100525 + Interview Questions in GENERAL QA IN GENERAL AWARENESS

1.	पर्वत प्रदेश में पावस कविता में पर्वत द्वारा प्रतिबिंब तालाब में देखना पर्वत के किन मनोभावों का स्पष्ट करना चाहता है
Answer» कविता में कवि ‘सुमित्रानंदन पंत’ पावस प्रदेश में प्रतिबिंबित पहाड़ के दृश्य का वर्णन करते हुए कहते हैं कि वर्षा ऋतु में पर्वत के चारों तरफ के तालाब जल से भर गए हैं। तालाबों में जल लबालब बह रहा है और वह जल इतना स्वच्छ एवं निर्मल है कि उस जल में पहाड़ का प्रतिबिंब दिखाई दे रहा है। तालाब के जल एक विशालकाय दर्पण का काम करने लगा है। उस जल रूपी दर्पण में उस विशालकाय पहाड़ के प्रतिबिंब को देखकर ऐसा लगता है कि मानो जैसे कि करधनी के आकार वाला कोई पहाड़ अपने हजारों फूल रूपी नयनों से तालाब रूपी दर्पण में अपने प्रतिबिंब को निहार रहा हो। पहाड़ पर उगने वाले असंख्य फूल उसकी आँखों का काम कर रहे हैं और उन फूलों सहित उस विशालकाय पर्वत का दर्पण रूपी में तालाब में दिखायी देने वाला प्रतिबिंब देखकर ऐसा लगता है, कि जैसे पर्वत की एक जोड़ी आँखें नही बल्कि फूल रूपी हजारों आँखें हैं, और उन हजारों आँखों से पर्वत उस विशालकाय तालाबी रूपी दर्पण में अपना प्रतिबिंब निहार रहा हो।

Discussion

2.	बचचन जी को संसार क्यों प्रिय नहीं है?
Answer» कवि को यह संसार इसलिए प्रिय नहीं है क्योंकि यह अपूर्ण और अधूरा है जबकि कवि सपनों की दुनिया में खोया रहता है जहाँ कोई अभाव नहीं है।

Discussion

3.	ऐसा छोटा दिल करने से कही व्यापार होता है। मुनोम जो ! इस भाव से आधे-पोने कोठे भी बिकंग तो भी अपना दोहरा लाभ है। आगे के राम जी मालिक हैं।" - व्याख्या लिखी।
Answer» please answer this

Discussion

4.	वह 'तोड़ती पत्थर' कविता का केन्द्रीय भाव स्पष्ट करते हुए कविता के उद्देषी लिखिए
Answer» इस कविता में कवि 'निराला' जी ने एक पत्थर तोड़ने वाली मजदूरी के माध्यम से शोषित समाज के जीवन की विषमता का वर्णन किया है। कविता का भाव सौंदर्य की दृष्टि से बहुत ही अद्भुत है। सड़क पर पत्थर तोड़ती एक मजदूर महिला का वर्णन कवि ने अत्यंत सरल शब्दों में किया है। वो तपती दोपहरी में बैठी हुई पत्थर तोड़ रही है।

Discussion

5.	संकलित दोहों की सप्रसंग व्याख्याएँ।सटपटाति-सी ससिमुखी, मुख चूँघट-पट ढाँकि।पावक-झर-सी झमकि कै, गई झरोखे झाँकि
Answer» पावक झर = आग की लपट। सटपटाति-सी = डरती हुई-सी। झमकिकै = नखरे की चाल से, गहनो की झनकार करके, चपलता से। डरती हुई-सी-वह चन्द्रबदनी (अपने) मुख को घूंघट से ढँककर अग्नि की लपट-सरीखी चंचलता के साथ झरोखे से झाँक गई। नोट - भाव यह है कि अपने गुरुजनों के डर से वह मुख पर आँचल डालकर झटपट खिड़की पर आई और (नायक को) देखकर चली गई।

5.

