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301 questions found · practise this subject as a set
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| # | Question | Subject and topic | Difficulty |
|---|---|---|---|
| 101 | The family y = Aeˣ + Be⁻ˣ, with A and B arbitrary constants, is the general solution of | Mathematics/Applied Mathematics Differential equations: basics |
Hard |
| 102 | The solution of dy/dx = 2x with y(0) = 1 is | Mathematics/Applied Mathematics Solving differential equations |
Easy |
| 103 | The integrating factor of dy/dx + 2y = eˣ is | Mathematics/Applied Mathematics Solving differential equations |
Easy |
| 104 | The general solution of dy/dx = y is | Mathematics/Applied Mathematics Solving differential equations |
Medium |
| 105 | Which of these differential equations is homogeneous? | Mathematics/Applied Mathematics Solving differential equations |
Medium |
| 106 | For x > 0, the general solution of dy/dx + y/x = x² is | Mathematics/Applied Mathematics Solving differential equations |
Hard |
| 107 | The magnitude of the vector 3i + 4j is | Mathematics/Applied Mathematics Vectors: basic concepts |
Easy |
| 108 | The unit vector in the direction of i + j + k is | Mathematics/Applied Mathematics Vectors: basic concepts |
Easy |
| 109 | The direction cosines of the vector 2i − j + 2k are | Mathematics/Applied Mathematics Vectors: basic concepts |
Medium |
| 110 | If l, m and n are the direction cosines of a line, then l² + m² + n² equals | Mathematics/Applied Mathematics Vectors: basic concepts |
Medium |
| 111 | A vector makes an angle of 45° with the x-axis and 60° with the y-axis. What acute angle does it make with th… | Mathematics/Applied Mathematics Vectors: basic concepts |
Hard |
| 112 | If a = 2i + 3j and b = i − j, then a + b equals | Mathematics/Applied Mathematics Vector algebra |
Easy |
| 113 | Compared with a non-zero vector a, the vector −2a has | Mathematics/Applied Mathematics Vector algebra |
Easy |
| 114 | P and Q have position vectors i + 2j and 4i + 8j. The point dividing PQ internally in the ratio 2 : 1 has pos… | Mathematics/Applied Mathematics Vector algebra |
Medium |
| 115 | For which value of λ are the vectors 2i + 3j − k and λi + 6j − 2k parallel? | Mathematics/Applied Mathematics Vector algebra |
Medium |
| 116 | P and Q have position vectors i + j and 3i + 5j. The point dividing PQ externally in the ratio 2 : 1 has posi… | Mathematics/Applied Mathematics Vector algebra |
Hard |
| 117 | The value of (i + 2j + 3k) · (2i − j + k) is | Mathematics/Applied Mathematics Scalar and vector products |
Easy |
| 118 | The cross product i × j equals | Mathematics/Applied Mathematics Scalar and vector products |
Easy |
| 119 | For which value of λ is 2i + λj + k perpendicular to i − 2j + 3k? | Mathematics/Applied Mathematics Scalar and vector products |
Medium |
| 120 | If |a| = 2, |b| = 3 and a · b = 3, the angle between a and b is | Mathematics/Applied Mathematics Scalar and vector products |
Medium |