Prepare for the DDCET exam with this comprehensive set of practice questions. Click an option to see if you are correct. The "Show Answer" button will reveal the solution without guessing.
Section 1: Basics of Science and Engineering
1. Which of the following is a vector quantity?
A. Temperature
B. Mass
C. Distance
D. Force
Correct Answer: D. Force
Explanation: A vector quantity has both magnitude and direction. Examples include displacement, velocity, acceleration, and force. A scalar quantity has only magnitude, like mass, time, volume, and temperature.
2. If a measurement has an absolute error of 0.02 cm and the measured value is 2.5 cm, what is the relative error?
A. 0.01
B. 0.04
C. 0.008
D. 0.08
Correct Answer: C. 0.008
Explanation: Relative Error is calculated as (Absolute Error) / (Measured Value).
Relative Error = 0.02 / 2.5 = 0.008.
3. If the length of an object is measured using a Vernier caliper with a least count of 0.01 cm, what is the precision of the measurement?
A. 1 mm
B. 0.1 mm
C. 0.01 mm
D. 100 mm
Correct Answer: B. 0.1 mm
Explanation: The precision of a measurement is indicated by the least count of the instrument. The least count is given as 0.01 cm. To convert cm to mm, we multiply by 10. So, 0.01 cm = 0.1 mm.
4. The screw gauge has a pitch of 0.5 mm and 100 divisions on the circular scale. What is the least count of the screw gauge?
A. 0.05 mm
B. 0.005 mm
C. 0.005 cm
D. 0.5 cm
Correct Answer: B. 0.005 mm
Explanation: Least Count (LC) of a screw gauge is calculated as (Pitch) / (Number of divisions on the circular scale).
LC = 0.5 mm / 100 = 0.005 mm.
5. In a measurement, if the measured value is 30 cm and the absolute error is 0.2 cm, what is the range of possible values?
A. 29.8 cm to 30.2 cm
B. 29.5 cm to 30.5 cm
C. 28 cm to 32 cm
D. 28.2 cm to 30.2 cm
Correct Answer: A. 29.8 cm to 30.2 cm
Explanation: The range of possible values is found by adding and subtracting the absolute error from the measured value.
Upper Limit = 30 cm + 0.2 cm = 30.2 cm
Lower Limit = 30 cm - 0.2 cm = 29.8 cm
So, the range is 29.8 cm to 30.2 cm.
6. If a measurement is 5.00 m with a precision of 0.01 m, how many significant figures are in the measurement?
A. 1
B. 2
C. 3
D. 4
Correct Answer: C. 3
Explanation: In a number with a decimal point, all non-zero digits are significant, and trailing zeros (zeros to the right of the last non-zero digit) are also significant. Therefore, in 5.00, the digits 5, 0, and 0 are all significant, giving a total of 3 significant figures.
7. The force that acts on an object moving in a circular path and is directed outward from the centre is called:
A. Centrifugal force
B. Centripetal force
C. Frictional force
D. Tension force
Correct Answer: A. Centrifugal force
Explanation: Centrifugal force is an apparent outward force on an object moving in a circular path. In contrast, centripetal force is the real force that pulls the object toward the center, keeping it in its circular path.
8. The equation for kinetic energy (KE) is:
A. KE = (1/2)mv²
B. KE = mgh/t
C. KE = Fdt
D. KE = P/t
Correct Answer: A. KE = (1/2)mv²
Explanation: Kinetic Energy (KE) is the energy an object possesses due to its motion. The formula is KE = ½ * mass * velocity², where 'm' is mass and 'v' is velocity.
9. The energy an object possesses due to its motion is called:
A. Potential energy
B. Kinetic energy
C. Elastic energy
D. Mechanical energy
Correct Answer: B. Kinetic energy
Explanation: Kinetic energy is defined as the energy that an object possesses due to its motion.
10. ______ is responsible for keeping an object moving in a circular path?
A. Centrifugal force
B. Centripetal force
C. Frictional force
D. Tension force
Correct Answer: B. Centripetal force
Explanation: Centripetal force is the force that acts on an object moving in a circular path, directed toward the center of the circle. This force is what keeps the object from moving in a straight line.
11. If a force of 10 N is applied to an object for 5 seconds, what is the impulse of force?
A. 2 Ns
B. 50 Ns
C. 15 Ns
D. 5 Ns
Correct Answer: B. 50 Ns
Explanation: Impulse is the product of force and the time duration over which it is applied. Impulse = Force × Time = 10 N × 5 s = 50 Ns.
12. The linear momentum of an object is defined as:
A. Mass x Acceleration
B. Mass x Velocity
C. Acceleration x Velocity
D. Mass / Volume
Correct Answer: B. Mass x Velocity
Explanation: Linear momentum is a vector quantity defined as the product of an object's mass and its velocity.