संकलित दोहों की सप्रसंग व्याख्याएँ।सटपटाति-सी ससिमुखी, मुख चूँघट-पट ढाँकि।पावक-झर-सी झमकि कै, गई झरोखे झाँकि

Answer»

पावक झर = आग की लपट। सटपटाति-सी = डरती हुई-सी। झमकिकै = नखरे की चाल से, गहनो की झनकार करके, चपलता से।

डरती हुई-सी-वह चन्द्रबदनी (अपने) मुख को घूंघट से ढँककर अग्नि की लपट-सरीखी चंचलता के साथ झरोखे से झाँक गई।

नोट - भाव यह है कि अपने गुरुजनों के डर से वह मुख पर आँचल डालकर झटपट खिड़की पर आई और (नायक को) देखकर चली गई।

Discussion

6.	When people are enslaved, what key do they have to the prison, according to M. Hamel? A) Their behaviour B) Power C) Aggressiveness D) Mother tongue
Answer» D) Mother tongue

Discussion

7.	Who was M Hamel
Answer» M Hamel was a French Teacher in a school of Alsace. He was sad because after Prussia's win over France in the French - Prussian war, orders were given to replace French with German in the schools of Alsace and Lorreins.

Discussion

8.	Sandesh lekhan on beti padhao beti bachao
Answer» बेटी बचाओ बेटी पढाओ देश में शक्षरता बाराओ

Discussion

9.	Sujan ne gaon mein kya banvaya
Answer» सुजान ने गाँव में एक पक्का कुआँ बनवाया \|

Discussion

10.	हो जाए न पथ में रात कहीं, मंजिल भी तो है दूर नहीं- यह सोच थका दिन का पंथी भी जल्दी-जल्दी चलता है! दिन जल्दी-जल्दी ढलता है!
Answer» प्रस्तुत पंक्तियाँ हमारी पाठ्यपुस्तक में संकलित गीत ‘दिन जल्दी-जल्दी ढलता है!’ से ली गयी हैं। ये पंक्तियाँ हरिवंश राय बच्चन द्वारा रचित गीत ‘निशानिमंत्रण’ से उद्धृत हैं। इन पंक्तियों में कवि जीवन यात्रा को पथ कह कर संबोधित कर रहे हैं। जिस प्रकार सूर्योदय के बाद सूर्यास्त निश्चित है उसी प्रकार जन्म के बाद मृत्यु निश्चित है, हर क्षण जीवन ढलता जा रहा है। इस जीवन यात्रा में यात्री दिन ढलने के पहले अपने गंतव्य तक पहुंचना चाहता है। अर्थात सारी सुख सुविधाएं और जिम्मेदारियाँ पूरी कर लेना चाहता है। ठीक वैसे ही जैसे एक पंछी दिन ढलने से पहले अपने घोंसले तक लौट आना चाहता है।

10.

हो जाए न पथ में रात कहीं, मंजिल भी तो है दूर नहीं- यह सोच थका दिन का पंथी भी जल्दी-जल्दी चलता है! दिन जल्दी-जल्दी ढलता है!

Answer»

प्रस्तुत पंक्तियाँ हमारी पाठ्यपुस्तक में संकलित गीत ‘दिन जल्दी-जल्दी ढलता है!’ से ली गयी हैं। ये पंक्तियाँ हरिवंश राय बच्चन द्वारा रचित गीत ‘निशानिमंत्रण’ से उद्धृत हैं।

इन पंक्तियों में कवि जीवन यात्रा को पथ कह कर संबोधित कर रहे हैं। जिस प्रकार सूर्योदय के बाद सूर्यास्त निश्चित है उसी प्रकार जन्म के बाद मृत्यु निश्चित है, हर क्षण जीवन ढलता जा रहा है। इस जीवन यात्रा में यात्री दिन ढलने के पहले अपने गंतव्य तक पहुंचना चाहता है। अर्थात सारी सुख सुविधाएं और जिम्मेदारियाँ पूरी कर लेना चाहता है। ठीक वैसे ही जैसे एक पंछी दिन ढलने से पहले अपने घोंसले तक लौट आना चाहता है।

