100525 + Interview Questions in GENERAL QA IN GENERAL AWARENESS Page 293 InterviewSolution

14601.	Last step of accounting process is :A. Provide information to various parties who are interested in business enterprise.B. Record transactions in the books.C. To make summary in the form of financial statements.D. To classify the transactions under separate heads in the ledger.
Answer» Correct Answer - A

Discussion

14602.	In case of laying gullies, siphons, intercepting traps, the cost also includes __________(a) setting and laying(b) bed concreting(c) connection to drains(d) setting, laying, bed concreting and connection to drains
Answer» Correct answer is (d) setting, laying, bed concreting and connection to drains To elaborate: A gully is a landform created by running water, eroding sharply into soil, typically on a hillside. Gullies resemble large ditches or small valleys, but are metres to tens of metres in depth and width. The word siphon is used to refer to a wide variety of devices that involve the flow of liquids through tubes. In a narrower sense, the word refers particularly to a tube in an inverted ‘U’ shape, which causes a liquid to flow upward, above the surface of a reservoir, with no pump, but powered by the fall of the liquid as it flows down the tube under the pull of gravity, then discharging at a level lower than the surface of the reservoir from which it came. Intercepting traps fitted in the length of a house drain, close to its connection to the sewer, which provides a water seal against foul gases rising up into the drain.

Discussion

14603.	Factory cost is not known as: a. Work Cost b. Industrial Cost c. Manufacturing Cost d. Production Cost
Answer» b. Industrial Cost Factory cost is not known as Industrial Cost. industrial cost

14603.

Factory cost is not known as: a. Work Cost b. Industrial Cost c. Manufacturing Cost d. Production Cost

Answer»

b. Industrial Cost

Factory cost is not known as Industrial Cost.

industrial cost

Discussion

14604.	Find the real numbers x and y if (x - iy)(3 + 5i) is the conjugate of -6 - 24i.1. 3, 32. -3, 33. 3, -34. None of these.
Answer» Correct Answer - Option 3 : 3, -3 Concept: The conjugate of the complex number a + bi is a - bi. Property of iota power: i² = -1 i⁴ = 1 Calculation: Given: (x - iy)(3 + 5i) is the conjugate of -6 - 24i According to the question, (x - iy)(3 + 5i) = -6 + 24i. ⇒ 3x + 5xi - 3yi - 5yi² = -6 + 24i ⇒ (3x + 5y) + (5x - 3y)i = -6 + 24i Comparing the real and imaginary parts, we get: 3x + 5y = -6 ...(1) 5x - 3y = 24 ...(2) Multiplying equation (1) by 3 and equation (2) by 5 and adding, we get: 9x + 25x = -18 + 120 34x = 102 x = 3 Using equation (1), we get: y = -3.

14604.

Find the real numbers x and y if (x - iy)(3 + 5i) is the conjugate of -6 - 24i.1. 3, 32. -3, 33. 3, -34. None of these.

Answer» Correct Answer - Option 3 : 3, -3

Concept:

The conjugate of the complex number a + bi is a - bi.

Property of iota power:

i² = -1

i⁴ = 1

Calculation:

Given: (x - iy)(3 + 5i) is the conjugate of -6 - 24i

According to the question, (x - iy)(3 + 5i) = -6 + 24i.

⇒ 3x + 5xi - 3yi - 5yi² = -6 + 24i

⇒ (3x + 5y) + (5x - 3y)i = -6 + 24i

Comparing the real and imaginary parts, we get:

3x + 5y = -6 ...(1)

5x - 3y = 24 ...(2)

Multiplying equation (1) by 3 and equation (2) by 5 and adding, we get:

9x + 25x = -18 + 120

34x = 102

x = 3

Using equation (1), we get:

y = -3.

Discussion

14605.	The reciprocal of a positive rational number is
Answer» The reciprocal of a positive rational number is always negative.

Discussion

14606.	Frame a quadratic equation whose one root is √5+√2
Answer» Given that one root of the quadratic equation is √5 + √2. ∴ Other root of the quadratic equation is √5 - √2. ∴ Required quadratic equation is (x - (√5 + √2)) (x - (√5 - √2)) = 0 ⇒ ((x - √5) - √2) ((x - √5) + √2) = 0 ⇒ (x - √5)² - 2 = 0 (∵ (a-b) (a+b) = a² - b²) ⇒ x² - 2√5x + 5 - 2 = 0 (∵ (a - b)² = a² - 2ab + b²) ⇒ x² - 2√5x + 3 = 0

14606.

Frame a quadratic equation whose one root is √5+√2

Answer»

Given that one root of the quadratic equation is √5 + √2.

∴ Other root of the quadratic equation is √5 - √2.