13. Two capacitors, C₁ = 3 µF and C₂ = 2 µF, are connected in series. Calculate the equivalent capacitance.
A. 1.2 µF
B. 5 µF
C. 6 µF
D. 1.5 µF
Correct Answer: A. 1.2 µF
Explanation: For capacitors in series, the reciprocal of the equivalent capacitance is the sum of the reciprocals of individual capacitances. 1/C = 1/C₁ + 1/C₂ = 1/3 + 1/2 = 5/6. Therefore, C = 6/5 = 1.2 µF.
14. A wire has a resistance of 8 Ω. If the current flowing through the wire is 2 A, calculate the voltage across the wire.
A. 4 V
B. 16 V
C. 4 W
D. 16 W
Correct Answer: B. 16 V
Explanation: According to Ohm's Law, Voltage (V) = Current (I) × Resistance (R). V = 2 A × 8 Ω = 16 V.
15. A charge of 2 µC is placed in an electric field of intensity 500 N/C. Calculate the force experienced by the charge.
A. 0.001 N
B. 0.01 N
C. 1000 N
D. 250 N
Correct Answer: A. 0.001 N
Explanation: The force (F) on a charge (q) in an electric field (E) is given by F = qE. First, convert 2 µC to Coulombs: 2 × 10⁻⁶ C. F = (2 × 10⁻⁶ C) × 500 N/C = 1000 × 10⁻⁶ N = 0.001 N.
16. Two point charges, Q₁ = +5 µC and Q₂ = -4 µC, are placed 2 meters apart. Calculate the magnitude of the force between them. (k = 9×10⁹ Nm²/C²)
A. 0.045 N
B. 0.45 N
C. 20 N
D. 10 N
Correct Answer: A. 0.045 N
Explanation: Using Coulomb's Law, F = k * |Q₁Q₂| / d². F = (9×10⁹) * |(5×10⁻⁶)(-4×10⁻⁶)| / (2²). F = (9×10⁹) * (20×10⁻¹²) / 4 = (180×10⁻³) / 4 = 45×10⁻³ N = 0.045 N.
17. The property of a material to oppose the flow of electric current is called:
A. Resistance
B. Conductance
C. Capacitance
D. Susceptance
Correct Answer: A. Resistance
Explanation: Electrical resistance is the measure of the opposition to current flow in an electrical circuit.
18. The reciprocal of resistance is known as:
A. Impedance
B. Conductance
C. Capacitance
D. Susceptance
Correct Answer: B. Conductance
Explanation: Conductance (G) is the ease with which electric current flows through a substance. It is the reciprocal of resistance (G = 1/R).
19. Which mode of heat transfer does not require a medium?
A. Conduction
B. Convection
C. Radiation
D. Both A and B
Correct Answer: C. Radiation
Explanation: Radiation is the transfer of heat through electromagnetic waves, such as infrared radiation. This process does not require a medium and can occur through a vacuum, which is how the sun's heat reaches Earth.
20. The transfer of heat through the bulk movement of a fluid is known as:
A. Conduction
B. Convection
C. Radiation
D. Expansion
Correct Answer: B. Convection
Explanation: Convection is heat transfer by the mass movement of a fluid (such as air or water). When the fluid is heated, it becomes less dense and rises, carrying heat with it.
21. Which temperature scale is an absolute temperature scale?
A. Celsius
B. Fahrenheit
C. Kelvin
D. Rankine
Correct Answer: C. Kelvin
Explanation: The Kelvin scale is an absolute temperature scale where 0 K represents absolute zero, the point at which all thermal motion ceases.
22. Specific heat is the heat capacity per unit _____.
A. Volume
B. Mass
C. Area
D. Temperature
Correct Answer: B. Mass
Explanation: Specific heat capacity is the amount of heat energy required to raise the temperature of one unit of mass of a substance by one degree.
23. Linear thermal expansion is most applicable to:
A. Gases
B. Liquids
C. Solids
D. Plasma
Correct Answer: C. Solids
Explanation: Linear thermal expansion describes the change in length of a solid material due to a change in temperature. Liquids and gases expand in volume (volumetric expansion).
24. Which material would generally have the highest thermal conductivity?
A. Wood
B. Rubber
C. Aluminium
D. Styrofoam
Correct Answer: C. Aluminium
Explanation: Metals like aluminium and copper are excellent thermal conductors, meaning they transfer heat efficiently. Materials like wood, rubber, and styrofoam are thermal insulators.