Discussion

11.	Samachar copy ke lekhan me kiske prayog se bachna chahiye
Answer» संपादकीय लेख की शैली प्रभावोत्पादक एवं सजीव होनी चाहिए। भाषा स्पष्ट, सशक्त और प्रखर हो। चुटीलेपन से भी लेख अपेक्षाकृत आकर्षक बन जाता है। संपादक की प्रत्येक बात में बेबाकीपन हो। ढुलमुल शैली अथवा हर बात को सही ठहराना अथवा अंत में कुछ न कहना-ये संपादकीय के दोष माने जाते हैं,अतः संपादक को इनसे बचना चाहिए।

Discussion

12.	ई) निम्नलिखित मुलावरों को अर्थ के साथ जोड़कर लिखिए :25. 1) रेग जमाना2) जी चुरानरक) अन्यधिक खुरा होना-ख) थाक जमाना3) पन-पार्नी बनानाग) मेहनत रो घचना4) फूले न समानाप्र) सम्मान धचाना
Answer» 1. आज भी लता मंगेशकर ने लोगो के मन मे अपना रंग जमाया हुआ है ।

Discussion

13.	निम्नलिखित प्रथम दो शब्दों के सूचित संबंधों के अनुरूप तीसरे शब्द का संबंधित शब्द लिखिए। भाद्रावती : लोहे और इस्पात :: मैसूर :
Answer» चंदन का आगार

Discussion

14.	‘काम आना’ इस मुहवरे अर्थ है।A. काम करनB. काम के आनाC. काम में जानाD. दूर करना
Answer» B. काम के आना

Discussion

15.	‘अध्यापक का अन्य लिंग रूप है।A. अद्यापकीB. अद्याथीC. अध्यापकनीD. अद्यापिका
Answer» Correct Answer is: D. अद्यापिका

Discussion

16.	‘लडर’ का अन्यलिंग रूप है?A. लहरीB. लहरेC. लहरोंD. लहराईयाँ
Answer» Correct Answer is: B. लहरे

Discussion

17.	‘सज्जन’ का विलोम शब्द लिखोA. सर्वज्ञB. सदाजारC. दुर्जनD. नीराजन
Answer» Correct Answer is: C. दुर्जन

Discussion

18.	‘पाप – पुण्य’ यह इस समास का उदाहरण है।A. तप्तुरूष.B. द्वंद्वC. कर्मधारयD. द्विगु
Answer» Correct Answer is: B. द्वंद्व

Discussion

19.	If \( x^{2}-a x+a-1=0 \) and \( x^{2}-4 x+a=0 \) have a common root then find the sum of all possible value(s) of a
Answer» Both quadratic equations \(x^2 - ax + a - 1 = 0\) and \(x^2 - 4x + a = 0\) have a common root. Let \(\alpha\) be common root \(\therefore \alpha^2 - 4\alpha + a = 0\) and \(\alpha^2 - a\alpha + a - 1 = 0\) \(\Rightarrow \alpha^2 - 4\alpha + a\) \(= \alpha^2 - a\alpha + a - 1\) \(\Rightarrow a\alpha\, - 4\alpha = -1\) \(\Rightarrow \alpha = \frac{-1}{a - 4}.\) i.e., both equations have common root \(x = \frac{-1}{a - 4}.\) \(\therefore\) \(\left(\frac{-1}{a - 4}\right)^2 - a\left(\frac{-1}{a - 4}\right)\) \(+\, a - 1 = 0\) \(\Rightarrow \frac{1}{(a - 4)^2} + \frac{a}{a - 4}\) \(+\, a - 1 = 0\) \(\Rightarrow (1 + a)(a - 4)\) \(+\, (a - 1)(a + 4)^2 = 0\) \(\Rightarrow\) (a - 1) \((a^2 - 8a + 16)\) \(+\, a^2 - 4a + 1 = 0\) \(\Rightarrow\) \(a^3 - 9a^2 + 24a - 16\) \(+\, a^2 - 4a + 1 = 0\) \(\Rightarrow\) \(a^3 - 8a^2 + 20a - 15 = 0\) sum of all possible values of a \(= \frac{-(-8)}{1} = 8.\)

19.

