| 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 |
| 121 |
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 |
| 122 |
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 |
| 123 |
The direction ratios of the line (x − 1)/2 = (y + 3)/(−1) = (z − 4)/3 are |
Mathematics/Applied Mathematics
Lines in space |
Easy |
| 124 |
The Cartesian equation of the line through (1, 2, 3) parallel to the vector 3i + 2j − 2k is |
Mathematics/Applied Mathematics
Lines in space |
Medium |
| 125 |
The direction ratios of the line joining (1, 2, 3) and (4, 0, 5) are |
Mathematics/Applied Mathematics
Lines in space |
Medium |
| 126 |
The direction cosines of the line (x − 1)/2 = (3 − y)/1 = (z + 2)/2 are |
Mathematics/Applied Mathematics
Lines in space |
Hard |
| 127 |
The angle between two lines with direction ratios 1, 2, −1 and 1, 0, 1 is |
Mathematics/Applied Mathematics
Angle and shortest distance between lines |
Easy |
| 128 |
Two lines in space are called skew lines when they |
Mathematics/Applied Mathematics
Angle and shortest distance between lines |
Easy |
| 129 |
The angle between two lines with direction ratios 1, 1, 0 and 0, 1, 1 is |
Mathematics/Applied Mathematics
Angle and shortest distance between lines |
Medium |
| 130 |
The distance between the parallel lines r = a₁ + λb and r = a₂ + μb is |
Mathematics/Applied Mathematics
Angle and shortest distance between lines |
Medium |
| 131 |
The shortest distance between the lines r = i + λj and r = 3k + μi is |
Mathematics/Applied Mathematics
Angle and shortest distance between lines |
Hard |
| 132 |
In a linear programming problem, the linear function that has to be maximised or minimised is called the |
Mathematics/Applied Mathematics
Terminology and formulation |
Easy |
| 133 |
In an LPP, the conditions x ≥ 0 and y ≥ 0 are called |
Mathematics/Applied Mathematics
Terminology and formulation |
Easy |
| 134 |
A firm makes x chairs and y tables, earning a profit of ₹30 per chair and ₹50 per table. Its objective is to |
Mathematics/Applied Mathematics
Terminology and formulation |
Medium |
| 135 |
Each chair needs 2 hours and each table needs 3 hours of carpentry, and at most 60 hours are available. If x … |
Mathematics/Applied Mathematics
Terminology and formulation |
Medium |
| 136 |
Food A contains 2 units of vitamin per kg and food B contains 1 unit per kg. A diet must supply at least 8 un… |
Mathematics/Applied Mathematics
Terminology and formulation |
Hard |
| 137 |
In the graphical method, if an LPP with a bounded feasible region has an optimal value, it occurs at |
Mathematics/Applied Mathematics
Graphical method |
Easy |
| 138 |
What are the corner points of the feasible region given by x + y ≤ 4, x ≥ 0, y ≥ 0? |
Mathematics/Applied Mathematics
Graphical method |
Easy |
| 139 |
Subject to x + y ≤ 4, x ≥ 0, y ≥ 0, the maximum value of Z = 3x + 2y is |
Mathematics/Applied Mathematics
Graphical method |
Medium |
| 140 |
A feasible region has corner points (0, 0), (5, 0), (3, 4) and (0, 6). The maximum of Z = 3x + 2y over it is |
Mathematics/Applied Mathematics
Graphical method |
Medium |
| 141 |
Subject to 2x + y ≤ 10, x + 3y ≤ 15, x ≥ 0 and y ≥ 0, the maximum value of Z = 3x + 4y is |
Mathematics/Applied Mathematics
Graphical method |
Hard |
| 142 |
The feasible region of an LPP is the |
Mathematics/Applied Mathematics
Feasible and optimal solutions |
Easy |
| 143 |
If no point satisfies all the constraints of an LPP at the same time, then the problem |
Mathematics/Applied Mathematics
Feasible and optimal solutions |
Easy |
| 144 |
The feasible region of an LPP is unbounded, and M is the largest value of Z = ax + by at its corners. If the … |
Mathematics/Applied Mathematics
Feasible and optimal solutions |
Medium |
| 145 |
The minimum value of Z = 2x + 3y subject to x + y ≥ 4, x ≥ 0 and y ≥ 0 is |
Mathematics/Applied Mathematics
Feasible and optimal solutions |
Medium |
| 146 |
For the LPP "maximise Z = x + 2y subject to x + y ≥ 2, x ≥ 0, y ≥ 0", which statement is correct? |
Mathematics/Applied Mathematics
Feasible and optimal solutions |
Hard |
| 147 |
If P(B) = 0.5 and P(A ∩ B) = 0.2, then P(A|B) equals |
Mathematics/Applied Mathematics
Conditional probability |
Easy |
| 148 |
A fair die is thrown and the number shown is known to be even. What is the probability that it is 6? |
Mathematics/Applied Mathematics
Conditional probability |
Easy |
| 149 |
Two fair coins are tossed. Given that at least one shows a head, what is the probability that both show heads? |
Mathematics/Applied Mathematics
Conditional probability |
Medium |
| 150 |
Two fair dice are thrown and the sum is 8. What is the probability that one of the dice shows 3? |
Mathematics/Applied Mathematics
Conditional probability |
Medium |