25. The distance between two successive points in a wave in the same phase is called:
A. Wavelength
B. Frequency
C. Amplitude
D. Periodic time
Correct Answer: A. Wavelength
Explanation: Wavelength (λ) is the spatial period of a periodic wave – the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase, such as two adjacent crests or troughs.
26. If the frequency of a wave is 50 Hz, what is its periodic time?
A. 0.02 s
B. 0.04 s
C. 0.5 s
D. 2 s
Correct Answer: A. 0.02 s
Explanation: Periodic time (T) is the reciprocal of frequency (f). T = 1/f = 1/50 Hz = 0.02 seconds.
27. Which property of a wave is related to its loudness in the case of sound waves?
A. Amplitude
B. Frequency
C. Wavelength
D. Periodic time
Correct Answer: A. Amplitude
Explanation: The amplitude of a sound wave determines its loudness or volume. A larger amplitude means a louder sound.
28. The SI unit of amplitude is:
A. Hertz
B. Second
C. Meter
D. Watt
Correct Answer: C. Meter
Explanation: Amplitude is the maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position. As it is a distance, its SI unit is the meter.
29. The change in direction of a wave when it crosses the boundary between two different media is called:
A. Reflection
B. Refraction
C. Diffraction
D. Absorption
Correct Answer: B. Refraction
Explanation: Refraction is the bending of a wave when it passes from one medium to another. This bending is caused by the change in the wave's speed.
30. According to Snell's Law, the angle of incidence is related to the angle of refraction by:
A. n₁sin(θ₁) = n₂sin(θ₂)
B. n₁cos(θ₁) = n₂cos(θ₂)
C. n₁cot(θ₁) = n₂cot(θ₂)
D. n₁tan(θ₁) = n₂tan(θ₂)
Correct Answer: A. n₁sin(θ₁) = n₂sin(θ₂)
Explanation: Snell's Law describes the relationship between the angles of incidence and refraction and the refractive indices of the two media. The formula is n₁sin(θ₁) = n₂sin(θ₂).
31. On burning magnesium ribbon in air, it produces a _____ flame.
A. Blue
B. Yellow
C. Dazzling white
D. Red
Correct Answer: C. Dazzling white
Explanation: When magnesium (Mg) burns in air (reacts with oxygen, O₂), it undergoes a chemical reaction to form magnesium oxide (MgO), producing a brilliant, dazzling white light.
32. Which of the following is a balanced chemical equation?
A. HNO₃ + Ca(OH)₂ → Ca(NO₃)₂ + H₂O
B. NaOH + H₂SO₄ → Na₂SO₄ + H₂O
C. BaCl₂ + H₂SO₄ → BaSO₄ + HCl
D. NaCl + AgNO₃ → AgCl + NaNO₃
Correct Answer: D. NaCl + AgNO₃ → AgCl + NaNO₃
Explanation: A balanced equation has the same number of atoms of each element on both the reactant and product sides. In option D, there is 1 Na, 1 Cl, 1 Ag, 1 N, and 3 O on both sides. The other options are unbalanced.
33. Which one of the following processes involve chemical reactions?
A. Storing of oxygen gas under pressure in a gas cylinder
B. Liquefaction of air
C. Keeping petrol in a china dish in the open
D. Heating copper wire in presence of air at high pressure
Correct Answer: D. Heating copper wire in presence of air at high pressure
Explanation: Heating copper in air causes it to react with oxygen to form a new substance, copper oxide (2Cu + O₂ → 2CuO). This is a chemical change. The other options describe physical changes (phase change, evaporation).
34. The chemical formula of hydrochloric acid is _____.
A. HCl
B. H₂SO₄
C. HNO₃
D. CH₃COOH
Correct Answer: A. HCl
Explanation: HCl is Hydrochloric Acid. H₂SO₄ is Sulfuric Acid, HNO₃ is Nitric Acid, and CH₃COOH is Acetic Acid.
35. Which of the following is an example of strong base?
A. NH₄OH
B. Ca(OH)₂
C. Both A and B
D. NaOH
Correct Answer: D. NaOH
Explanation: A strong base is one that completely dissociates or ionizes in a solution. Sodium hydroxide (NaOH) completely splits into Na⁺ and OH⁻ ions in water, making it a strong base.
36. Which of the following is an example of weak acid?
A. Hydrochloric acid
B. Acetic acid
C. Sulphuric acid
D. Nitric acid
Correct Answer: B. Acetic acid
Explanation: Weak acids only partially ionize in water. Acetic acid (CH₃COOH) is a classic example of a weak acid. Hydrochloric, sulfuric, and nitric acids are strong acids.
