100525 + Interview Questions in GENERAL QA IN GENERAL AWARENESS

1.	If a pressure of 400 Pa acts on 20 m2 area, what is the value force?(a) 2 KN(b) 4 KN(c) 6KN(d) 8KN
Answer» Correct option is (d) 8KN Explanation: Force = Pressure*Area.

Discussion

2.	This is not an advantage of Centrifugal compressor(a) Maintenance cost is low (b) Less space required (c) Free from vibrations (d) Suitable for very high compression
Answer» (d) Suitable for very high compression Suitable for very high compression is not an advantage of Centrifugal compressor.

2.

This is not an advantage of Centrifugal compressor(a) Maintenance cost is low (b) Less space required (c) Free from vibrations (d) Suitable for very high compression

Answer»

(d) Suitable for very high compression

Suitable for very high compression is not an advantage of Centrifugal compressor.

Discussion

3.	Zero percent relative saturation means(a) 100 % vapour in the air(b) 75% vapour in the air(c) 50% vapour in the air(d) No vapour in the air
Answer» Correct option is (d) No vapour in the air Explanation: Zero percent relative saturation means no vapour in the air.

Discussion

4.	When the air temperature rises the saturation mixing ratio(a) Increases(b) Decreases(c) Remains same(d) None of the mentioned
Answer» The correct choice is (a) Increases Explanation: When the air temperature rises the saturation mixing ratio increases.

Discussion

5.	The density of liquid A is 1.6 g cm-3 and its height h(A) = 16.9 cm, then the density of oil B of height h(B) = 30 cm in the U-tube is about(a) 0.90 g/cm3(b) 1.12 g/cm3(c) 2.24 g/cm3(d) 3.54 g/cm3
Answer» The correct choice is (a) 0.90 g/cm3 To elaborate: Pressure at point ‘b’ = Atmospheric pressure + ρB ghB Pressure at point ‘a’ = Atmospheric pressure + ρAghA Pressures at point ‘a’ = point ‘b’.

Discussion

6.	Pressure can`t be expressed as(a) N/m2(b) Pa/m2(c) atm(d) mm of Hg
Answer» The correct answer is (b) Pa/m2 Explanation: Pa is the unit of pressure, not Pa/m2.

Discussion

7.	What is the value of P`r?(a) 1.11(b) 2.11(c) 3.11(d) 4.11
Answer» Correct choice is (b) 2.11 The explanation: P`r = P/P`c.

Discussion

8.	ε = ∆ϕ/∆t, to which law does this equation refer ?
Answer» Faraday's law of Induction.

Discussion

9.	Change in temperature on Fahrenheit scale is?(a) 1.389 ˚F(b) 37.72˚F(c) 460 ˚F(d) None of the mentioned
Answer» Correct answer is (a) 1.389 ˚F Explanation: ∆˚C = 1.8 ∆˚F.

Discussion

10.	An object is once immersed in oil and once in water. The loss in weight would be(a) More in water(b) More in oil(c) Equal in both oil and water(d) None of the mentioned
Answer» The correct choice is (b) More in oil The best explanation: Density of oil is more than water so there will be more buoyancy force.

Discussion

11.	A technique of estimating physical properties of compound by using properties of molecular group of elements in the compound. Is called(a) Group contribution method(b) Generalized group method(c) Kay`s Method(d) None of the mentioned
Answer» The correct answer is (a) Group contribution method The best explanation: A technique of estimating physical properties of compound by using properties of molecular group of elements in the compound is called Group contribution method.

Discussion

12.	Which is used to prevent damage due to overloading of current ?
Answer» Fuse is used to prevent damage due to overloading of current.

Discussion

13.	The degree of saturation is the ratio of the ______ humidity to the _______ humidity at the same __________(a) Actual specific, saturated specific, temperature(b) Saturated specific, actual specific, pressure(c) Actual specific, saturated specific, pressure(d) Saturated specific, actual specific, temperature
Answer» Correct answer is (a) Actual specific, saturated specific, temperature Explanation: The degree of saturation is the ratio of the actual specific humidity to the saturated specific humidity at the same temperature.