∴ Required quadratic equation is (x - (√5 + √2)) (x - (√5 - √2)) = 0

⇒ ((x - √5) - √2) ((x - √5) + √2) = 0

⇒ (x - √5)² - 2 = 0 (∵ (a-b) (a+b) = a² - b²)

⇒ x² - 2√5x + 5 - 2 = 0 (∵ (a - b)² = a² - 2ab + b²)

⇒ x² - 2√5x + 3 = 0

Discussion

14607.	If [(x, 2),(18, x)] = [(6, 2),(18, 6)] then which is the value of x ?(A) 6 (B) –6 (C) ±6(D) None of these
Answer» The value of x = ±6

Discussion

14608.	If ∇= \(\begin{bmatrix}a_{11} & a_{12} & a_{13} \\[0.3em]a_{21} & a_{22} & a_{23} \\[0.3em]a_{31} & a_{32} & a_{33}\end{bmatrix}\) and Aij is co- factors of aij, then ∇ is equal to what?
Answer» if ∇ =\(\begin{bmatrix} a_{11} & a_{12} & a_{13} \\[0.3em] a_{21} & a_{22} & a_{23} \\[0.3em] a_{31} & a_{32} & a_{33} \end{bmatrix}\) and A_ij is co- factors of a_ij. ⇒ ∇= a₁₁\(\begin{bmatrix} a_{22} & a_{23} \\[0.3em] a_{32} & a_{33} \end{bmatrix}\)_-a₁₂\(\begin{bmatrix} a_{21} & a_{23} \\[0.3em] a_{31} & a_{33} \end{bmatrix}\)₊a₁₃\(\begin{bmatrix} a_{21} & a_{22} \\[0.3em] a_{31} & a_{32} \end{bmatrix}\)(By expanding determinant along row R₁) ⇒ ∇= a₁₁(-1)¹⁺¹\(\begin{bmatrix} a_{22} & a_{23} \\[0.3em] a_{32} & a_{33} \end{bmatrix}\) - a₁₂(−1) ¹⁺²\(\begin{bmatrix} a_{21} & a_{23} \\[0.3em] a_{31} & a_{33} \end{bmatrix}\)+ a₁₃(−1)¹⁺¹ \(\begin{bmatrix} a_{21} & a_{22} \\[0.3em] a_{31} & a_{32} \end{bmatrix}\). ⇒ ∇= a₁₁A₁₁ + a₁₂A₁₂+ a₁₃A₁₃. (By definition of cofactor of element of matrix. ) Also, if we expanding determinant along row R₂, we get ∇= a₂₁A₂₁ + a₂₂A₂₂ + a₂₃A₂₃. And if we expanding determinant along row R₃, we get ∇= a₃₁A₃₁ + a₃₂A₃₂ + a₃₃A₃₃. Therefore, we can write ∇ as ∇= a_i₁A_i₁ + a_i₂A_i₂ + a_i₃A_i₃, where 1 ≤ i≤ 3. Therefore, ∇ = \(\sum_{j}^{3}\) a_ijA_ij , where 1 ≤ i ≤ 3.

14608.

If ∇= \(\begin{bmatrix}a_{11} & a_{12} & a_{13} \\[0.3em]a_{21} & a_{22} & a_{23} \\[0.3em]a_{31} & a_{32} & a_{33}\end{bmatrix}\) and Aij is co- factors of aij, then ∇ is equal to what?

Answer»

if ∇ =\(\begin{bmatrix} a_{11} & a_{12} & a_{13} \\[0.3em] a_{21} & a_{22} & a_{23} \\[0.3em] a_{31} & a_{32} & a_{33} \end{bmatrix}\) and A_ij is co- factors of a_ij.

⇒ ∇= a₁₁\(\begin{bmatrix} a_{22} & a_{23} \\[0.3em] a_{32} & a_{33} \end{bmatrix}\)_-a₁₂\(\begin{bmatrix} a_{21} & a_{23} \\[0.3em] a_{31} & a_{33} \end{bmatrix}\)₊a₁₃\(\begin{bmatrix} a_{21} & a_{22} \\[0.3em] a_{31} & a_{32} \end{bmatrix}\)(By expanding determinant along row R₁)

⇒ ∇= a₁₁(-1)¹⁺¹\(\begin{bmatrix} a_{22} & a_{23} \\[0.3em] a_{32} & a_{33} \end{bmatrix}\) - a₁₂(−1) ¹⁺²\(\begin{bmatrix} a_{21} & a_{23} \\[0.3em] a_{31} & a_{33} \end{bmatrix}\)+ a₁₃(−1)¹⁺¹ \(\begin{bmatrix} a_{21} & a_{22} \\[0.3em] a_{31} & a_{32} \end{bmatrix}\).

⇒ ∇= a₁₁A₁₁ + a₁₂A₁₂+ a₁₃A₁₃. (By definition of cofactor of element of matrix. )

Also, if we expanding determinant along row R₂, we get ∇= a₂₁A₂₁ + a₂₂A₂₂ + a₂₃A₂₃.

And if we expanding determinant along row R₃, we get ∇= a₃₁A₃₁ + a₃₂A₃₂ + a₃₃A₃₃.

Therefore, we can write ∇ as ∇= a_i₁A_i₁ + a_i₂A_i₂ + a_i₃A_i₃, where 1 ≤ i≤ 3.

Therefore, ∇ = \(\sum_{j}^{3}\) a_ijA_ij , where 1 ≤ i ≤ 3.