37. Which gas is produced by the reaction of acid with metal?
A. Hydrogen
B. Oxygen
C. Carbon dioxide
D. Nitrogen
Correct Answer: A. Hydrogen
Explanation: When a reactive metal reacts with an acid, it displaces hydrogen from the acid to form a salt and release hydrogen gas. Example: Zn + 2HCl → ZnCl₂ + H₂.
38. Which of the following oxides of iron would be obtained on the prolonged reaction of iron with steam?
A. FeO
B. Fe₂O₃
C. Fe₃O₄
D. Fe₂O₃ and Fe₃O₄
Correct Answer: C. Fe₃O₄
Explanation: The reaction of iron with steam produces iron(II,III) oxide (also known as magnetite) and hydrogen gas. The balanced equation is 3Fe + 4H₂O → Fe₃O₄ + 4H₂.
39. Which of the following is the correct property for ionic compounds?
A. Low melting and boiling points
B. High melting point and low boiling point
C. High melting and boiling points
D. Low melting point and high boiling point
Correct Answer: C. High melting and boiling points
Explanation: Ionic compounds are held together by strong electrostatic forces between oppositely charged ions in a crystal lattice. A large amount of thermal energy is required to break these bonds, resulting in high melting and boiling points.
40. The arrangement for Copper, Tin, Lead and Mercury, according to the reactivity series, is:
A. Tin > Lead > Copper > Mercury
B. Lead > Copper > Mercury > Tin
C. Copper > Mercury > Tin > Lead
D. Mercury > Tin > Lead > Copper
Correct Answer: A. Tin > Lead > Copper > Mercury
Explanation: In the reactivity series of metals, Tin (Sn) is more reactive than Lead (Pb), which is more reactive than Copper (Cu), which is more reactive than Mercury (Hg).
41. What is the full form of CPU?
A. Computer Processing Unit
B. Computer Principle Unit
C. Central Processing Unit
D. Control Processing Unit
Correct Answer: C. Central Processing Unit
Explanation: CPU stands for Central Processing Unit, the primary component of a computer that performs most of the processing.
42. What is smallest unit of the information?
A. Byte
B. Bit
C. MB
D. GB
Correct Answer: B. Bit
Explanation: A bit (binary digit) is the smallest unit of data in a computer, representing a 0 or a 1. A byte consists of 8 bits.
43. What does the abbreviation HTML stand for?
A. Hyper Text Markup Language
B. Hyper Type Markup Language
C. Hyper Text Markdown Language
D. High Text Markup Language
Correct Answer: A. Hyper Text Markup Language
Explanation: HTML stands for HyperText Markup Language, the standard language for creating web pages.
44. Which of the following is MS Office Suite's software program?
A. Microsoft Word
B. Microsoft Excel
C. Microsoft PowerPoint
D. All of the above
Correct Answer: D. All of the above
Explanation: Microsoft Office Suite includes Word (word processor), Excel (spreadsheet), and PowerPoint (presentation software), among others.
45. What is the default extension of a Microsoft Excel file?
A. .msxcl
B. .xcl
C. .xlsx
D. .xlsm
Correct Answer: C. .xlsx
Explanation: Since Office 2007, the default file extension for Microsoft Excel workbooks is .xlsx.
46. Which one of the following is an aquatic ecosystem?
A. Wetland
B. Desert
C. Mountain
D. Island
Correct Answer: A. Wetland
Explanation: Aquatic ecosystems are environments where the primary medium is water. Wetlands, oceans, lakes, and rivers are all examples of aquatic ecosystems.
47. Which one of the following is the indirect use of forests?
A. Medicinal plants
B. Checking soil erosion
C. Building material
D. Grazing
Correct Answer: B. Checking soil erosion
Explanation: Indirect uses of forests are the benefits they provide to the environment, such as preventing soil erosion, regulating climate, and purifying water. Direct uses involve harvesting resources like timber or medicinal plants.
48. Gardens are examples of _____.
A. Natural ecosystems
B. Artificial ecosystems
C. Ecology
D. Environment
Correct Answer: B. Artificial ecosystems
Explanation: Gardens, farms, and aquariums are examples of artificial or man-made ecosystems because they are created and maintained by humans.
49. Which of the following is a non-renewable energy resource?
A. solar
B. methane
C. hydroelectric
D. coal
Correct Answer: D. coal
Explanation: Non-renewable resources are finite and cannot be easily replenished. Coal, oil, and natural gas are fossil fuels, which are non-renewable. Solar, methane (biogas), and hydroelectric are considered renewable.
50. Which of the following are the primary causes of water pollution?
A. Plants
B. Animals
C. Human activities
D. None of these
Correct Answer: C. Human activities
Explanation: The primary causes of water pollution are overwhelmingly from human activities, such as industrial waste, agricultural runoff, oil spills, and improper waste disposal. (Note: The source PDF incorrectly listed 'D' as the answer, but the explanation clearly points to human activities).