Discussion

14.	Representation of the different phase of a compound on a two or three dimensional graph is(a) Block diagram(b) Equilibrium diagram(c) Phase diagram(d) None of the mentioned
Answer» Right choice is (c) Phase diagram To elaborate: Representation of the different phase of a compound on a two or three dimensional graph is called Phase diagram.

Discussion

15.	Boiling temperature of water in Fahrenheit scale is(a) 112(b) 213(c) 212(d) 121
Answer» Correct choice is (c) 212 To elaborate: Boiling temperature of water is 100 ˚C.

Discussion

16.	Boiling occurs at ________ temperature and _______ pressure, the process appears as a point in ____ diagram.(a) Constant, constant, P-T(b) Variable, constant, P-T(c) Constant, variable, V-T(d) Variable, variable, V-T
Answer» Right option is (a) Constant, constant, P-T The explanation is: Boiling occurs at constant temperature and constant pressure, the process appears as a point in P-T diagram.

Discussion

17.	For a given system, number of variables is 6 and number of equations is 4. What is the number of degrees of freedom?(a) 2(b) 4(c) 6(d) 8
Answer» The correct option is (a) 2 The explanation: Number of degrees of freedom = 6 – 4 = 2.

Discussion

18.	Which protection device is used in circuit to prevent the filter from overloading current? (a) MCB (b) RCCB (c) Fuse (d) ELCB
Answer» Correct answer is (a) MCB

Discussion

19.	\( \begin{bmatrix}5 & 7 & 2 \\[0.3em]0 & 1 & 0 \\[0.3em]0 & 0 & 0\end{bmatrix}=\)(A) 5(B) 16(C) 21(D) 0
Answer» Correct option is: (D) 0

Discussion

20.	Find 17th term of sequence whos: nth term is given by a = 4n – 3. term of sequence whos
Answer» a₁₇ = 4(17) – 3 = 68 – 3 = 65

Discussion

21.	∫ tanx dx =(A) log \|sec x\| + k(B) k - log \|sec x\|(C) k + log \|sin x\|(D) k - log \|sin x\|
Answer» Correct option is: (A) log \|sec x\| + k Correct option is (A):-\(\underline{\rm\log \|\sec x\|+k}\)

Discussion

22.	∫ sec23xdx =(A) \(k+\frac{sec^23x}{3}\)(B) \(k+\frac{tan3x}{3}\)(C) tan3x + k(D) k - tan3x
Answer» Correct option is: (B) \(k+\frac{tan3x}{3}\) Use Integration by Substitution. Let u=3x, du=3 dx , then \(\rm dx=\dfrac{1}{3} \) Using u and du above, rewrite ∫ sec²(3x) dx. \(\\\displaystyle \implies\rm\int \dfrac{\sec^{2}u}{3} \, du\) \(\\\displaystyle \implies \rm\dfrac{1}{3}\int \sec^{2}u \, du\) \(\\ \implies \rm \dfrac{\tan u}{3}\) Substitute u=3x back into the original integral. \(\\ \implies \rm\dfrac{\tan{3x}}{3}\) \(\\ \bigstar\quad\boxed{\rm\dfrac{\tan{3x}}{3}+k}\quad\bigstar\) Hence,Correct option is (B)

Discussion

23.	The direction cosines of the z-axis are(A) (0, 0, 0)(B) (1, 0, 0)(C) (0, 1, 0)(D) (0, 0, 1)
Answer» Correct option is: (D) (0, 0, 1)

Discussion

24.	The minimum value of z = 2x + 3y subject to x + y ≤ 2, x ≥ 0, y ≥ 0 is(A) 10(B) 6(C) 4(D) 0
Answer» Correct option is: (D) 0

Discussion

25.	At which of the following points, Z = 12x + 13y has the minimum value subject to constraints x + y ≤ 3, x ≥ 0, y ≥ 0 ?(A) (3, 0)(B) (0, 3)(C) (0, 0)(D) none of these
Answer» Correct option is: (C) (0, 0)

Discussion

26.	The function f(x) = \(\begin{cases} \frac{e^{3x}-e^{-5x}}{x}&, \quad \text{if } x≠0\\ k &, \quad \text{if } x=0 \end{cases}\) is continuous at x = 0 for the value of k,as :{(e3x-e-5x)/x, if x ≠ 0 k, if x = 0(a) 3(b) 5(c) 2(d) 8
Answer» Option : (d) 8 Answer (d) 8 . . .