Discussion

14609.	If Δ = [(a11, a12, a13),(a21, a22, a23),(a31, a32, a33)] and Aij is the co-factor of aij then which is the following value of Δ?(A) a11A11 – a21A21 + a31A31 (B) a11A12 + a21A22 + a31A32(C) a11A11 + a21A21 + a31A31 (D) A11 + A12 + A13
Answer» (C) a₁₁A₁₁ + a₂₁A₂₁ + a₃₁A₃₁

Discussion

14610.	In ∆MNP, ∠MNP = 90˚, seg NQ ⊥ seg MP, MQ = 9, QP = 4, find NQ.
Answer» NQ2 = MQ × QP ................. (Theorem of Geometric mean) = 9 × 4 = 36 ∴ NQ = 6

14610.

In ∆MNP, ∠MNP = 90˚, seg NQ ⊥ seg MP, MQ = 9, QP = 4, find NQ.

Answer»

NQ2 = MQ × QP ................. (Theorem of Geometric mean)

= 9 × 4

= 36

∴ NQ = 6

Discussion

14611.	Seg NQ is the bisector of ∠N of ∆MNP. If MN= 5, PN =7, MQ = 2.5 then find QP.
Answer» MN = 5, PN = 7, MQ = 2.5, QP = ? From the figure MN / NP = MQ / QP........(Angle bisector theorem) ∴ 5 / 2.5 = 7 / QP 5 × QP = 7 × 2.5 ∴ QP = 7. 25 / 5 ∴ QP = 3.5

14611.

Seg NQ is the bisector of ∠N of ∆MNP. If MN= 5, PN =7, MQ = 2.5 then find QP.

Answer»

MN = 5, PN = 7, MQ = 2.5, QP = ?

From the figure MN / NP = MQ / QP........(Angle bisector theorem)

∴ 5 / 2.5 = 7 / QP

5 × QP = 7 × 2.5

∴ QP = 7. 25 / 5

∴ QP = 3.5

Discussion

14612.	O is a point on side PQ of a APQR such that PO = QO = RO, then(a) RS² = PR × QR(b) PR² + QR² = PQ²(c) QR² = QO² + RO²(d) PO² + RO² = PR²
Answer» In ΔPQR , PO=OQ=RO (given) Now , in ΔPSR , PO=OR (given) ∴∠1=∠P [Angles opposite to equal sides in a triangle are equal] Similarly , in ∠ORQ , RO=OQ (given) ∠Q=∠2 Now , in ΔPQR , ∠P+∠Q+∠PRQ=180^∘ [By Angle sum property of a triangle] ⇒∠1+∠2+(∠1+∠2)=180^∘ ⇒2(∠1+∠2)=180^∘ ⇒∠1+∠2=90^∘ ⇒∠PRQ=90^∘ By Pythagoras theorem , we have PQ²=QR²+PQ² option B is correct

14612.

O is a point on side PQ of a APQR such that PO = QO = RO, then(a) RS² = PR × QR(b) PR² + QR² = PQ²(c) QR² = QO² + RO²(d) PO² + RO² = PR²

Answer»

In ΔPQR ,

PO=OQ=RO (given)

Now , in ΔPSR ,

PO=OR (given)

∴∠1=∠P [Angles opposite to equal sides in a triangle are equal]

Similarly , in ∠ORQ ,

RO=OQ (given)

∠Q=∠2

Now , in ΔPQR ,

∠P+∠Q+∠PRQ=180^∘

[By Angle sum property of a triangle]

⇒∠1+∠2+(∠1+∠2)=180^∘

⇒2(∠1+∠2)=180^∘

⇒∠1+∠2=90^∘

⇒∠PRQ=90^∘

By Pythagoras theorem , we have

PQ²=QR²+PQ²

option B is correct

Discussion

14613.	यदि किसी त्रिभुज के लम्ब केंद्र तथा केन्द्रक समान है, तब त्रिभुज ज्ञात करे?A. ScaleneB. Right anlgedC. EquilateralD. Obtuse
Answer» Correct Answer - C In Equilateral triangle Orthocenter, in center, circumcenter and centroid coincide

Discussion

14614.	किसी त्रिभुज के तीनो शीर्ष लम्बो की लम्बाई समान है। त्रिभुज है।A. obtuseB. EquilateralC. rightD. Isosceles
Answer» Correct Answer - B If three altitudes are equal then the triangle is Equilateral

Discussion

14615.	`angleA + 1/2 angleB+ angleC=140^(@)`, then `angleB` is `angleA +1/2angleB + angleC=140^(@)`, हे, तब `angleB` हे।A. `50^(@)`B. `80^(@)`C. `40^(@)`D. `60^(@)`
Answer» Correct Answer - B According to question, `angleA + 1/2 angleB+ angleC = 140^(@)`………….(i) As we know that `angleA+angleB+angleC=180^(@)` ……………(iii) Compare equation (i) and (ii) `1/2angleB= 40^(@)` `angleB=90^(@)`

Discussion

14616.	यदि एक त्रिभुज के तीनो कोण `(x+15)^(@)` और `(2x)/3+30^(@)` तो त्रिभुज क्या हे।A. isoscelesB. equilateralC. right angledD. scalene
Answer» Correct Answer - B According to question, `rArr (x+15^(@))+((6x)/5+6)^(@)+((2x)/3+30)^(@)` `=180^(@)` `angleA + angleB + angleC=180^(@)` `rArr x+(6x)/5+(2x)/3=180^(@)-(15+6+30)` `rArr 43x = 129 xx 15` `x=45^(@)` `rArr` Each angle `rArr (x+15)^(2)= 45+15 = 60^(@)` `rArr ((2x)/3+30)^(@)=60^(@)` `therefore` All three angles are equal `60^(@)` `therefore` Triangle will be equilateral triangle.