Section 2: Aptitude Test (Mathematics and Soft Skill)
2. If order of matrix A is 4x3, order of matrix B is 3x5 and order of matrix ABC is 4x2 then order of matrix C is?
A. 4x2
B. 3x2
C. 2x2
D. 5x2
Correct Answer: D. 5x2
Explanation: For matrix multiplication to be possible, the number of columns in the first matrix must equal the number of rows in the second.
A (4x3) * B (3x5) results in a matrix AB of order (4x5).
Let the order of matrix C be (m x n).
(AB) (4x5) * C (m x n) must result in ABC (4x2).
For this multiplication, the columns of AB must match the rows of C, so m=5.
The resulting matrix order will be (rows of AB x columns of C), which is (4 x n).
Since we know the final order is 4x2, n must be 2.
Therefore, the order of matrix C is 5x2.
3. For square matrix A if A⁻¹ = adj(A) then |A| = ?
A. 1
B. 0
C. -1
D. None of above
Correct Answer: A. 1
Explanation: The formula for the inverse of a matrix is A⁻¹ = adj(A) / |A|. If A⁻¹ = adj(A), then adj(A) = adj(A) / |A|. This implies that |A| must be equal to 1.
4. If A = [[4, 6], [2, 1]] and B = [[1, -3], [-1, 2]], then (A+B)⁻¹ = ?
A. 1/12 * [[3, -3], [-1, 5]]
B. 1/12 * [[5, -3], [-1, 3]]
C. 1/12 * [[5, -1], [-3, 3]]
D. 1/12 * [[3, -1], [-3, 5]]
Correct Answer: A. 1/12 * [[3, -3], [-1, 5]]
Explanation: First find A+B: [[4+1, 6-3], [2-1, 1+2]] = [[5, 3], [1, 3]].
Next, find the determinant |A+B| = (5*3) - (3*1) = 15 - 3 = 12.
Then, find the adjugate adj(A+B) by swapping the diagonal elements and negating the off-diagonal elements: [[3, -3], [-1, 5]].
Finally, (A+B)⁻¹ = adj(A+B) / |A+B| = 1/12 * [[3, -3], [-1, 5]].
5. The period of sin(x/3) + tan(x/4) is?
A. 6π
B. 12π
C. 24π
D. 10π
Correct Answer: B. 12π
Explanation: The period of sin(ax) is 2π/|a| and the period of tan(bx) is π/|b|.
Period of sin(x/3) is 2π / (1/3) = 6π.
Period of tan(x/4) is π / (1/4) = 4π.
The period of the sum is the Least Common Multiple (LCM) of the individual periods. LCM(6π, 4π) = 12π.
6. (sin2A + sin8A) / (cos2A + cos8A) = ?
A. cot5A
B. tan10A
C. tan5A
D. None of above
Correct Answer: C. tan5A
Explanation: Using sum-to-product formulas:
sinC + sinD = 2sin((C+D)/2)cos((C-D)/2)
cosC + cosD = 2cos((C+D)/2)cos((C-D)/2)
So, [2sin(5A)cos(-3A)] / [2cos(5A)cos(-3A)] = sin(5A)/cos(5A) = tan(5A).
8. Angle between vector ā and (1,1,1) is 60°. If direction cosines of ā are l, m, n then l+m+n = ?
A. 1/2
B. √3/2
C. 2/√3
D. 1
Correct Answer: B. √3/2
Explanation: The direction cosines of (1,1,1) are (1/√3, 1/√3, 1/√3).
cosθ = l₁l₂ + m₁m₂ + n₁n₂.
cos60° = l(1/√3) + m(1/√3) + n(1/√3).
1/2 = (l+m+n)/√3.
l+m+n = √3/2.
9. If vectors (m, 3, 5) and (m, m-1, -3) are perpendicular to each other then m = ?
A. 3 or -6
B. -3 or 6
C. 3 or 6
D. -3 or -6
Correct Answer: A. 3 or -6
Explanation: If two vectors are perpendicular, their dot product is 0.
(m)(m) + (3)(m-1) + (5)(-3) = 0.
m² + 3m - 3 - 15 = 0.
m² + 3m - 18 = 0.
(m+6)(m-3) = 0. So, m = 3 or m = -6.
10. Equation of line perpendicular to line 3x-2y+7=0 and passes through (3, 2) is:
A. 3x+2y-11=0
B. 2x+3y-5=0
C. 2x+3y+12=0
D. 2x+3y-12=0
Correct Answer: D. 2x+3y-12=0
Explanation: The slope of 3x-2y+7=0 is 3/2. The slope of a perpendicular line is the negative reciprocal, which is -2/3.
