vec b = 6\hat i + 8\hat k\) |
| A. | 1/2 |
| B. | 1/12 |
| C. | \(\frac {3\sqrt{41}}{25}\) |
| D. | \(\frac {3\sqrt{31}}{25}\) |
| Answer» D. \(\frac {3\sqrt{31}}{25}\) | |
| 648. |
If a + b + c = 5, and a2 + b2 + c2 = 33, then find the value of a3 + b3 + c3 - 3abc |
| A. | 192 |
| B. | 185 |
| C. | 180 |
| D. | 195 |
| Answer» C. 180 | |
| 649. |
If x + y = 4, then what is the value of \(\frac{2}{{x - 2}} + \frac{2}{{y - 2}}?\) (x, y ≥ 0) |
| A. | -1 |
| B. | 0 |
| C. | 4 |
| D. | 16 |
| Answer» C. 4 | |
| 650. |
Directions: In this question two equations numbered I and II are given. You have to solve both the equations and find out the correct option.I. x2 – 17x + 72 = 0II. y2 – 17y + 70 = 0 |
| A. | x > y |
| B. | x < y |
| C. | x ≥ y |
| D. | x ≤ y |
| E. | x = y or no relationship could be established |
| Answer» F. | |