Science and Engineering Basics

Basics of Science and Engineering (BE-01)

• Force is a vector quantity.
• If a measurement has an absolute error of 0.02 cm and the measured value is 2.5 cm, the relative error is 0.008.
• Using a Vernier calliper with a least count of 0.01 cm, the precision of the measurement is 0.01 mm.
• For a screw gauge with a pitch of 0.5 mm and 100 divisions on the circular scale, the least count is 0.005 mm.
• Measuring 30 cm with an absolute error of 0.2 cm yields a range of possible values between 29.8 cm and 30.2 cm.
• A measurement of 5.00 m with a precision of 0.01 m has 3 significant figures.
• The force that acts on an object moving in a circular path and is directed outward from the center is called centrifugal force.
• Kinetic energy (KE) equation: KE =(1/2)mv².
• The energy possessed by an object due to motion is kinetic energy.
• Centripetal force is responsible for keeping an object moving in a circular path.
• Applying a force of 10 N to an object for 5 seconds results in an impulse of force of 50 N s.
• Linear momentum is defined as Mass × Velocity.
• For two capacitors in series, C1=3 μF and C2= 2 μF, the equivalent capacitance is 1.2 μF.
• With a resistance of 8 Ω and a current of 2 A, the voltage across the wire is 16 V.
• A charge of 2 μC in an electric field of 500 N/C experiences a force of 0.001 N.
• Two point charges, Q1=+5 μC and Q2=−4 μC, placed 2 meters apart experience a force magnitude of 0.045 N.
• A material's property to oppose electric current flow is called resistance.
• Conductance is the reciprocal of resistance.
• Radiation is an example of heat transfer that needs no medium.
• Convection is heat transfer through bulk fluid movement.
• The Kelvin scale is an absolute temperature scale.
• Specific heat is heat capacity per unit mass.
• Linear thermal expansion is most applicable to solids.
• Aluminium generally has the highest thermal conductivity.
• Wavelength is the distance between two successive points in phase on a wave.
• A wave with a frequency of 50 Hz has a periodic time of 0.02 s.
• The amplitude of a wave relates to loudness for sound waves.
• The SI unit of amplitude is the meter.
• Refraction is the change in wave direction when crossing media boundaries.
• Snell's Law states: n1 sin(θ1) = n2 sin(θ2).
• Burning magnesium ribbon in air produces a dazzling white flame.
• NaOH + H2SO4  Na2SO4 + H2O is a balanced chemical equation.
• Liquefaction of air involves chemical reactions.
• The chemical formula for hydrochloric acid is HCl.
• NaOH is an example of a strong base.
• Acetic acid is an example of a weak acid.
• The reaction of acid with metal produces Hydrogen gas.
• Prolonged reaction of iron with steam yields Fe3O4 oxide of iron.
• Ionic compounds have high melting and boiling points.
• Copper, Tin, Lead and Mercury arranged by reactivity is: Tin > Lead > Copper > Mercury.

Computer Basics

• CPU stands for Computer Processing Unit.
• Bit is the smallest unit of information.
• HTML stands for Hyper Text Markup Language.
• Microsoft Word is an MS Office Suite software program.

Microsoft Excel

• The default extension for a Microsoft Excel file is .xlsx.

Ecosystems

• A wetland is an aquatic ecosystem.
• Checking soil erosion is an indirect use of forests.

Gardens

• Gardens are artificial ecosystems.

Energy

• Coal is a non-renewable energy resource.

Pollution

• Human activities are primary causes of water pollution.

Mathematics & Soft Skill (BE-02)

• If -2 1 4 = 86 then x = 2 4 0 6

• If the order of matrix A is 4  3, the order of matrix B is 3  5 and order of matrix ABC is 4  2 then the order of matrix C is 5  2

• For a square matrix A if A = adjA then A = 1 −1

• If A = 4 6 and B =  1 −3  then ( A + B ) = 1  3 −3     −1 2 1  −1 2  12  −1 5 

• Period of sin x + tan  x is 24     3 4

• sin 2 A + sin 8 A = tan 5A cos 2 A + cos8 A

• sec75 = 2 2 3 −1

• Angle between vector a and (1,1,1) is 60. If direction cosines of a are l , m, n then l + m + n = 2 3

• If vectors (m,3,5) and (m, m −1, −3) are perpendicular to each other then m = 0 Equation of line perpendicular to line 3x − 2 y + 7 = 0 and passes through (3, 2) is 2 x + 3 y − 12 = 0

• Radius of circle 2 x + 2 y + 2 x + 4 y − 2 = 0 is 7 2 2

• If f ( x) = tan x then f (45 ) + f (30 ) = 3 −1 3

• 3n + 5n − 7 = 3 lim 2
  n → 5n + 6n − 2 5

• ex + sin x − 1 = 2 lim
  x →0 x

• d (log e (sin x)) = cot x dx

• d ( x log e x) = loge x + 1 dx dy cos sin

• If x = a(1 + sin ), y = a(1 − cos) then = sin dx

• If equation of motion of moving object is s = t − 6t + 9t + 7 then at t = 2,3 the second object changes its direction. 2

• sin x cos xdx = sin x +c 4 4

• xedx = xex − ex + c

• sin x =  sin x + cos x 4

• 2x = loge ( 2) 1+ x

• If log2 ( log3 x ) = 1 then x = _____

• Mean of 3,5,a,4,6 is 5 then a=7

Reading Comprehension Passage

• A celestial figure appeared before Raj because Raj was a kind and hardworking person.
• Goddess Swaraswati appeared before Raj in the guise of an old woman.
• The king challenged Raj to weave a fabric depicting the spirit of Ganges.
• Raj gathered inspiration for his weaving by visiting the river Ganges.
• Disguise is the one-word substitute for 'an act of changing one's appearance' from the passage.

Communication Skills

• Feedback ensures completion of the communication cycle.
• Non-verbal communication means communication without words.
• The sender transmits the message.
• Semantic barrier to communication arises due to problems of language.
• The movement of body, facial expressions, hand movements, gestures, etc. while communicating refer to Kinesics.
• The address of the recipient of the letter is called Inside Address.
• After receiving a letter of complaint, a Letter of Adjustment is drafted in response.
• C.W.O. stands for Cash With Order in business letters or emails.
• Ease of communication is an advantage of email.
• BCC stands for Blind Carbon Copy in email.
• Simple present tense is used in the headlines of newspapers.
• The train had left before we reached the station.
• Rima is a good dancer. The underlined word “good” in the sentence given is an adjective.
• Unless you work hard, you will succeed in the university Examination.
• One of my friends is old.
• The correct spelling is Vacuum.
• The correct spelling is Entrepreneur.
• He reads a book now is the correct sentence.
• I don’t use public transport daily is the correct sentence.
• Do I have a pen? is the correct sentence.