The equation of the new line is y - y₁ = m(x - x₁).
y - 2 = -2/3(x - 3).
3(y - 2) = -2(x - 3).
3y - 6 = -2x + 6.
2x + 3y - 12 = 0.
11. Radius of circle 2x²+2y²+2x+4y-2=0 is:
A. 7
B. √7
C. 3/2
D. √(3/2)
Correct Answer: C. 3/2
Explanation: To find the radius, first get the equation in the standard form x²+y²+2gx+2fy+c=0 by dividing by 2: x² + y² + x + 2y - 1 = 0. Here, 2g=1 (so g=1/2), 2f=2 (so f=1), and c=-1. The radius formula is r = √(g²+f²-c).
r = √((1/2)² + 1² - (-1)) = √(1/4 + 1 + 1) = √(9/4) = 3/2. (Note: The answer in the source PDF is incorrect; this is the mathematically correct solution).
Explanation: To find the limit at infinity of a rational function, divide the numerator and denominator by the highest power of n, which is n². lim (n→∞) (3 + 5/n - 7/n²)/(5 + 6/n - 2/n²) = (3+0-0)/(5+0-0) = 3/5.
14. lim (x→0) (eˣ + sinx - 1)/x = ?
A. 0
B. 2
C. 1
D. None of above
Correct Answer: B. 2
Explanation: Substituting x=0 gives (1+0-1)/0 = 0/0, an indeterminate form. Using L'Hopital's Rule, we differentiate the numerator and denominator: lim (x→0) (eˣ + cosx) / 1 = (e⁰ + cos0) / 1 = (1+1)/1 = 2.
15. d/dx(logₑ(sinx)) = ?
A. cot x
B. tan x
C. cosec x
D. None of the above
Correct Answer: A. cot x
Explanation: Using the chain rule: d/dx(ln(u)) = (1/u) * du/dx. Let u = sinx, so du/dx = cosx. The derivative is (1/sinx) * cosx = cosx/sinx = cotx.
16. d/dx(x logₑx) = ?
A. 1/x
B. (x+1)/x
C. logₑx + x
D. logₑx + 1
Correct Answer: D. logₑx + 1
Explanation: Using the product rule (uv)' = u'v + uv': d/dx(x) * logₑx + x * d/dx(logₑx) = 1 * logₑx + x * (1/x) = logₑx + 1.
17. If x = a(1+sinθ), y = a(1-cosθ) then dy/dx = ?
A. cotθ
B. sinθ
C. tanθ
D. secθ
Correct Answer: C. tanθ
Explanation: This is parametric differentiation. dy/dx = (dy/dθ) / (dx/dθ). dy/dθ = a(sinθ). dx/dθ = a(cosθ). dy/dx = (a sinθ) / (a cosθ) = tanθ.
18. If equation of motion of moving object is s = t³-6t²+9t+7 then at t = __ second object changes its direction.
A. 2, 3
B. 1, 2
C. 1, 3
D. 2, 3
Correct Answer: C. 1, 3
Explanation: The object changes direction when its velocity (v) is zero. Velocity is the derivative of the position (s). v = ds/dt = 3t² - 12t + 9. Set v=0: 3(t² - 4t + 3) = 0. (t-1)(t-3) = 0. So, t = 1 and t = 3.
19. ∫sin⁵x cosx dx = ?
A. sin⁴x / 4 + c
B. sin⁶x / 6 + c
C. 5 sin⁴x + c
D. 6 sin⁶x + c
Correct Answer: B. sin⁶x / 6 + c
Explanation: Use substitution. Let u = sinx, then du = cosx dx. The integral becomes ∫u⁵ du = u⁶/6 + c. Substituting back, we get sin⁶x / 6 + c.
20. ∫x eˣ dx = ?
A. xeˣ + eˣ + c
B. eˣ - x + c
C. eˣ + x + c
D. xeˣ - eˣ + c
Correct Answer: D. xeˣ - eˣ + c
Explanation: Use integration by parts (∫u dv = uv - ∫v du). Let u = x, dv = eˣ dx. Then du = dx, v = eˣ. ∫x eˣ dx = x eˣ - ∫eˣ dx = xeˣ - eˣ + c.
21. ∫₀^(π/2) (sinx)/(sinx+cosx) dx = ?
