Saved Bookmarks
This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If two cubes of sides 1 cm each are joined end to end then what is the total surface area ofthe resultant cuboid? |
|
Answer» Dimensions of the cuboid formed are length=L=2cm,Breadth=B=1cmand height=H=1cm Surface area of cuboid formed=2(lb+bh+lh ) ` 2(2+1+2)=10(cm)^2` |
|
| 2. |
A force of 0.12 newton for 3 second and body mass 0.4 kg of rest If the velocity gain by the body. |
|
Answer» f = ma, u = 0 \(f = m\frac{(v-u)}{t}\) f x t = m (v) \(\frac{f \times t}{m} = v\) \(\frac{f \times t}{m} = \frac{0.12 \times 3}{0.4}\) = 9 v = 9 m/s. |
|
| 3. |
Equation of a common tangent to `x^(2)+y^(2)=16" and "9x^(2)+25y^(2)=225` is :A. `3x+2y=5`B. `sqrt(7x)+3y=16`C. `x+sqrt(7)y=6`D. `sqrt(7)x-sqrt(11)y=2` |
|
Answer» Correct Answer - B `{:(because,a.b.c" are in A.P.",implies,a+c=2b,implies,1+(c)/(a)-(2b)/(a)=0),(implies,1+alphabeta+2(alpha+beta)=0,implies,1+99+2(alpha+beta)=0,implies,alpha+beta=-50):}` |
|
| 4. |
Why sky is blue? |
|
Answer» As white light passes through our atmosphere, tiny air molecules cause it to 'scatter'. The scattering caused by these tiny air molecules (known as Rayleigh scattering) increases as the wavelength of light decreases. ... Therefore, blue light is scattered more than red light and the sky appears blue during the day. because sky have a light blue than colour blend the sea The sunlight that reaches the earth’s atmosphere is scattered in all directions by the gases and dust particles present in the atmosphere.
|
|
| 5. |
" (f) "(2+x)/(2-x) |
|
Answer» Break Up Fraction `f * (2 / (2 + -x) + x / (2 + -x))` Distribute `2 f / (2 + -x) + (x * f) / (2 + -x)` |
|
| 6. |
If `y=ax^(2)+bx+c` is the reflection of parabola `y=x^(2)-4x+1` about the line `y=3,a+b+c=`A. 1B. 2C. 3D. 4 |
|
Answer» Correct Answer - B `sqrt((x+3)(x-2))-(x-2)=sqrt((x-2)(x-5))` For the equation to be defined `x in (-oo,-3] uu [2,oo)" and "x in (-oo,2]uu[5,oo)` `therefore x in (-oo,-3]uu[5,oo)uu{2}` On solving we get `x=2,6,-(10)/(3)` |
|
| 7. |
A fair coin 1 marked on one face and 6 on the other face and a fair die are both tossed. find the probability that the sum of numbers that turn up is (i) 3 (ii) 12. |
|
Answer» Coin has faces marked with 1, 6. A fair die has faces marked as 1, 2, 3, 4, 5, 6. ∴ total number of equally likely cases = 2 × 6 = 12 (i) Favourable case is (1, 2) i.e., 1 only. ∴ red. probability = 1/12 (ii) Favourable case is (6, 6) i.e. 1 only. ∴ req d. probability = 1/12 |
|
| 8. |
Speaking in front of a large group makes most people nervous. But the use of 3Ps method will help in getting over fears, and become a confident and effective speaker. What are these Ps? a. prepare, Practice, Post b. prepare, Practice, Put c. prepare, Practice, Patience d. prepare, Practice, Perform |
|
Answer» d. Prepare, Practice, Perform Speaking in front of a large group makes most people nervous. But the use of 3Ps method will help in getting over fears, and become a confident and effective speaker. these Ps are Prepare, Practice, Perform. |