Discussion

14617.	`DeltaABC` में, यदि `2angleA=3angleB=6angleC` हे, `angleB` का मान हे।A. `60^(@)`B. `30^(@)`C. `45^(@)`D. `90^(@)`
Answer» Correct Answer - A According to question, Given, `2angleA= 3angleB` `(angleA)/(angleB)= 3/2` `(3angleB)=(6angleC)` `(angleB)/(angleC)= 6/3 = 2/1` To make anlge `angleB` same `therefore angleA : angleB: angleC` `3 : 2: 1` As we know that `angleA+angleB+angleC= 180^(@)` `x=30^(@)` `angleB =2x=60^(@)`

Discussion

14618.	What is the value of 'a' for the equation x2 + ax + 2a - 3 = 0 has real roots?1. a ∈ (-\(\rm \infty\), 2]2. a ∈ (2, 6)3. a ∈ (6, \(\rm \infty\))4. (-∞, 2] ∪ [6, ∞)
Answer» Correct Answer - Option 4 : (-∞, 2] ∪ [6, ∞) Concept: The roots of a quadratic equation ax² +bx + c = 0 are real if: b² - 4ac ≥ 0 Calculation: Given equation x2 + ax + 2a - 3 = 0 ⇒ x2 + ax + (2a - 3) = 0 So, for real roots: a² - 4 × 1 × (2a - 3) ≥ 0 ⇒ a² - 8a + 12 ≥ 0 ⇒ (a - 6)(a - 2) ≥ 0 ⇒ a ∈ (-∞, 2] ∪ [6, ∞)

14618.

What is the value of 'a' for the equation x2 + ax + 2a - 3 = 0 has real roots?1. a ∈ (-\(\rm \infty\), 2]2. a ∈ (2, 6)3. a ∈ (6, \(\rm \infty\))4. (-∞, 2] ∪ [6, ∞)

Answer» Correct Answer - Option 4 : (-∞, 2] ∪ [6, ∞)

Concept:

The roots of a quadratic equation ax² +bx + c = 0 are real if:

b² - 4ac ≥ 0

Calculation:

Given equation x2 + ax + 2a - 3 = 0

⇒ x2 + ax + (2a - 3) = 0

So, for real roots:

a² - 4 × 1 × (2a - 3) ≥ 0

⇒ a² - 8a + 12 ≥ 0

⇒ (a - 6)(a - 2) ≥ 0

⇒ a ∈ (-∞, 2] ∪ [6, ∞)

Discussion

14619.	What would be the area of a circle whose diameter is 35 cm?A. 962.5 sq cmB. 875.5 sq cmC. 981.5 sq cmD. 886.5 sq cm
Answer» Correct Answer - A Radius = 17.5 cm Area of the circle `=22/7xx17.5xx17.5=9.62.5 sq. cm`

Discussion

14620.	The perimeter of a square is thrice the perimeter of R rectangle. If the perimeter of the square is 84 cm and tllc length of the rectangle is 8 cm, what is the difference between the breadth of the rectangle and the side of the square?A. 15 cmB. 19 cmC. 10 cmD. 8 cm
Answer» Correct Answer - A Permeter of the square = 84 cm Perimeter of the rectangle = 28 cm Permeter of the rectangle = 2(l+b) or, 2(8 + b) = 28 cm or, b =14-8 = 6 cm `:. " Breadth of the rectangle "= 6 cm` Side of the square `=84/4=21 cm` Dofference = 21 - 6 = 15 cm

Discussion

14621.	One of the angles ofa parallelogram is 45°: What will be the sum of the larger angle and twice the smaller angle of the parallelogram?A. `228^@`B. `224^@`C. `225^@`D. `222^@`
Answer» Correct Answer - C Second angle of parallelogram =`180^@-45^@=135^@` `:. " Required value "=135^@+2^@xx45^@` `=135^@+90^@=225^@`

Discussion

14622.	A rightcircular cone and a right circular cylinder have equal base and equal height.If the radius of the base and the height are in the ratio 5 : 12, then theratio of the total surface area of the cylinder to that of the cone is(a) 3 : 1 (b) 13 : 9 (c) 17 : 9 (d) 34 : 9A. `3:1`B. `13:9`C. `17:9`D. `34:9`
Answer» Correct Answer - C let the radius of the base are 5k and 12k respectively `:.("Total surface area of the cylinder")/("Total surface area of the cone ")` `=(2pirxxh+2pir^2)/(pirsqrt(r^2+h^2+pir))` `=(2h+2r)/(sqrt(r^2+h^2)+r)+(24k+10k)/(sqrt(25k^2+144k^2)+5k)` `=(34k)/(13k+5k)=(34k)/(18k)=17/9or 17 :9`

