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| # | Question | Subject and topic | Difficulty |
|---|---|---|---|
| 4361 | The general solution of dy/dx = y is | Mathematics/Applied Mathematics Solving differential equations |
Medium |
| 4362 | Which of these differential equations is homogeneous? | Mathematics/Applied Mathematics Solving differential equations |
Medium |
| 4363 | For x > 0, the general solution of dy/dx + y/x = x² is | Mathematics/Applied Mathematics Solving differential equations |
Hard |
| 4364 | The magnitude of the vector 3i + 4j is | Mathematics/Applied Mathematics Vectors: basic concepts |
Easy |
| 4365 | The unit vector in the direction of i + j + k is | Mathematics/Applied Mathematics Vectors: basic concepts |
Easy |
| 4366 | The direction cosines of the vector 2i − j + 2k are | Mathematics/Applied Mathematics Vectors: basic concepts |
Medium |
| 4367 | If l, m and n are the direction cosines of a line, then l² + m² + n² equals | Mathematics/Applied Mathematics Vectors: basic concepts |
Medium |
| 4368 | 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 |
| 4369 | If a = 2i + 3j and b = i − j, then a + b equals | Mathematics/Applied Mathematics Vector algebra |
Easy |
| 4370 | Compared with a non-zero vector a, the vector −2a has | Mathematics/Applied Mathematics Vector algebra |
Easy |
| 4371 | 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 |
| 4372 | For which value of λ are the vectors 2i + 3j − k and λi + 6j − 2k parallel? | Mathematics/Applied Mathematics Vector algebra |
Medium |
| 4373 | 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 |
| 4374 | The value of (i + 2j + 3k) · (2i − j + k) is | Mathematics/Applied Mathematics Scalar and vector products |
Easy |
| 4375 | The cross product i × j equals | Mathematics/Applied Mathematics Scalar and vector products |
Easy |
| 4376 | For which value of λ is 2i + λj + k perpendicular to i − 2j + 3k? | Mathematics/Applied Mathematics Scalar and vector products |
Medium |
| 4377 | If |a| = 2, |b| = 3 and a · b = 3, the angle between a and b is | Mathematics/Applied Mathematics Scalar and vector products |
Medium |
| 4378 | The area of the parallelogram whose adjacent sides are a = i + j and b = j + k is | Mathematics/Applied Mathematics Scalar and vector products |
Hard |
| 4379 | The vector equation of the line through the point with position vector a and parallel to the vector b is | Mathematics/Applied Mathematics Lines in space |
Easy |
| 4380 | The direction ratios of the line (x − 1)/2 = (y + 3)/(−1) = (z − 4)/3 are | Mathematics/Applied Mathematics Lines in space |
Easy |