|
| 9. |
This is a type of Tube bender (a) Spring type (b) Lever type (c) Both (a) and (b) (d) None of the above |
|
Answer» Correct answer is (c) Both (a) and (b) |
|
| 10. |
While buying a dress, you want to negotiate with a shopkeeper to reduce the price. Which communication skill is needed here? a. Inform b. Influence c. Express feeling d. Commanding |
|
Answer» b. Influence While buying a dress, you want to negotiate with a shopkeeper to reduce the price. Influence communication skill is needed here. |
|
| 11. |
Which tool is used to check the current in the circuit? (a) Tester (b) Voltmeter (c) Wattmeter (d) Screw driver |
|
Answer» Correct answer is (a) Tester |
|
| 12. |
This component is also known as Chilling coil. (a) Evaporator (b) Condenser (c) Compressor (d) None of the above |
|
Answer» (a) Evaporator Evaporator component is also known as Chilling coil. |
|
| 13. |
Which tool is used to check the gauge of wires? (a) Wire gauge (b) Meter tape (c) Vernier calliper (d) Tester |
|
Answer» Correct answer is (a) Wire gauge |
|
| 14. |
Quality factor is also known as ___a) Voltage magnification b) Current magnification c) Resistance magnification d) Impedance magnification |
|
Answer» Correct option: a) Voltage magnification |
|
| 15. |
The simple Vapour compression Refrigeration system is made up of four fundamental processes(a) (i) expansion (ii) vaporization (iii) compression (iv) condensation (b) (i) Heating (ii) compression (iii) condensation (iv) contraction (c) (i) Heating (ii) expansion (iii) compression (iv) contraction (d) (i) expansion (ii) vaporization (iii) condensation (iv) contraction |
|
Answer» (a) (i) expansion (ii) vaporization (iii) compression (iv) condensation The simple Vapour compression Refrigeration system is made up of four fundamental processes (i) expansion (ii) vaporization (iii) compression (iv) condensation |
|
| 16. |
Different value of a, b and c are given and their sum is d. Arrange the value of d in increasing order(1) d1 < d2 < d3 < d4 (2) d1 = d2 = d3 = d4 (3) d4 < d1 < d2 = d3 (4) d4 < d3 < d2 < d1 |
||||||||||||||||||||||||||||||
|
Answer» Answer is (3) d4 < d1 < d2 = d3
|
|||||||||||||||||||||||||||||||
| 17. |
Efficiency of a transformer is maximum at a. Leading power factor b. Lagging power factor c. Unity power factor d. None of these |
|
Answer» Correct option: c. Unity power factor |
|
| 18. |
What is the unit of Electric Power? (a) Watt (b) Ampere (c) Volt (d) Ohm |
|
Answer» Correct answer is (a) Watt |
|
| 19. |
Which joint is used to connect two cables to each other at a right angle? (a) Simple Joint (b) T Joint (c) Britannia Joint (d) Straight joint |
|
Answer» Correct answer is (b) T Joint |
|
| 20. |
The major parts of a domestic refrigerator are (a) Insulated cabinet (b) Refrigerating system (c) Both (a) and (b) (d) None of the above |
|
Answer» Correct answer is (c) Both (a) and (b) |
|
| 21. |
How many kilowatt (KW) is equal to 1000 watt? (a) 1 KW (b) 0.1 KW (c) 0.5 KW (d) 0.2 KW |
|
Answer» Correct answer is (a) 1 KW |