Discussion

14623.	What would be the circumference of a circle whose area is 745.36 sq cm?A. 94.4cmB. 88.8cmC. 96.8cmD. 87.4cm
Answer» Correct Answer - C We know area, `pir^2=745.36` `rArr 22/7xxr^2=745.36` `rArr r^2=(745.36xx7)/22=237.16` `:.r=sqrt237.16=15.4 cm` `:. " Circumference of circle"=2p[ir=2xx22/7xx15.4` `=96.8 cm`

Discussion

14624.	A shopkeeper sells a Bulb to Nirmal earns 40% profit on it. Nirmal sells the Bulb to kamlesh at Rs. 630 at a loss of 10%. What is the cost price of the bulb?1. Rs. 3002. Rs. 5003. Rs. 7004. Rs. 9005. Rs. 100
Answer» Correct Answer - Option 2 : Rs. 500 Given: Profit of Shopkeeper = 40% Selling price of bulb for Nirmal = Rs. 630 Loss of Nirmal = 10% Formula Used: Cost price × (100 + Profit %)/100 = Selling price Cost price × (100 – Loss %)/100 = Selling price Calculation: Cost price of bulb for Nirmal = Selling Price of bulb for Shopkeeper ⇒ Cost price of bulb for Nirmal = (630 × 100)/(100 – 10) = Rs. 700 Selling Price of bulb for Shopkeeper = Rs. 700 ⇒ Cost price of bulb for shopkeeper = (700 × 100)/(100 + 40) = Rs. 500 ∴ Cost price of the bulb is Rs. 500.

14624.

A shopkeeper sells a Bulb to Nirmal earns 40% profit on it. Nirmal sells the Bulb to kamlesh at Rs. 630 at a loss of 10%. What is the cost price of the bulb?1. Rs. 3002. Rs. 5003. Rs. 7004. Rs. 9005. Rs. 100

Answer» Correct Answer - Option 2 : Rs. 500

Given:

Profit of Shopkeeper = 40%

Selling price of bulb for Nirmal = Rs. 630

Loss of Nirmal = 10%

Formula Used:

Cost price × (100 + Profit %)/100 = Selling price

Cost price × (100 – Loss %)/100 = Selling price

Calculation:

Cost price of bulb for Nirmal = Selling Price of bulb for Shopkeeper

⇒ Cost price of bulb for Nirmal = (630 × 100)/(100 – 10) = Rs. 700

Selling Price of bulb for Shopkeeper = Rs. 700

⇒ Cost price of bulb for shopkeeper = (700 × 100)/(100 + 40) = Rs. 500

∴ Cost price of the bulb is Rs. 500.

Discussion

14625.	The ratio of circumferences of two circles is 4:5 then the ratio of their areas is – (A) 4:5 (B) 5:4 (C) 16:25 (D) 25:16
Answer» Correct answer is (C) 16:25

Discussion

14626.	Ratio between curved surface area and total surface area of a circular cylinder is 3 : 5. If curved surface area is `7392 cm^3` then what is the height of cylinder.A. 48B. 21C. 47D. 42
Answer» Correct Answer - D According to question, `(2pirh)/(2pir(r+h))=3/5` `5h=3r+3h` `2h=3r and 2pirh=7392` `2xx22/7xx2/3hxxh=7392` `h=42` `:." Height of cylinder "=42 cm`

Discussion

14627.	The length of rectangular plot is thrice its breadth. If the area of the rectangular plot is 6075 sq. metres, what is its length?A. 145 metersB. 130 metersC. 75 metersD. 45 metres
Answer» Correct Answer - D Let breadth of rectangular plot is b cm length of rectangular plot, l = 3b `lxxb=6075` `rArr 3b^2=6075` `rArrb^2=2025` `rArrb=45` `:." Length of the side of the square" =3xx45 cm=35 cm`

Discussion

14628.	The ratio of the diameter of base and height of a cylinder is 3 : 5. Find the radius of the cyliner if the approximate volume of cylinder-is `5263 cm^3`?A. `21/2cm`B. `7/2 cm`C. `21 cm`D. `7.93 cm`
Answer» Correct Answer - D Let diameter of base be 3x cm & height of cylinder be 5x cm `:." radius"=(3x)/2=1.5x cm` we know, Volume of cylinder `=pir^2h (r to"radius", hto"height")` ATQ, `pir^2h=5263` `22/7xx(9x^2)/4xx5x=5263` `x=5.29 cm` Radius = 7.93 cm

Discussion

14629.	The sides of a triangular field are 41 m, 40 m and 9 m. The number of rose beds that can be prepared in the field if each rose bed, on an average, needs 900 square cm space,A. 2000B. 1800C. 900D. 800
Answer» Correct Answer - A Area of triangular field `sqrt(s(s-a)(s-b)(s-c))` `s=(a+b+c)/2=(41+40+9)/2=45m` `"Area"=sqrt(45xx(45-41)xx(45-40)xx(45-9))` `=sqrt(45xx4xx5xx36)=180m^2=1800000cm^2` Number of rose bed `=1800000/900=2000.`