26.

The function f(x) = \(\begin{cases} \frac{e^{3x}-e^{-5x}}{x}&, \quad \text{if } x≠0\\ k &, \quad \text{if } x=0 \end{cases}\) is continuous at x = 0 for the value of k,as :{(e3x-e-5x)/x, if x ≠ 0 k, if x = 0(a) 3(b) 5(c) 2(d) 8

Answer»

Option : (d) 8

Answer (d) 8

.

Discussion

27.	A Linear Programming Problem is as follows :Minimise z = 2x + ySubject to the constraints x ≥ 3, x ≤ 9, y ≥ 0 x - y ≥ 0, x + y ≤ 14The feasible region has :(a) 5 corner points including (0,0) and (9,5)(b) 5 corner points including (7,7) and (3,3)(c) 5 corner points including (14,0) and (9,0)(d) 5 corner points including (3,6) and (9,5)
Answer» Option : (b) 5 corner points including (7,7) and (3,3)

Discussion

28.	Let set X = {1,2,3} and a relation R is defined in X as : R = {(1,3),(2,2),(3,2)}, then minimum ordered pairs which should be added in relation R to make it reflexive and symmetric are :(a) {(1,1),(2,3),(1,2)}(b) {(3,3),(3,1),(1,2)}(c) {(1,1),(3,3),(3,1),(2,3)}(d) {(1,1),(3,3),(3,1),(1,2)}
Answer» Option : (c) {(1,1),(3,3),(3,1),(2,3)}

Discussion

29.	If a matrix A is both symmetric and skew symmetric, then A is necessarily a :(a) Diagonal matrix(b) Zero square matrix(c) Square matrix(d) Identity matrix
Answer» Option : (b) Zero square matrix

Discussion

30.	If (x2 + y2)2 = xy, then dy/dx is :(a) \(\frac{y+4x(x^2+y^2)}{4y(x^2+y^2)-x}\)(b) \(\frac{y-4x(x^2+y^2)}{x+4(x^2+y^2)}\) (c) \(\frac{y-4x(x^2+y^2)}{4y(x^2+y^2)-x}\) (d) \(\frac{4y(x^2+y^2)-x}{y-4x(x^2+y^2)}\)
Answer» Option : (c) \(\frac{y-4x(x^2+y^2)}{4y(x^2+y^2)-x}\)

Discussion

31.	The principal value of cos-1(1/2) + sin-1(-(1/√2)) is :(a) \(\frac{\pi}{12}\) (b) π(c) \(\frac{\pi}{3}\) (d) \(\frac{\pi}{6}\)
Answer» Option : (a) \(\frac{\pi}{12}\)

Discussion

32.	Three points P(2x, x+3), Q(0,x) and R(x+3,x+6) are collinear, then x is :(a) 0(b) 2(c) 3(d) 1
Answer» Option : (d) 1

Discussion

33.	An urn contains 3 white and 6 red balls. Four balls are drawn one by onewith replacement from the urn. Find the probability distribution of the number of red ballsdrawn. Also find mean and variance of the distribution.
Answer» There are total 9 balls Success:drawing a red ball. `n=4,P=6/9=2/3,q=1/3` P(r red balls)=P(X=r) `=nC_rP^rQ^(n-r)=4C_r(2/3)^r(1/3)^(4-r)` `=4C_r2^r/3^4` Mean=`sumx_iP_i` `=0+8/81+(224)/81+(332)/81+(416)/81` `=(0+8+48+96+64)/81=2.66` Variance=`sumx_i^2P(x=x_i)-mu^2` `=(0+8+96+288+256-276)/81` `=124/27`.