If \( x^{2}-a x+a-1=0 \) and \( x^{2}-4 x+a=0 \) have a common root then find the sum of all possible value(s) of a

Answer»

Both quadratic equations \(x^2 - ax + a - 1 = 0\) and \(x^2 - 4x + a = 0\) have a common root.

Let \(\alpha\) be common root

\(\therefore \alpha^2 - 4\alpha + a = 0\) and \(\alpha^2 - a\alpha + a - 1 = 0\)

\(\Rightarrow \alpha^2 - 4\alpha + a\) \(= \alpha^2 - a\alpha + a - 1\)

\(\Rightarrow a\alpha\, - 4\alpha = -1\)

\(\Rightarrow \alpha = \frac{-1}{a - 4}.\)

i.e., both equations have common root \(x = \frac{-1}{a - 4}.\)

\(\therefore\) \(\left(\frac{-1}{a - 4}\right)^2 - a\left(\frac{-1}{a - 4}\right)\) \(+\, a - 1 = 0\)

\(\Rightarrow \frac{1}{(a - 4)^2} + \frac{a}{a - 4}\) \(+\, a - 1 = 0\)

\(\Rightarrow (1 + a)(a - 4)\) \(+\, (a - 1)(a + 4)^2 = 0\)

\(\Rightarrow\) (a - 1) \((a^2 - 8a + 16)\) \(+\, a^2 - 4a + 1 = 0\)

\(\Rightarrow\) \(a^3 - 9a^2 + 24a - 16\) \(+\, a^2 - 4a + 1 = 0\)

\(\Rightarrow\) \(a^3 - 8a^2 + 20a - 15 = 0\)

sum of all possible values of a \(= \frac{-(-8)}{1} = 8.\)

Discussion

20.	a lottery of 60 tickets numbered 1 to 60, two tickets are drawn simultaneously. Find the probability that (i) both the tickets drawn have prime numbers: (ii) none of the tickets drawn has prime number.
Answer» 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59 are prime numbers between 1 to 60. Total prime numbers = 17. Total tickets = 60. Number of ways to drawn 2 tickets from 60 tickets is n(s) \(= 60 C_2.\) (i) Number of ways to drawn 2 tickets from tickets which numbered as prime numbers is \(n(E_1) = 17 C_2\) \(\therefore\) Probability that both drawn tickets are prime numbers is \(p(E_1) = \frac{n(E_1)}{n(s)} = \frac{17\,C_2}{60\,C_2}\) \(= \cfrac{\frac{17 \times 16}{2!}}{\frac{60 \times 59}{2!}}\) \(= \frac{17 \times 16}{60 \times 59} = \frac{17 \times 4}{15 \times 59}\) \(= \frac{68}{885}.\) (ii) Number of ways to drawn 2 tickets from those tickets which numbered as non prime numbers is \(n(E_2) = 60 - 17 C_2 = 43 C_2.\) \(\therefore\) Probability that none of the tickets has prime number is \(P(E_2) = \frac{n(E_2)}{n(s)}\) \(= \frac{43\, C_2}{60\, C_2}\) \(= \cfrac{\frac{43 \times 42}{2!}}{\frac{60 \times 59}{2!}}\) \(= \frac{43 \times 42}{60 \times 59} = \frac{43 \times 21}{30 \times 59}\) \(= \frac{903}{1770}\)

20.

a lottery of 60 tickets numbered 1 to 60, two tickets are drawn simultaneously. Find the probability that (i) both the tickets drawn have prime numbers: (ii) none of the tickets drawn has prime number.

Answer»

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59 are prime numbers between 1 to 60.

