| 4351 |
The area under y = x² from x = 0 to x = 3, above the x-axis, is |
Mathematics/Applied Mathematics
Applications of integrals |
Medium |
| 4352 |
The area of the part of the circle x² + y² = 16 lying in the first quadrant is |
Mathematics/Applied Mathematics
Applications of integrals |
Medium |
| 4353 |
The area of the region bounded by the parabola y² = 4x and the line x = 4 is |
Mathematics/Applied Mathematics
Applications of integrals |
Hard |
| 4354 |
The order of the differential equation d³y/dx³ + 2 d²y/dx² + dy/dx = 0 is |
Mathematics/Applied Mathematics
Differential equations: basics |
Easy |
| 4355 |
The degree of (d²y/dx²)² + (dy/dx)³ + y = 0 is |
Mathematics/Applied Mathematics
Differential equations: basics |
Easy |
| 4356 |
The degree of the differential equation d²y/dx² + sin(dy/dx) = 0 is |
Mathematics/Applied Mathematics
Differential equations: basics |
Medium |
| 4357 |
How many arbitrary constants appear in the general solution of a differential equation of order 3? |
Mathematics/Applied Mathematics
Differential equations: basics |
Medium |
| 4358 |
The family y = Aeˣ + Be⁻ˣ, with A and B arbitrary constants, is the general solution of |
Mathematics/Applied Mathematics
Differential equations: basics |
Hard |
| 4359 |
The solution of dy/dx = 2x with y(0) = 1 is |
Mathematics/Applied Mathematics
Solving differential equations |
Easy |
| 4360 |
The integrating factor of dy/dx + 2y = eˣ is |
Mathematics/Applied Mathematics
Solving differential equations |
Easy |
| 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 |
| 4381 |
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 |
| 4382 |
The direction ratios of the line joining (1, 2, 3) and (4, 0, 5) are |
Mathematics/Applied Mathematics
Lines in space |
Medium |
| 4383 |
The direction cosines of the line (x − 1)/2 = (3 − y)/1 = (z + 2)/2 are |
Mathematics/Applied Mathematics
Lines in space |
Hard |
| 4384 |
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 |
| 4385 |
Two lines in space are called skew lines when they |
Mathematics/Applied Mathematics
Angle and shortest distance between lines |
Easy |
| 4386 |
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 |
| 4387 |
The distance between the parallel lines r = a₁ + λb and r = a₂ + μb is |
Mathematics/Applied Mathematics
Angle and shortest distance between lines |
Medium |
| 4388 |
The shortest distance between the lines r = i + λj and r = 3k + μi is |
Mathematics/Applied Mathematics
Angle and shortest distance between lines |
Hard |
| 4389 |
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 |
| 4390 |
In an LPP, the conditions x ≥ 0 and y ≥ 0 are called |
Mathematics/Applied Mathematics
Terminology and formulation |
Easy |
| 4391 |
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 |
| 4392 |
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 |
| 4393 |
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 |
| 4394 |
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 |
| 4395 |
What are the corner points of the feasible region given by x + y ≤ 4, x ≥ 0, y ≥ 0? |
Mathematics/Applied Mathematics
Graphical method |
Easy |
| 4396 |
Subject to x + y ≤ 4, x ≥ 0, y ≥ 0, the maximum value of Z = 3x + 2y is |
Mathematics/Applied Mathematics
Graphical method |
Medium |
| 4397 |
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 |
| 4398 |
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 |
| 4399 |
The feasible region of an LPP is the |
Mathematics/Applied Mathematics
Feasible and optimal solutions |
Easy |
| 4400 |
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 |