Discussion

34.	The points on the curve x2 /9 + y2 /25 = 1, where tangent is parallel to x-axis are :(a) (±5, 0) (b) (0, ±5) (c) (0, ±3) (d) (±3, 0)
Answer» Option : (b) (0, ±5)

Discussion

35.	Write the number of all possible matrices of order `2xx2`with each entry `1,2,or3.`
Answer» A `2xx2` order matrix will contain `4` elements. We have to create these matrices using `3` numbers that are `1`,`2` or `3`. So, total number of all possible matrices are `3^4 = 81`. Some of the examples of such matrices are, `[[1,2],[2,3]],[[1,1],[2,2]],[[3,3],[1,1]],` `[[1,1],[1,1]],[[2,2],[2,2]],[[3,3],[3,3]].` Similarly, we can create `81` matrices with these three numbers.

Discussion

36.	If siny = xcos(a+y), then dx/dy is :(a) \(\frac{cos\,a}{cos^2(a+y)}\)(b) \(\frac{-cos\,a}{cos^2(a+y)}\)(c) \(\frac{cos\,a}{sin^2y}\)(d) \(\frac{-cos\,a}{sin^2y}\)
Answer» Option : (a) \(\frac{cos\,a}{cos^2(a+y)}\)

Discussion

37.	A function f : R → R is defined as f(x) = x3 + 1. Then the function has :(a) no minimum value (b) no maximum value (c) both maximum and minimum value (d) neither maximum value nor minimum value
Answer» Option : (d) neither maximum value nor minimum value

Discussion

38.	The number of all possible matrices of order 2 x 3 with each entry 1 or 2 is :(a) 16 (b) 6 (c) 64 (d) 24
Answer» Option : (c) 64

Discussion

39.	If E and F are two events such that P(E) = 1/4, p(F) = 1/2 and p (E and F) = 1/8 P(not E and not F).
Answer» P(not E) = 3/4 P(not F) = 1/2 P(not E or not F) = 7/8 P(not E or not F) = 3/8

39.

If E and F are two events such that P(E) = 1/4, p(F) = 1/2 and p (E and F) = 1/8 P(not E and not F).

Answer»

P(not E) = 3/4 P(not F) = 1/2

P(not E or not F) = 7/8

P(not E or not F) = 3/8

Discussion

40.	Let A = {1. 2. 3……… 141. Define a relation R from A to A by R = {(x, y): 3x – y = 0 x,y ε A}. Write ‘R’ in roaster form, write its Domain and Range.
Answer» y = 3 x R = {(1,3),(2,6), (3,9), (4, 12)} Domain of R = {1, 2, 3, 4} Range of R = {3, 6, 9, 12) Codomain of R = {1, 2, 3, ….. 14}

40.

Let A = {1. 2. 3……… 141. Define a relation R from A to A by R = {(x, y): 3x – y = 0 x,y ε A}. Write ‘R’ in roaster form, write its Domain and Range.

Answer»

y = 3 x R = {(1,3),(2,6), (3,9), (4, 12)}

Domain of R = {1, 2, 3, 4}

Range of R = {3, 6, 9, 12)

Codomain of R = {1, 2, 3, ….. 14}

Discussion

41.	Differential of log [log(log x5 )] w.r.t. x is :(a) \(\frac{5}{x\,log\,(x^5)\,log\,(log\,x^5)}\)(b) \(\frac{5}{x\,log\,(log\,x^5)}\)(c) \(\frac{5x^4}{log\,(x^5)\,log\,(log\,x^5)}\)(d) \(\frac{5x^4}{log\,x^5\,log\,(log\,x^5)}\)
Answer» Option : (a) \(\frac{5}{x\,log\,(x^5)\,log\,(log\,x^5)}\)

Discussion

42.	Find the general solution of 2cos2x + 3sinx = 0.
Answer» 2cos²2x + 3sinx = 0 2(1 – sin²2x) + 3sinx = 0 2 – 2sin²2x + 3sinx = 0 2sin²2x – 3sinx – 2 = 0 2sin²2x – 4sinx + sinx – 2 = 0 2sin x(sin x – 2)+1 (sinx – 2) = 0 (sin x – 2)(2sin x + 1) = 0 sin x – 2 = 0 or 2 sin x + 1 = 0 sin x = 2 or sin x = -1/2

42.