|
| 22. |
______ harvested ice from rivers and lakes as early as 1000 BC (a) Indians (b) French (c) Americans (d) Chinese |
|
Answer» (d) Chinese Chinese harvested ice from rivers and lakes as early as 1000 BC. |
|
| 23. |
A wire made by inserting two or three different wires in a strong insulation is called _______ (a) Single Strand Conductor (b) Flexible wire (c) Pole wire (d) Cable |
|
Answer» Correct answer is (d) Cable |
|
| 24. |
An electrical pressure that drives transmission of electric current is known as _____ (a) Power (b) Resistor (c) Voltage (d) Transistor |
|
Answer» Correct answer is (c) Voltage |
|
| 25. |
Speed of the universal motor is a) Dependent on frequency of supply b) Proportional to frequency of supply b) Independent of frequency of supply c) None of the above |
|
Answer» Correct option: b) Independent of frequency of supply |
|
| 26. |
A transformer oil used in an electrical transformer must be free from _____ a) Gases b) Odour c) Sludge d) Moisture |
|
Answer» Correct option: d) Moisture |
|
| 27. |
The starting torque of a capacitor start motor is a) zero b) low c) same as rated torqued) more than rated torque. |
|
Answer» Correct option: b) low |
|
| 28. |
The efficiency of an induction motor is about a) 100% b) 80-90% c) 50-60% d) Less than 50% |
|
Answer» Correct option: b) 80-90% |
|
| 29. |
What will happen if DC shunt motor is connected across AC supply? a) Will run at normal speed b) Will not run c) Will Run at lower speed d) Burn due to heat produced in the field winding |
|
Answer» Correct option: d) Burn due to heat produced in the field winding |
|
| 30. |
RMS stands for __ a) Root Mean Square b) Root Mean Sum c) Root Maximum sum d) Root Minimum Sum |
|
Answer» Correct option: a) Root Mean Square |
|
| 31. |
A good heating element should have a) High resistivity and low melting point b) Low resistivity and high melting pointc) High resistivity and high melting point d) Low resistivity and low melting point |
|
Answer» Correct option: c) High resistivity and high melting point |
|
| 32. |
The chords of contact of a point with respect to a hyperbola and its auxillary circle are perpendicular, then the point lies on :A. One of the directricesB. one of the asymptotesC. conjugate hyperbolaD. Axis of hyperbola |
|
Answer» Correct Answer - A (i) Let `theta = tan^(-1)2." "x=sin2theta=(2tantheta)/(1+tan^(2)theta)=(4)/(5)` Let `alpha=tan^(-1).(4)/(3), " "y=sin.(alpha)/(2)=sqrt((1-cosalpha)/(2))=sqrt((1-3//5)/(2))=sqrt((1)/(5))` (ii) Take tan on both sides `((3)/(4)+(1)/(7))/(1-(3)/(28))=tan.(pi)/(4)` (iii) Put `x = tan theta. " "therefore 6theta-8theta+4theta=(pi)/(3)impliestheta=(pi)/(6)`. `(because2 thetain "I quadrant"impliessin^(-1)(sin2theta)=2theta,cos^(-1)(cos2theta)=2theta,tan^(-1)(tan2theta)=2theta)` (iv) `tan^(-1)((1)/(5))lttan^(-1)(sqrt(2)-1)" "therefore0lt2tan^(-1)((1)/(5))lt(pi)/(4)` |
|
| 33. |
What is the range of the Signum function: -(a) \( (-1,1) \)(b) \( \{-1,1\} \)(c) \( \{-1,0,1\} \)(d) \( (-1,0,1) \) |
|
Answer» range of signum function is { -1, 0,1}
