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# Engineering

## Machine Learning, Blockchain, Robotics, IoT and more

# Set 2

#### Let P (x) = x^2 + bx + c, where b and c are integer. If P (x) is a factor of both x^4 + 6x^2 + 25 and 3x^4 + 4x^2 + 28x + 5, find the value of P(1).

#### If b > a , then the equation, (x - a) (x - b) - 1 = 0, has :

#### If roots of the equation x^2 -10cx -11d =0 are a, b and those of x^2 – 10ax – 11b = 0 are c, d, then find the value of a + b + c + d. (a, b, c and d are distinct numbers)

#### STATEMENT – 1 A balloon ascends from the surface of earth with constant speed. When it was at a height 50 m above the ground, a packet is dropped from it. To an observer on the balloon, the displacement of the packet, from the moment it is dropped to the moment it reaches the surface of earth, is 50 m. STATEMENT – 2 Displacement (vector) depends upon the reference frame used to measure it.

#### STATEMENT – 1 : If air resistance is considered then time of ascent and time of descent will be different. STATEMENT – 2 : Magnitudes of acceleration will be different in upwards and downward motion.

#### In 1.0 sec. a particle goes from point A to point B moving in a semicircle of radius 1.0 m. The magnitude of average velocity is :

#### Calculate the molarity of pure water using its density to be 1000 kg m^(-3)

#### 20% surface sites have adsorbed N2 . On heating N2 gas evolved from sites and were collected at 0.001 atm and 298 K in a container of volume is 2.46 cm3 . Density of surface sites is 6.023×10^14/cm2 and surface area is 1000 cm2 , find out the no. of surface sites occupied per molecule of N2 .

#### To 500 ml of 2M impure H2SO4 sample, NaOH soluton 1 M was slowly added & the following plot was obtained. The percentage purity of H2SO4 sample and slope of the curve respectively are:

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