Find the general solution of 2cos2x + 3sinx = 0.

Answer»

2cos²2x + 3sinx = 0

2(1 – sin²2x) + 3sinx = 0

2 – 2sin²2x + 3sinx = 0

2sin²2x – 3sinx – 2 = 0

2sin²2x – 4sinx + sinx – 2 = 0

2sin x(sin x – 2)+1 (sinx – 2) = 0

(sin x – 2)(2sin x + 1) = 0

sin x – 2 = 0 or 2 sin x + 1 = 0

sin x = 2 or sin x = -1/2

Discussion

43.	If E and F are the evens such that P(E) = 1/4, P(F) = 1/2 and P(E and F) = 1/8. Find (i) P (E or F) (ii) P (not E and not F)
Answer» (i) P(E or F) = P(E ∪ F) = P(E) + P(F) - P(E ∩ F) = 1/4 + 1/2 - 1/7 = (7 + 14 - 4)/28 = [17/28] (ii) P(E' ∩ F') = P(E ∪ F)' = 1 - P(E ∪ F) = 1 - 17/28 = 11/28

43.

If E and F are the evens such that P(E) = 1/4, P(F) = 1/2 and P(E and F) = 1/8. Find (i) P (E or F) (ii) P (not E and not F)

Answer»

(i) P(E or F) = P(E ∪ F) = P(E) + P(F) - P(E ∩ F)

= 1/4 + 1/2 - 1/7 = (7 + 14 - 4)/28 = [17/28]

(ii) P(E' ∩ F') = P(E ∪ F)' = 1 - P(E ∪ F) = 1 - 17/28 = 11/28

Discussion

44.	A group consists of 5 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has at least one boy and one girl.
Answer» Number of ways of selecting 1B and 4G = ⁷C₁ × ⁵C₄ = 35 2B and 36 =⁷C₂ × ⁵C₃ = 210 3B and 2G = ⁷C₃ × ⁵C₂ = 350 4B and 1G = ⁷C₄ × ⁵C₁ = 175 (+) Total number of selections = 770.

44.

A group consists of 5 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has at least one boy and one girl.

Answer»

Number of ways of selecting

1B and 4G = ⁷C₁ × ⁵C₄ = 35

2B and 36 =⁷C₂ × ⁵C₃ = 210

3B and 2G = ⁷C₃ × ⁵C₂ = 350

4B and 1G = ⁷C₄ × ⁵C₁ = 175 (+)

Total number of selections = 770.

Discussion

45.	The intersection of any two disjoint sets If \( (2)^{x+1}=(3)^{1-x} \), find the value of \( x \)
Answer» 2^{x + 1} = 3 ^{1 - x} ⇒ 2^x. 2 = 3.3^-x ⇒ 2^x . 3^x = 3/2 (On multiplying both sides by 3^x) ⇒ 6^x = 3/2 (\(\because\) a^xb^x = ab^x) ⇒ x = log₆3/2 ⇒ x = \(\frac{log 3-log 2}{log 6}\) = \(\frac{0.4771-0.3010}{0.778}\) = \(\frac{0.1761}{0.778}\) = 0.226

45.

The intersection of any two disjoint sets If \( (2)^{x+1}=(3)^{1-x} \), find the value of \( x \)

Answer»

2^{x + 1} = 3 ^{1 - x}

⇒ 2^x. 2 = 3.3^-x

⇒ 2^x . 3^x = 3/2 (On multiplying both sides by 3^x)

⇒ 6^x = 3/2 (\(\because\) a^xb^x = ab^x)

⇒ x = log₆3/2

⇒ x = \(\frac{log 3-log 2}{log 6}\) = \(\frac{0.4771-0.3010}{0.778}\)

= \(\frac{0.1761}{0.778}\) = 0.226

Discussion

46.	Solve the equation x2 + x/√2 + 1 = 0
Answer» x = (- 1 ± √(1 - 8))/2√2 ⇒ x = (-1 √7i)/2√2

46.

