महाराष्ट्र अभियंता सेवा पूर्व परीक्षा २०१७

The iron loss in a 10 KVA transformer is 1 kW and the full load copper losses are 2 kW. The maximum efficiency occurs at a load of

The power in a three-phase circuit is measured by the two-wattmeter method. The reading indicated on the two wattmeters are W₁ and W₂. The total power in the circuit is not given by

The equation for 25 cycles per second current sine wave having RMS value of 30 Ampere, will be

How is the form factor for sinusoidal alternating quantities with Im as the peak value expressed?

The area enclosed between the straight line y = x and the parabola y = x² in the x-y plane is

The quadratic approximation of f(x) = x³ - 3x² – 5 at the point x = 0 is

A cubic polynomial with real coefficients 

As x varies from -1 to 3, which one of the following describes the behaviour of the function f(x) = x³ – 3x² + 1 ?

If z = e^{ax + by} f (ax – by), then b equals to

Let A be an n xn matrix with rank r (0 < r < n). Then AX = 0 has p independent solutions, where p is 

How is the crest factor of alternating quantities expressed ?

The value of passing through the straight line joining (0, 0, 0) and (2, 1, 3) is

Expansion of (1 + x)^1/x up to the term containing x² is given as

The minimum value of 

Find for what value of k, the set of equations  equations
2x – 3y + 62 -- 5t = 3 

y - 4z + t = 1

4x - 5y + 8z - 9t = k 

has an infinite number of solutions for equal to

If x = e^u tan v, y = e^u sec v, then the value of 

Cauchy's homogeneous linear differential form is given as 

sin (log x), then the particular integral will be

For (D² +4D+3)Y= 3e^2x,the particular integral is 

 dx is equal to

The volume of the region enclosed by the cone z = and paraboloid