Discussion

14630.	The circumference of a circle is 56 cm. Find the approximate area of square if the radius is two times of the side of a square.A. `18 cm^2`B. `32 cm^2`C. `25 cm^2`D. `20cm^2`
Answer» Correct Answer - D ATQ, `2pir=56 cm` `rArr2xx22/7xxr=56 m` `rArr r=(56xx7)/44=98/11 cm` Side of a square `=98/(2xx11)=49/11 cm` `:." Area of square"=("side")^2=(49/11)^2` `=2401/121~~20 cm^2`

Discussion

14631.	A slice from a circular pizza of diameter 14 inches is cut in a such a way that each slice of pizza has a central angle of `45^@`. What is the area of each slice of Pizza(in square inches)?A. 16.25B. 19.25C. 18.25D. 17.25
Answer» Correct Answer - B D = 14 `R=D/2=14/2=7` Area of each slice of Pizza `=pir^2 theta/360` `=(22/7)xx7xx7xx(45^@/360)` `=19.25`

Discussion

14632.	Two concentric circles are centred at O. The area of shaded region, if outer and inner radii are 14 cm and 7 cm respectively, is(a) 462 cm2 (b) 154 cm2 (c) 231 cm2 (d) 308 cm2
Answer» Correct answer is (a) 462 cm²

Discussion

14633.	`x=acostheta+bsintheta`and `y=asintheta-bcostheta,`show that `y^2(d^2y)/(dx^2)-x(dy)/(dx)+y=0`
Answer» `y = asintheta-bcostheta` `x = acostheta+bsintheta` `=>dx/(d theta) = -asintheta+bcostheta` `=>dy/(d theta) = ` `:.dy/dx = dy/(d theta)*(d theta)/dx = (acostheta+bsintheta)/(-asintheta+bcostheta)` `=>dy/dx = x/(-y)` `=>(d^2y)/dx^2 = (-y + xdy/dx)/y^2` `=>y^2(d^2y)/dx^2-xdy/dx+y =0`

Discussion

14634.	The electron affinity of sulphur is greater than oxygen .why
Answer» Due to small size and high electron density of oxygen compared to sulphur, interelectronic repulsion is higher in oxygen, resulting in less energy being released when an electron is added to oxygen, due to lesser stability after electron is added, which is due to the interelectronic repulsion in the small oxygen atom. Hence electron affinity value is lower. It is an abnormality and exception to the general periodic trend of electronic affinity values.

Discussion

14635.	Two blocks A and B of equal masses mkg each are connected by a light thread, which passes over a massless pulley as shown. Both the blocks lie on wedge of mass mkg. Assume friction to be absent everywhere and both the blocks to be always in contact with the wedge. The wedge lying over smooth horizontal surface is pulled towards right with constant acceleration a (m/s2). (g is acceleration due to gravity).Normal reaction (in N) acting on block A.(A) m/5(3g + 4a)(B) m/5(3g - 4a)(c) m/5(4g + 3a)(D) m/3(4g - 3a)
Answer» (D) m/3(4g - 3a)

Discussion

14636.	Two blocks A and B of equal masses mkg each are connected by a light thread, which passes over a massless pulley as shown. Both the blocks lie on wedge of mass mkg. Assume friction to be absent everywhere and both the blocks to be always in contact with the wedge. The wedge lying over smooth horizontal surface is pulled towards right with constant acceleration a (m/s2). (g is acceleration due to gravity).Normal reaction (in N) acting on block B is(A) m/5(3g + 4a)(B) m/5(3g - 4a)(c) m/5(4g + 3a)(D) m/3(4g - 3a)
Answer» (A) m/5(3g + 4a)

Discussion

14637.	Equal weights of Mercury and Iodine are allowed to react completely to form a mixture of Mercurous and mercuric iodide leaving none of the reactants. calculate the ratio by weight of Hg2I2 and HgI2 formed.(Hg=200 , I=127)
Answer» Lets take x gm of Hg and x gm of I2 present in the initial mixture Hg + I2 → HgI2 2Hg + I2 → Hg2I2 Actually mercuric iodide (HgI2) cant be made by reacting iodine with mercury. Pure Mercurous iodide actually forms when we add mercury to iodine . So the ratio is 1 : 0

14637.

Equal weights of Mercury and Iodine are allowed to react completely to form a mixture of Mercurous and mercuric iodide leaving none of the reactants. calculate the ratio by weight of Hg2I2 and HgI2 formed.(Hg=200 , I=127)

Answer»

Lets take x gm of Hg and x gm of I2 present in the initial mixture

Hg + I2 → HgI2

2Hg + I2 → Hg2I2

Actually mercuric iodide (HgI2) cant be made by reacting iodine with mercury. Pure Mercurous iodide actually forms when we add mercury to iodine . So the ratio is 1 : 0

Discussion

14638.	A box of mass 8 kg ios placed on a roulgh inclined plane of inclination `30^(@)` Its downward motion cn be prevented byu applying a horizontal force F, then value of F for which friction between the block and the incline surface is minimum isA. `80/sqrt(3)`B. `40sqrt(3)`C. `40/sqrt(3)`D. `80sqrt(3)`
Answer» Correct Answer - B

Discussion

14639.	A steam engine intakes 50g of steam at 100°C per minute and cools it down to 20°C. If latent heat of vaporization of steam is 540 cal g1, then the heat rejected by the steam engine per minute is × 103 cal.
Answer» Answer is 31 Heat rejected = mL_f + mSΔT = (50 x 540) + 50 (1) (100-20) = 31000 Cal = 31 x 10³ Cal

14639.

