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Questions and Answers
Which of the following series converge?
Which of the following series converge?
- $\frac {\pi^n}{ln(n^{10})}$
- $\frac{100^n}{(n+1)!}$ (correct)
- $\frac{(2n+1)!}{(n+4)!}$
- $1^{\frac{n}{100}}$ (correct)
The unit vectors orthogonal to the vector -i + 2j + 2k and making equal angles with the X and Y axes are
The unit vectors orthogonal to the vector -i + 2j + 2k and making equal angles with the X and Y axes are
- $\frac{1}{3}(2i+2j-k)$ (correct)
- $\frac{1}{\sqrt{3}}(i+j-k)$
- $\frac{1}{3}(i-2j-2k)$
- $\frac{1}{3}(2i-2j-k)$
If a, b, c are three non-coplanar vectors such that a + b + c = ad and a = b + c + d, then (a + b) . c is equal to?
If a, b, c are three non-coplanar vectors such that a + b + c = ad and a = b + c + d, then (a + b) . c is equal to?
(α + β)č
The valve of $\frac{5\Gamma(\frac{2}{3})}{3\Gamma(\frac{5}{3})}$ is (Γ is gamma function)
The valve of $\frac{5\Gamma(\frac{2}{3})}{3\Gamma(\frac{5}{3})}$ is (Γ is gamma function)
The value of $B(\frac{3}{2}, \frac{2}{2})$ is (B is beta function)
The value of $B(\frac{3}{2}, \frac{2}{2})$ is (B is beta function)
If the plane 2ax - 3ay + 4az + 6 = 0 passes through the mid-point of the joining the centers of the sphere x² + y² + z² + 6x - 8y - 2z = 13 and x² + y² + z² - 10x + 4y - 2z = 9, then 'a' is equal to?
If the plane 2ax - 3ay + 4az + 6 = 0 passes through the mid-point of the joining the centers of the sphere x² + y² + z² + 6x - 8y - 2z = 13 and x² + y² + z² - 10x + 4y - 2z = 9, then 'a' is equal to?
Which of the following functions is not periodic?
Which of the following functions is not periodic?
If f(x) = (x² + y²) i - 2xj + 2yzk, then the value of ∫∫F.nds, where S is surface of the plane 2x + y + 2z = 6 in the first octant, is
If f(x) = (x² + y²) i - 2xj + 2yzk, then the value of ∫∫F.nds, where S is surface of the plane 2x + y + 2z = 6 in the first octant, is
The directional derivative of f(x , y, z) = xyz + yz² at the point (1, 1, 1) in the direction of (i + j + k) is
The directional derivative of f(x , y, z) = xyz + yz² at the point (1, 1, 1) in the direction of (i + j + k) is
The vector F = (2x + yz) i + (4y + zx) j - (6z - xy) k is
The vector F = (2x + yz) i + (4y + zx) j - (6z - xy) k is
A spherical balloon is being inflated so that its volume increases uniformly at the rate of 40 cm³/min. At r = 8 cm, its surface area increases at the rate of
A spherical balloon is being inflated so that its volume increases uniformly at the rate of 40 cm³/min. At r = 8 cm, its surface area increases at the rate of
The value of $d^2y/dx^2$ if x³ - 2x²y² + y³ = 0 when y(1) = 1, is equal to?
The value of $d^2y/dx^2$ if x³ - 2x²y² + y³ = 0 when y(1) = 1, is equal to?
The radius of convergence of the series $\sum_{n=0}^{\infty}\frac{(3x+4)^n}{(n+2)3^n}$ is
The radius of convergence of the series $\sum_{n=0}^{\infty}\frac{(3x+4)^n}{(n+2)3^n}$ is
Which of the following giving the type of body and its acceleration of centre of mass on rolling without slipping down on incline '' is incorrect?
Which of the following giving the type of body and its acceleration of centre of mass on rolling without slipping down on incline '' is incorrect?
A particle of mass m is projected from the ground with a velocity u at an angle above the horizontal. The work done by the gravitational force in time t = $\frac{usin\theta}{g}$ is
A particle of mass m is projected from the ground with a velocity u at an angle above the horizontal. The work done by the gravitational force in time t = $\frac{usin\theta}{g}$ is
How many kg of water must fall per second on the blades of a turbine in order to generate 1 MW of electrical power? (g = 10 m/s²)
How many kg of water must fall per second on the blades of a turbine in order to generate 1 MW of electrical power? (g = 10 m/s²)
In a hydroelectric power station, the height of dam is 10 m. How many kg of water must fall per second on the blades of a turbine in order to generate 1 MW of electrical power? (g = 10 m/s²)
In a hydroelectric power station, the height of dam is 10 m. How many kg of water must fall per second on the blades of a turbine in order to generate 1 MW of electrical power? (g = 10 m/s²)
A particle of mass m is moving in a horizontal circle of radius r, under a centripetal force equal to $\frac{k}{r}$, where k is a constant. The total energy of the particle is
A particle of mass m is moving in a horizontal circle of radius r, under a centripetal force equal to $\frac{k}{r}$, where k is a constant. The total energy of the particle is
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Study Notes
Mathematics
- Series Convergence: Some series converge, while others don't. Specific series I,II, III and IV are given and need to be assessed for convergence
- Unit Vectors: Unit vectors orthogonal to a given vector are calculated, These vectors form equal angles with the x and y-axes.
- Coplanar Vectors: Three non-coplanar vectors satisfy a specific equation; The equation relates the vectors.
- Gamma Function: The value of a specific gamma function expression is asked for.
- Beta function: Another function (Beta function), the value for certain conditions is required.
- Matrix Operations: Problems involving matrix inverses and specific matrix operations.
- Systems of Linear Equations: The value of k is found for a system of linear equations such that a non-trivial solution is possible.
Engineering Mechanics
- Rolling Bodies: Acceleration of a centre of mass for rolling bodies down an inclined plane is discussed.
- Pendulum: Restoring forces are identified in a simple pendulum scenario.
- Oscillating Systems: The time period of small oscillations of a system comprising identical particles connected by a light spring is investigated.
- Force and Acceleration: Newton's laws are applied to two blocks connected by a string on a horizontal frictionless surface.
- Gravitational Force: Problems involving gravitational force in scenarios involving projectile motion are considered.
- Work and Energy: Calculating work done by gravitational force is assessed.
- Circular Motion: Determining net force acting on a particle in circular motion.
- Inclined Plane: Coefficients friction on inclined plane are investigated.
- Forces and Moments: Net torque generated by forces acting on a wheel is calculated.
- Energy and Momentum: Converting kinetic energy from one value to another.
- Rolling Motion: Analyzing the linear acceleration of a solid sphere as it moves under a constant force.
- Uniform Motion: Calculating the velocity and acceleration of a body experiencing a non-uniform motion.
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