|
|
| 34. |
A chord PQ of the hyperbola `xy=c^2` is tangent to the hyperbola `x^2 / a^2 - y^2 / b^2 = 1` Find the locus of the middle point of PQ. |
| Answer» Given, hyperbola `xy = c^2`Let its chord `PQ` has the mid point `(h,k)``Eqn.` of chord with a given point`T = S_1`From eqn. of hyperbola, tangent:`T= 2*xy/2 = c^2``rArr T = (xy + xy)/2 - c^2`At point `(h,k)``T = (hy + kx)/2 - c^2``S_1` refers to point satisfying eqn. of hyperbola.`S_1 = hk - c^2``:. (hy+kx)/2 - c^2 = hk - c^2``rArr kx + hy = 2hk``hy = 2hk - kx``y = (2hk - kx)/h` ..... (from `eq.1`)This is the chord which is tangent to another hyperbola:`x^/a^2 - y^2/b^2 = -1`Applying condition of tangencySatisfying eq. of hyperbola and eq. of tangent.`x^2/a^2 - (2hk - kx)^2/(h^2*y^2) = -1` (From `eq. 1`)Simplifying`x^2/a^2 - (4h^2*k^2 + k^2*x^2 - 4h*k^2*x)/h^2*b^2 = -1``rArr x^2/a^2 - (4h^2*k^2)/(h^2*b^2) - (k^2*x^2)/(h^2*b^2) + (4h*k^2*x)/(h^2*b^2) + 1 = 0``rArr (1/a^2 - k^2/(h*b^2))*x^2 + (4*k^2/(h*b^2))*x + ( 1 - 4*k^2/b^2)`This must have equal roots and `D = 0``D = (4k^2/(h*b^2))^2 - 4*(1/a^2 - k^2/(h^2*b^2))(1 - 4k^2/b^2) = 0``rArr 4k^4/(h^2*b^4) - (1/a^2 - 4*k^2/(a^2.b^2) - k^2/(h^2*b^2) + 4k^4/(h^2*b^4)) = 0``rArr 4k^4/(h^2*b^4) - 1/a^2 + 4*k^2/(a^2.b^2) + k^2/(h^2*b^2) - 4k^4/(h^2*b^4) = 0``rArr 4k^2/(a^2*b^2) + k^2/(h^2*b^2) = 1/a^2`Required locus:`4y^2/(a^2*b^2) + y^2/(x^2*b^2) = 1/a^2` | |
| 35. |
P is a variable points on the hyperbola `x^2/a^2-y^2/b^2=1` whose vertex is `A(a,0)` The locus of the middle points AP isA. `((2x-a)^(2))/a^(2)-(2y^(2))/b^(2)=1`B. `((2x-a)^(2))/a^(2)-(4y^(2))/b^(2)=1`C. `((2x-a)^(2))/a^(2)-(8y^(2))/b^(2)=1`D. None of these |
|
Answer» Correct Answer - 2 Let the point P be `(a sectheta, b tantheta)` and A(a, 0), let the point of AP be (h, k) `therefore h=(a+asectheta)/2 and k=(btantheta)/2` `rArr(2h-a)/a=sectheta…(i)` and `(2k)/b=tantheta…(ii)` Squaring and Subtracting (ii) from (i) we get `rArr((2h-a)^(2))/a^(2)-(4y^(2))/b^(2)=1` |
|
| 36. |
If `intf(x)dx=g(x),then intx^(11)f(x^(6))dx` is equal toA. `1/6[x^(6)g(x^(6))-intx^(5)g(x^(6))]+C`B. `1/6x^(6)g(x^(6))-intx^(5)g(x^(6))dx+C`C. `1/6[x^(6)g(x^(6))-5intx^(5)g(x^(6))dx]+C`D. None of these |
|
Answer» Correct Answer - 2 `I=intx^(11)f(x^(6))dx` put `x^(6)=trArr6x^(5)dx=dt` `I=1/6inttf(t)dt` `=1/6[tg(t)-intg(t)dt]` `=1/6[x^(6)g(x^(6))-intg(x^(6))d(x^(6))]` `=1/6[x^(6)g(x^(6))-6intx^(5)g(x^(6))dx]` `=1/6x^(6)g(x^(6))-intx^(5)g(x^(6))dx+C` |
|
| 37. |
The degree of the differential equation y(x) = 1 + dy/dx + 1/1.2(dy/dx)2 + 1/1.2.3(dy/dx)3 + .... is _________.(a) 2 (b) 3 (c) 1 (d) 4 |
|
Answer» The correct answer is: (c) 1 |
|
| 38. |
The order and degree of the differential equation p d2y/dx2 + (dy/dx)1/3 + x1/4 = 0 are respectively _______. (a) 2, 3 (b) 3, 3 (c) 2, 6(d) 2, 4 |
|
Answer» The correct answer is : (a) 2, 3 |
|
| 39. |
Solve the differential equation: tan y dy/dx = cos (x + y) + cos (x - y) |
|
Answer» tan y dy/dx = cos (x + y) + cos(x – y) tan y dy/dx = cos x cos y – sin x sin y + cos x cos y + sin x sin y tan y dy/dx = 2 cos x cos y seperating the variables \(\int\)tany/cosy dy = 2∫cos x dx ⇒ ∫sec y tan y dy = 2∫cos x dx sec y = 2 sin x + c |