A steam engine intakes 50g of steam at 100°C per minute and cools it down to 20°C. If latent heat of vaporization of steam is 540 cal g1, then the heat rejected by the steam engine per minute is × 103 cal.

Answer»

Answer is 31

Heat rejected = mL_f + mSΔT

= (50 x 540) + 50 (1) (100-20)

= 31000 Cal

= 31 x 10³ Cal

Discussion

14640.	A thermodynamic process undergoes a cyclic process ABCDEBFGA as shown in the figure. Find the quantity of heat supplied to the system over one complete cycle. A. `(pi)/(4)`B. `(3pi)/(2)`C. `2 pi`D. `(5 pi)/(2)`
Answer» Correct Answer - C `Delta Q = Delta U + Delta W = Delta W` [ `:. Delta U = 0` (cyclic process) ] `= [pi ((3)/(2))^(2) - pi ((1)/(2))^(2)] = (pi)/(4) (9 - 1) = 6.28 J`

Discussion

14641.	An ideal gas is taken around the cycle ABCA as shown in P-V diagram. The net work done by the gas during the cycle is equal to : A. `12P_(1)V_(1)`B. `6P_(1)V_(1)`C. `5P_(1)V_(1)`D. `P_(1)V_(1)`
Answer» Correct Answer - 3 Work done by the gas in the cyclic process `=` Area bounded `(`ABCA`)=5P_(1)V_(1)`

Discussion

14642.	The time dependence of a physical quantity P is given by `P=P_(0) exp (-alpha t^(2))`, where `alpha` is a constant and t is time. The constant `alpha`A. Is dimensionlessB. Has dimensions `T^(-2)`C. Has dimensions of PD. Has dimensions `T^(2)`
Answer» Correct Answer - B `alphat^(2)` must be dimensionless

Discussion

14643.	Two bodies (M) and (N) of equal masses are suspended from two separate massless springs of spring constants (k_1) and (k_2) respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of (M) to the of (N) is.A. `(k_1)/(k_2)`B. `sqrt(k_1//k_2)`C. `(k_2)/(k_1)`D. `sqrt(k_2//k_1)`
Answer» Correct Answer - D Both the bodies oscillate in simple harmonic motion for which the maximum velocities will be `v_(1) = a_(1) omega_(1) = a_(1) xx (2 pi)/(T_(1))` `v_(2) = a_(2) omega_(2) = a_(2) xx (2 pi)/(T_(2))` Given that `v_(1) = v_(2)` `a_(1) xx (2pi)/(T_(1)) = a_(2) xx (2pi)/(T_(2))` `rArr (a_(1))/(a_(2)) = (T_(1))/(T_(2)) = (2 pi sqrt((m)/(k_(1))))/(2pi sqrt((m)/(k_(2)))) = sqrt((k_(2))/(k_(1)))`.

Discussion

14644.	A uniform rod of length (L) and mass (M) is pivoted at the centre. Its two ends are attached to two springs of equal spring constants (k). The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle (theta) in one direction and released. The frequency of oscillation is. ? .A. `(1)/(2 pi) sqrt((2 k)/(M))`B. `(1)/(2 pi) sqrt((k)/(M))`C. `(1)/(2 pi) sqrt((6 k)/(M))`D. `(1)/(2 pi) sqrt((24 k)/(M))`
Answer» Correct Answer - C Restoring torque `=-2xx k((l)/(2) theta)(l)/(2)=(I d^(2) theta)/(dt^(2))` `(d^(2) theta)/(dt^(2)) = ((kl^(2))/(2)(-theta))/((ml^(2))/(12))` `rArr omega = sqrt((6k)/(M))` `f = (omega)/(2pi) = (1)/(2 pi) sqrt((6k)/(m))`.

Discussion

14645.	A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (vertically). If the acceleration of the system is g/8, then the ratio of the masses is:(1) 8: 1 (2) 9: 7 (3) 4: 3 (4) 5: 3
Answer» (2) The ratio of the masses is 9 : 7. Explanation: Since the string is inextensible, therefore both the masses will have same acceleration a. Also, the string is frictionless and massless therefore it will have same tension at both the ends. Suppose m₂ is greater then m₁ which means m₂ is coming down and m₁ is going up. Using Newton's Second Law of motion on the block of mass m₁ T - m₁g = m₁a Again, applying the second law on the block of mass m₂ m₂g - T = m₂a Given that a = g/8 or g = 8a 8m₂a - T = m₂a T = 7m₂a Substitute this value of T in the first equation 7m₂a - 8m₁a = m₁a 7m₂ = 9m₁

14645.

A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (vertically). If the acceleration of the system is g/8, then the ratio of the masses is:(1) 8: 1 (2) 9: 7 (3) 4: 3 (4) 5: 3

Answer»

(2) The ratio of the masses is 9 : 7.