A. π/4
B. π/2
C. π
D. None of the above
Correct Answer: A. π/4
Explanation: Using the property ∫₀ᵃ f(x)dx = ∫₀ᵃ f(a-x)dx. Let I = ∫₀^(π/2) (sinx)/(sinx+cosx) dx. I = ∫₀^(π/2) sin(π/2-x)/(sin(π/2-x)+cos(π/2-x)) dx = ∫₀^(π/2) (cosx)/(cosx+sinx) dx. Adding the two equations: 2I = ∫₀^(π/2) (sinx+cosx)/(sinx+cosx) dx = ∫₀^(π/2) 1 dx = [x] from 0 to π/2 = π/2. So, 2I = π/2, which means I = π/4.
22. ∫₁² (2x)/(1+x²) dx = ?
A. logₑ(1/2)
B. logₑ(5/2)
C. logₑ(5)
D. logₑ(2)
Correct Answer: B. logₑ(5/2)
Explanation: Let u = 1+x², then du = 2x dx. The integral is ∫(1/u)du = ln|u| = ln|1+x²|. Evaluating from 1 to 2: [ln(1+2²)] - [ln(1+1²)] = ln(5) - ln(2) = ln(5/2).
23. If log₂(log₃x) = 1 then x = ?
A. 9
B. 3
C. 6
D. 27
Correct Answer: A. 9
Explanation: If log₂(A) = 1, then A = 2¹. So, log₃x = 2. If log₃x = 2, then x = 3². So, x = 9.
24. 3^(log₉4) = ?
A. 2
B. 3
C. 1
D. 4
Correct Answer: A. 2
Explanation: Using the change of base formula, log₉4 = log₃4 / log₃9 = log₃(2²) / log₃(3²) = (2 log₃2) / 2 = log₃2. So the expression is 3^(log₃2). Using the property a^(logₐb) = b, the answer is 2.
25. If mean of 3, 5, a, 4, 6 is 5, then a = ?
A. 5
B. 6
C. 7
D. 8
Correct Answer: C. 7
Explanation: The mean is the sum of the numbers divided by the count. (3+5+a+4+6) / 5 = 5. (18+a) / 5 = 5. 18 + a = 25. a = 7.
26. Passage: In the ancient city of Varanasi... Why did a celestial figure appear before Raj?
A. Because of Raj's prayer
B. Because of black magic
C. Because Raj was a devotee to goddess.
D. Because Raj was a kind and hardworking person.
Correct Answer: D. Because Raj was a kind and hardworking person.
Explanation: The passage states the celestial figure was "Impressed by Raj's kindness" and saw him working "diligently on his loom," indicating his kindness and hard work were the reasons for her appearance.
27. Passage: ... Who appeared before Raj in the guise of an old woman?
A. Goddess Swaraswati
B. Goddess Lakshami
C. Goddess Paravati
D. Goddess Durga
Correct Answer: A. Goddess Swaraswati
Explanation: The passage explicitly states, "It was Saraswati, the goddess of knowledge, disguised as an old woman."
28. Passage: ... What did the king challenge Raj to weave?
A. Fabric praising the King
B. Fabric with celestial patterns
C. Fabric capturing the essence of the river
D. Fabric depicting a battle
Correct Answer: C. Fabric capturing the essence of the river
Explanation: The passage says, "...challenged Raj to weave a fabric that could capture the essence of the river itself."
29. Passage: ... How did Raj gather inspiration for the challenge?
A. By visiting the mountains
B. By visiting the temple
C. By worshipping the goddess
D. By visiting the river Ganges
Correct Answer: D. By visiting the river Ganges
Explanation: The text states, "Raj embarked on a journey to gather inspiration from the Ganges."
30. Passage: ... Find one word substitute for 'an act of changing one's appearance' from the passage.
A. Celestial
B. Disguise
C. Contemplation
D. Intrigue
Correct Answer: B. Disguise
Explanation: The word 'disguise' is used in the passage ("...disguised as an old woman") and it means to alter one's appearance to conceal one's identity.
31. Which of the following ensures completion of the process of communication cycle?
A. Channel
B. Encoding
C. Feedback
D. Decoding
Correct Answer: C. Feedback
Explanation: Feedback is the response from the receiver back to the sender. It confirms that the message was received and understood, thereby completing the communication loop or cycle.
32. _____ communication means communication without words.
A. Written
B. Verbal
C. Non-verbal
D. Reading
Correct Answer: C. Non-verbal
Explanation: Non-verbal communication includes gestures, facial expressions, body language, and tone of voice to convey messages without using spoken or written words.
33. The person who transmits the message is called _____.
A. Channel
B. Sender
C. Receiver
D. Respondent
Correct Answer: B. Sender
Explanation: The sender (or encoder) is the person who initiates the communication process by creating and sending a message.
34. Semantic barrier to communication arises due to problems of _____.
A. Language
B. Expressions
C. Psychology
D. Technology
Correct Answer: A. Language
Explanation: Semantic barriers are related to the meaning of words and symbols. They occur when the sender and receiver interpret the language differently, leading to misunderstanding.