Solve the equation x2 + x/√2 + 1 = 0

Answer»

x = (- 1 ± √(1 - 8))/2√2

⇒ x = (-1 √7i)/2√2

Discussion

47.	A bag contain 9 discs of which 4 are red, 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the Probability that it will be (i) red (ii) yellow (iii) blue
Answer» Total ball = 4 Red + 3 blue + 2 yellow = 9 ball (i) P (red ball) = 4/9 (ii) P (Yellow) = 2/9 (iii) P (blue) = 3/9 = 1/3.

47.

A bag contain 9 discs of which 4 are red, 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the Probability that it will be (i) red (ii) yellow (iii) blue

Answer»

Total ball = 4 Red + 3 blue + 2 yellow = 9 ball

(i) P (red ball) = 4/9

(ii) P (Yellow) = 2/9

(iii) P (blue) = 3/9 = 1/3.

Discussion

48.	Insert 3 arithmetic means between 8 & 24.
Answer» a_n = a + (n + 1)d 24 = 8 + (y – 1)d ∴ 16 = 4d ⇒ d=4 3Means are [12,16, 20 ]

48.

Insert 3 arithmetic means between 8 & 24.

Answer»

a_n = a + (n + 1)d

24 = 8 + (y – 1)d

∴ 16 = 4d ⇒ d=4

3Means are [12,16, 20 ]

Discussion

49.	Find the equation of the parabola with vertex at the origin, axis along x – axis and passing through the point (2, 3) also find its focus,
Answer» y² = 4ax, (2,3) ⇒ 9 = 4a(2) ⇒ a = 9/8 Equn. is y² = 4(9/8) x ⇒ y² = 9/2x Focus = (9/8, 0)

49.

Find the equation of the parabola with vertex at the origin, axis along x – axis and passing through the point (2, 3) also find its focus,

Answer»

y² = 4ax, (2,3) ⇒ 9 = 4a(2) ⇒ a = 9/8

Equn. is y² = 4(9/8) x ⇒ y² = 9/2x Focus = (9/8, 0)

Discussion

50.	One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally. likely, calculate the probability that the card will be (a) a diamond (b) not a diamond (c) a black card
Answer» (i) Let A: Card drawn is diamond. ∴ n(A) = 13 → favourable number of events. P(A) = (favourable number of events)/(total number of events) = 13/52 = 1/4 (ii) P(Ā ) = P(not A) = 1 – P(A) = 1 – 1/4 = 3/4 (iii) There are 26 black cards ∴ P(black) = 522

50.

One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally. likely, calculate the probability that the card will be (a) a diamond (b) not a diamond (c) a black card

Answer»

(i) Let A: Card drawn is diamond.

∴ n(A) = 13 → favourable number of events.

P(A) = (favourable number of events)/(total number of events) = 13/52 = 1/4

(ii) P(Ā ) = P(not A) = 1 – P(A) = 1 – 1/4 = 3/4

(iii) There are 26 black cards

∴ P(black) = 522

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If a pressure of 400 Pa acts on 20 m2 area, what is the value force?(a) 2 KN(b) 4 KN(c) 6KN(d) 8KN

This is not an advantage of Centrifugal compressor(a) Maintenance cost is low (b) Less space required (c) Free from vibrations (d) Suitable for very high compression

Zero percent relative saturation means(a) 100 % vapour in the air(b) 75% vapour in the air(c) 50% vapour in the air(d) No vapour in the air

When the air temperature rises the saturation mixing ratio(a) Increases(b) Decreases(c) Remains same(d) None of the mentioned

The density of liquid A is 1.6 g cm-3 and its height h(A) = 16.9 cm, then the density of oil B of height h(B) = 30 cm in the U-tube is about(a) 0.90 g/cm3(b) 1.12 g/cm3(c) 2.24 g/cm3(d) 3.54 g/cm3

Pressure can`t be expressed as(a) N/m2(b) Pa/m2(c) atm(d) mm of Hg

What is the value of P`r?(a) 1.11(b) 2.11(c) 3.11(d) 4.11

ε = ∆ϕ/∆t, to which law does this equation refer ?