Explanation:

Since the string is inextensible, therefore both the masses will have same acceleration a. Also, the string is frictionless and massless therefore it will have same tension at both the ends.

Suppose m₂ is greater then m₁ which means m₂ is coming down and m₁ is going up.

Using Newton's Second Law of motion on the block of mass m₁

T - m₁g = m₁a

Again, applying the second law on the block of mass m₂

m₂g - T = m₂a

Given that a = g/8 or g = 8a

8m₂a - T = m₂a

T = 7m₂a

Substitute this value of T in the first equation

7m₂a - 8m₁a = m₁a

7m₂ = 9m₁

Discussion

14646.	Two masses A and B of 3kg and 2kg are connected by a long inextensible string which passes over a massless and frictionless pulley. Initially the height of both the masses from the ground is same and equal to 1 metre. When the masses are released. Mass A hits the ground and gets stuck to the ground. Consider the length of the string as large, so that the pulley does not obstruct the motion of masses A and B `[g = 10 m//s^(2)]` A. The impulse A exerts on ground is `6N-S`B. The impulse A exerts on ground is 2N-SC. B reaches a maximum height of 2.2 m from the groundD. B reaches maximum height from the ground 1.2 sec after being released.
Answer» Correct Answer - A::C::D `a=(3-2)/(3+2)g=2m//s^(2)` gtbrgt `V^(2)=u^(2)+2as rArr V^(2)=2xx2xx1 rArr V=2m//s` Impulse A exterts `J = 3 xx 2 = 6N-S` For block B, `0 - (2)^(2) = 2(-10)S` `S = 0.2 m` `S = ut(1) + (1)/(2) at_(1)^(2)` `1 = (1)/(2) 2t_(1)^(2)" "t_(2) = 0.2 S`

Discussion

14647.	Two men of unequal masses hold on to the two sections of a light rope passing over a smooth light pulley. Which of the following are possible? (A) The lighter man is stationary while the heavier man slides with some acceleration (B) The heavier man is stationary while the lighter man climbs with some acceleration (C) The two men slide with the same acceleration in the same direction (D) The two men move with accelerations of the same magnitude in opposite directions
Answer» A) The lighter man is stationary while the heavier man slides with some acceleration (B) The heavier man is stationary while the lighter man climbs with some acceleration (D) The two men move with accelerations of the same magnitude in opposite directions

14647.

Two men of unequal masses hold on to the two sections of a light rope passing over a smooth light pulley. Which of the following are possible? (A) The lighter man is stationary while the heavier man slides with some acceleration (B) The heavier man is stationary while the lighter man climbs with some acceleration (C) The two men slide with the same acceleration in the same direction (D) The two men move with accelerations of the same magnitude in opposite directions

Answer»

A) The lighter man is stationary while the heavier man slides with some acceleration

(B) The heavier man is stationary while the lighter man climbs with some acceleration

(D) The two men move with accelerations of the same magnitude in opposite directions

Discussion

14648.	The diagram shows particles A and B, of masses 0.2kg and mkg respectively, connected by a light inextensible string which passes over a fixed smooth peg. The system is released from rest, with B at a height of 0.25m above the floor. B descends, hitting the floor 0.5s later. All resistance to motion may be ignored. (a) Find the acceleration of B as it descends. (b) Find the tension in the string while B is descending and find also the value of m. (c) When B hits the floor it comes to rest immediately, and the string becomes slack. Find the length of time for which B remains at rest on the ground before being jerked into motion again.
Answer» (a) 2 ms^-2 , (b) 2.4 N, 0.3 (c) 0.2 s

Discussion

14649.	A block of weight W is suspended from a spring balance. The lower surface of the block rests on a weighing machine. The spring balance reads W1 and the weighing machine reads W2. (W, W1, W2 are in the same unit): (A) W = W1 + W2 if the system is at rest (B) W > W1 + W2 if the system moves down with some acceleration (C) W1 > W2 if the system moves up with some acceleration (D) no relation between W1 and W2 can be obtained with the given description of the system
Answer» (A) W = W₁+ W₂ if the system is at rest (B) W > W₁ + W₂ if the system moves down with some acceleration (D) no relation between W₁ and W₂ can be obtained with the given description of the system

14649.

A block of weight W is suspended from a spring balance. The lower surface of the block rests on a weighing machine. The spring balance reads W1 and the weighing machine reads W2. (W, W1, W2 are in the same unit): (A) W = W1 + W2 if the system is at rest (B) W > W1 + W2 if the system moves down with some acceleration (C) W1 > W2 if the system moves up with some acceleration (D) no relation between W1 and W2 can be obtained with the given description of the system

Answer»

(A) W = W₁+ W₂ if the system is at rest

(B) W > W₁ + W₂ if the system moves down with some acceleration

(D) no relation between W₁ and W₂ can be obtained with the given description of the system

Discussion

14650.	A flexible chain of weight W hangs between two fixed points A & B which are at the same horizontal level. The inclination of the chain with the horizontal at both the points of support is θ. What is the tension of the chain at the mid point?(A) W/2.cosecθ(B) W/2.tanθ(C) W/2.cotθ(D) none
Answer» (C) W/2.cotθ

Discussion

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