|
| 40. |
If A = \(\begin{bmatrix} 2 &3\\ 5&-2\end{bmatrix}\)be such that λA-1 = A, then λ is _______.(a) 17(b) 14(c) 19(d) 21 |
|
Answer» The correct answer is : (c) 19 |
|
| 41. |
The general solution of the differential equation log \(\hat {\left (\frac{dy}{dx}\right)}\) = = x + y is ______. (a) ex + ey = c (b) ex + e-y = c (c) e-x + ey = c (d) e-x + e-y = c |
|
Answer» (b) ex + e-y = c |
|
| 42. |
Which of the following is a discrete random variable? I. The number of cars crossing a particular signal in a day. II. The number of customers in a queue to buy train tickets at a moment. III. The time taken to complete a telephone call. (a) I and II (b) II only (c) III only (d) II and III |
|
Answer» The correct answer is: (a) I and II |
|
| 43. |
Find the values in the interval (1, 2) of the mean value theorem satisfied by the function f(x) = x – x2 for 1 ≤ x ≤ 2. |
|
Answer» f(1) = 0 and f(2) = -2. Clearly f(x) is defined and differentiable in 1 < x < 2. Therefore, by the Mean Value Theorem, there exists a c ∈(1, 2) such that f'(c) = \(\frac {f(2)−f(1)}{2 -1}\) = 1 – 2c That is, 1 – 2c = -2 ⇒ c = 3/2 |
|
| 44. |
In finding the differential equation corresponding toy = emx where m is the arbitrary constant, then m is ____. (a) y/y'(b) y'/y(c) y’ (d) y |
|
Answer» The correct answer is : (b) y'/y |
|
| 45. |
The differential equation corresponding to xy = c2 where c is an arbitrary constant, is ______. (a) xy”+ x = 0 (b) y” = 0 (c) xy’ + y = 0 (d) xy”- x = 0 |
|
Answer» (c) xy’ + y = 0 |
|
| 46. |
The slope of the tangent to the curve at any point is the reciprocal of four times the ordinate at that point. The curve passes through (2, 5). Find the equation of the curve. |
|
Answer» Slope of the tangent is the reciprocal of four times the ordinate i.e., dy/dx = 1/4y 4∫y dy = ∫ dx 4(y2)/2 = x + c ⇒ 2y2 = x + c Passes through (2, 5) ∴ c = 50 – 2 = 48 Equation of the curve is 2y2 = x + 48 |
|
| 47. |
The order and degree of the differential equation are (d2y/dx2) + (dy/dx)1/3 + x1/4 = 0 respectively. (a) 2, 3 (b) 3, 3 (c) 2, 6 (d) 2, 4 |
|
Answer» The correct answer is : (a) 2, 3 |
|
| 48. |
If p is true and q is false then which of the following is not true? (a) p → q is false(b) p ∨ q is true (c) p ∧ q is false (d) p ↔ q is true |
|
Answer» (d) p ↔ q is true |
|
| 49. |
Let X be random variable with probability density function f(x) = \(\begin{cases}\frac{2}{x^3}&x≥1\\ 0&x<1 \end{cases}\)Which of the following statement is correct (a) both mean and variance exist (b) mean exists but variance does not exist (c) both mean and variance do not exist (d) variance exists but mean does not exist |
|
Answer» (b) mean exists but variance does not exist |
|
| 50. |
If f(x) = \(\begin {cases} 2x, &0≤x≤a \\0,&otherwise\end{cases}\) is a probability density function of a random variable, then the value of a is _________. (a) 1 (b) 2 (c) 3 (d) 4 |
|
Answer» The correct answer is : (a) 1 |
|