Change in temperature on Fahrenheit scale is?(a) 1.389 ˚F(b) 37.72˚F(c) 460 ˚F(d) None of the mentioned

An object is once immersed in oil and once in water. The loss in weight would be(a) More in water(b) More in oil(c) Equal in both oil and water(d) None of the mentioned

A technique of estimating physical properties of compound by using properties of molecular group of elements in the compound. Is called(a) Group contribution method(b) Generalized group method(c) Kay`s Method(d) None of the mentioned

Which is used to prevent damage due to overloading of current ?

Representation of the different phase of a compound on a two or three dimensional graph is(a) Block diagram(b) Equilibrium diagram(c) Phase diagram(d) None of the mentioned

Boiling temperature of water in Fahrenheit scale is(a) 112(b) 213(c) 212(d) 121

Boiling occurs at ________ temperature and _______ pressure, the process appears as a point in ____ diagram.(a) Constant, constant, P-T(b) Variable, constant, P-T(c) Constant, variable, V-T(d) Variable, variable, V-T

For a given system, number of variables is 6 and number of equations is 4. What is the number of degrees of freedom?(a) 2(b) 4(c) 6(d) 8

Which protection device is used in circuit to prevent the filter from overloading current? (a) MCB (b) RCCB (c) Fuse (d) ELCB

\( \begin{bmatrix}5 &amp; 7 &amp; 2 \\[0.3em]0 &amp; 1 &amp; 0 \\[0.3em]0 &amp; 0 &amp; 0\end{bmatrix}=\)(A) 5(B) 16(C) 21(D) 0

Find 17th term of sequence whos: nth term is given by a = 4n – 3. term of sequence whos

∫ tanx dx =(A) log |sec x| + k(B) k - log |sec x|(C) k + log |sin x|(D) k - log |sin x|

∫ sec23xdx =(A) \(k+\frac{sec^23x}{3}\)(B) \(k+\frac{tan3x}{3}\)(C) tan3x + k(D) k - tan3x

The direction cosines of the z-axis are(A) (0, 0, 0)(B) (1, 0, 0)(C) (0, 1, 0)(D) (0, 0, 1)

The minimum value of z = 2x + 3y subject to x + y ≤ 2, x ≥ 0, y ≥ 0 is(A) 10(B) 6(C) 4(D) 0

At which of the following points, Z = 12x + 13y has the minimum value subject to constraints x + y ≤ 3, x ≥ 0, y ≥ 0 ?(A) (3, 0)(B) (0, 3)(C) (0, 0)(D) none of these

The function f(x) = \(\begin{cases} \frac{e^{3x}-e^{-5x}}{x}&amp;, \quad \text{if } x≠0\\ k &amp;, \quad \text{if } x=0 \end{cases}\) is continuous at x = 0 for the value of k,as :{(e3x-e-5x)/x, if x ≠ 0 k, if x = 0(a) 3(b) 5(c) 2(d) 8

Let set X = {1,2,3} and a relation R is defined in X as : R = {(1,3),(2,2),(3,2)}, then minimum ordered pairs which should be added in relation R to make it reflexive and symmetric are :(a) {(1,1),(2,3),(1,2)}(b) {(3,3),(3,1),(1,2)}(c) {(1,1),(3,3),(3,1),(2,3)}(d) {(1,1),(3,3),(3,1),(1,2)}

If a matrix A is both symmetric and skew symmetric, then A is necessarily a :(a) Diagonal matrix(b) Zero square matrix(c) Square matrix(d) Identity matrix

If (x2 + y2)2 = xy, then dy/dx is :(a) \(\frac{y+4x(x^2+y^2)}{4y(x^2+y^2)-x}\)(b) \(\frac{y-4x(x^2+y^2)}{x+4(x^2+y^2)}\) (c) \(\frac{y-4x(x^2+y^2)}{4y(x^2+y^2)-x}\) (d) \(\frac{4y(x^2+y^2)-x}{y-4x(x^2+y^2)}\)