35. The movement of body, facial expressions, hand movements, gestures, etc. while communicating refer to _____.
A. Proxemics
B. Kinesics
C. Paralanguage
D. Appearance
Correct Answer: B. Kinesics
Explanation: Kinesics is the study of body language, including gestures, posture, facial expressions, and other bodily movements as a means of communication.
36. The address of the receiver in a formal letter is called the _____.
A. Outside address
B. Sender's address
C. Inside Address
D. Header
Correct Answer: C. Inside Address
Explanation: In a business or formal letter, the Inside Address is the recipient's address, placed below the sender's address and the date.
37. After receiving a letter of complaint, which kind of letter is drafted in response?
A. Letter of Inquiry
B. Order Letter
C. Sales Letter
D. Letter of Reply
Correct Answer: D. Letter of Reply
Explanation: A Letter of Reply (or adjustment letter) is drafted to respond to a complaint, addressing the issue and explaining the actions to be taken.
38. C.W.O. in business letter or email stands for _____.
A. Cash Without Order
B. Cash With Offer
C. Cash With Order
D. Company With Order
Correct Answer: C. Cash With Order
Explanation: C.W.O. stands for Cash With Order, a payment term indicating that the payment for goods must be made at the time the order is placed.
39. Which of the following is an advantage of an email?
A. Desired length
B. Ease of communication
C. Lower cost
D. All of the above
Correct Answer: D. All of the above
Explanation: Email offers numerous advantages, including low cost, speed, ease of use, the ability to send messages of various lengths, and the option to attach files.
40. BCC in email stands for _____.
A. Blind Carbon Copy
B. Below Carbon Copy
C. Business Carbon Copy
D. Business Client Company
Correct Answer: A. Blind Carbon Copy
Explanation: BCC stands for Blind Carbon Copy. Recipients in the BCC field receive the email, but their email addresses are hidden from all other recipients.
41. _____ tense is used in the headlines of newspapers.
A. Simple present tense
B. Simple past tense
C. Simple future tense
D. Present continuous tense
Correct Answer: A. Simple present tense
Explanation: Newspaper headlines often use the simple present tense to make past events sound more immediate and dramatic.
42. The train _____ before we reached the station.
A. Left
B. has left
C. had left
D. will be left
Correct Answer: C. had left
Explanation: The past perfect tense ("had left") is used to describe an action that was completed before another action in the past ("we reached").
43. Rima is a good dancer. The underlined word "good" in the sentence given is _____.
A. a noun
B. an adjective
C. a verb
D. an adverb
Correct Answer: B. an adjective
Explanation: An adjective is a word that describes a noun. In this sentence, "good" describes the noun "dancer".
44. _____ you work hard, you will succeed in the university Examination.
A. Though
B. But
C. Unless
D. If
Correct Answer: D. If
Explanation: "If" is used to introduce a conditional clause. The sentence sets a condition (working hard) for a result (succeeding).
45. One of my friends _____ old.
A. am
B. is
C. are
D. has
Correct Answer: B. is
Explanation: The subject of the sentence is "One", which is singular. Therefore, it requires the singular verb "is".
46. Choose the correct spelling.
A. Vaccum
B. Vacuum
C. Vacumm
D. Veccum
Correct Answer: B. Vacuum
Explanation: The correct spelling is V-A-C-U-U-M.
47. Choose the correct spelling.
A. Enterpreneur
B. Entreorenure
C. Entrepreneur
D. Enterprenure
Correct Answer: C. Entrepreneur
Explanation: The correct spelling is E-N-T-R-E-P-R-E-N-E-U-R.
48. Choose the correct sentence in present continuous tense:
A. He is reading a book now.
B. He reads a book now.
C. He read a book now.
D. He has reading a book now.
Correct Answer: A. He is reading a book now.
Explanation: The present continuous tense is formed with the subject + the present tense of 'to be' (is/am/are) + the '-ing' form of the verb.
49. Choose the correct negative sentence.
A. I don't use public transport daily.
B. I didn't use public transport daily.
C. I not use public transport daily.
D. I not using public transport daily.
Correct Answer: A. I don't use public transport daily.
Explanation: For the simple present tense, the negative is formed using "do/does + not" (contracted to don't/doesn't) + the base form of the verb.
50. Choose the correct sentence.
A. Have I a pen?
B. Has I a pen?
C. Do I have a pen?
D. Do I has a pen?
Correct Answer: C. Do I have a pen?
Explanation: In modern English, questions about possession are typically formed with the auxiliary verb "do" ("Do you have...?"). The verb "have" remains in its base form.
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