The principal value of cos-1(1/2) + sin-1(-(1/√2)) is :(a) \(\frac{\pi}{12}\) (b) π(c) \(\frac{\pi}{3}\) (d) \(\frac{\pi}{6}\)

Three points P(2x, x+3), Q(0,x) and R(x+3,x+6) are collinear, then x is :(a) 0(b) 2(c) 3(d) 1

An urn contains 3 white and 6 red balls. Four balls are drawn one by onewith replacement from the urn. Find the probability distribution of the number of red ballsdrawn. Also find mean and variance of the distribution.

The points on the curve x2 /9 + y2 /25 = 1, where tangent is parallel to x-axis are :(a) (±5, 0) (b) (0, ±5) (c) (0, ±3) (d) (±3, 0)

Write the number of all possible matrices of order `2xx2`with each entry `1,2,or3.`

If siny = xcos(a+y), then dx/dy is :(a) \(\frac{cos\,a}{cos^2(a+y)}\)(b) \(\frac{-cos\,a}{cos^2(a+y)}\)(c) \(\frac{cos\,a}{sin^2y}\)(d) \(\frac{-cos\,a}{sin^2y}\)

A function f : R → R is defined as f(x) = x3 + 1. Then the function has :(a) no minimum value (b) no maximum value (c) both maximum and minimum value (d) neither maximum value nor minimum value

The number of all possible matrices of order 2 x 3 with each entry 1 or 2 is :(a) 16 (b) 6 (c) 64 (d) 24

If E and F are two events such that P(E) = 1/4, p(F) = 1/2 and p (E and F) = 1/8 P(not E and not F).

Let A = {1. 2. 3……… 141. Define a relation R from A to A by R = {(x, y): 3x – y = 0 x,y ε A}. Write ‘R’ in roaster form, write its Domain and Range.

Differential of log [log(log x5 )] w.r.t. x is :(a) \(\frac{5}{x\,log\,(x^5)\,log\,(log\,x^5)}\)(b) \(\frac{5}{x\,log\,(log\,x^5)}\)(c) \(\frac{5x^4}{log\,(x^5)\,log\,(log\,x^5)}\)(d) \(\frac{5x^4}{log\,x^5\,log\,(log\,x^5)}\)

Find the general solution of 2cos2x + 3sinx = 0.

If E and F are the evens such that P(E) = 1/4, P(F) = 1/2 and P(E and F) = 1/8. Find (i) P (E or F) (ii) P (not E and not F)

A group consists of 5 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has at least one boy and one girl.

The intersection of any two disjoint sets If \( (2)^{x+1}=(3)^{1-x} \), find the value of \( x \)

Solve the equation x2 + x/√2 + 1 = 0

A bag contain 9 discs of which 4 are red, 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the Probability that it will be (i) red (ii) yellow (iii) blue

Insert 3 arithmetic means between 8 &amp; 24.

Find the equation of the parabola with vertex at the origin, axis along x – axis and passing through the point (2, 3) also find its focus,

One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally. likely, calculate the probability that the card will be (a) a diamond (b) not a diamond (c) a black card

Boiling occurs at ____ temperature and _ pressure, the process appears as a point in __ diagram.(a) Constant, constant, P-T(b) Variable, constant, P-T(c) Constant, variable, V-T(d) Variable, variable, V-T

\( \begin{bmatrix}5 & 7 & 2 \\[0.3em]0 & 1 & 0 \\[0.3em]0 & 0 & 0\end{bmatrix}=\)(A) 5(B) 16(C) 21(D) 0

The function f(x) = \(\begin{cases} \frac{e^{3x}-e^{-5x}}{x}&, \quad \text{if } x≠0\\ k &, \quad \text{if } x=0 \end{cases}\) is continuous at x = 0 for the value of k,as :{(e3x-e-5x)/x, if x ≠ 0 k, if x = 0(a) 3(b) 5(c) 2(d) 8

Insert 3 arithmetic means between 8 & 24.