Total prime numbers = 17.

Total tickets = 60.

Number of ways to drawn 2 tickets from 60 tickets is n(s) \(= 60 C_2.\)

(i) Number of ways to drawn 2 tickets from tickets which numbered as prime numbers is \(n(E_1) = 17 C_2\)

\(\therefore\) Probability that both drawn tickets are prime numbers is \(p(E_1) = \frac{n(E_1)}{n(s)} = \frac{17\,C_2}{60\,C_2}\) \(= \cfrac{\frac{17 \times 16}{2!}}{\frac{60 \times 59}{2!}}\)

\(= \frac{17 \times 16}{60 \times 59} = \frac{17 \times 4}{15 \times 59}\) \(= \frac{68}{885}.\)

(ii) Number of ways to drawn 2 tickets from those tickets which numbered as non prime numbers is \(n(E_2) = 60 - 17 C_2 = 43 C_2.\)

\(\therefore\) Probability that none of the tickets has prime number is \(P(E_2) = \frac{n(E_2)}{n(s)}\) \(= \frac{43\, C_2}{60\, C_2}\) \(= \cfrac{\frac{43 \times 42}{2!}}{\frac{60 \times 59}{2!}}\)

\(= \frac{43 \times 42}{60 \times 59} = \frac{43 \times 21}{30 \times 59}\) \(= \frac{903}{1770}\)

Discussion

21.	\(y = \frac{x \,cos^{-1} x}{\sqrt{1- x^2}} - log(\sqrt{1 - x^2})\)Find dy/dx?
Answer» \(y = \frac{x \,cos^{-1} x}{\sqrt{1- x^2}} - log(\sqrt{1 - x^2})\) Let x = cosθ then cos^-1x = θ and \(=\sqrt{1- x^2} = \sqrt{1 - cos^2\theta} = \sqrt{sin^2\theta} = sin\theta\) \(\therefore y = \frac{\theta cos\theta}{sin\theta} - log \, sin \theta \) \(= \theta cot \theta - log\, sin\theta\) \(\therefore \frac{dy}{dx} = \frac{dy}{d\theta} . \frac{d\theta}{dx}\) \(= \frac d{d\theta} (\theta cot\theta - log \, sin\theta) \frac{d\theta}{dx}\) \(= -\theta cosec^2\theta + cot \theta - \frac{cos\theta}{sin\theta} \;\frac{d\theta}{dx}\) \(= \frac{-\theta}{sin^2\theta} + \frac{-1}{sin\theta}\) \(\left(\because \frac{dx}{d\theta } = - sin\theta⇒\frac{d\theta}{dx } = \frac{-1}{sin\theta} \right)\) \(= \frac{\theta}{sin^3\theta}\) \(= \frac{cos^{-1}x}{(1-x^2)^{3/2}}\) \((\because sin \theta = \sqrt{1 - cos^2\theta} = \sqrt{1 - x^2})\) Hence, \(\frac{dy}{dx} = \frac{cos^{-1}x}{(1 - x^2)^{3/2}}\).

21.

\(y = \frac{x \,cos^{-1} x}{\sqrt{1- x^2}} - log(\sqrt{1 - x^2})\)Find dy/dx?

Answer»

\(y = \frac{x \,cos^{-1} x}{\sqrt{1- x^2}} - log(\sqrt{1 - x^2})\)

Let x = cosθ

then cos^-1x = θ

and

\(=\sqrt{1- x^2} = \sqrt{1 - cos^2\theta} = \sqrt{sin^2\theta} = sin\theta\)

\(\therefore y = \frac{\theta cos\theta}{sin\theta} - log \, sin \theta \)

\(= \theta cot \theta - log\, sin\theta\)

\(\therefore \frac{dy}{dx} = \frac{dy}{d\theta} . \frac{d\theta}{dx}\)

\(= \frac d{d\theta} (\theta cot\theta - log \, sin\theta) \frac{d\theta}{dx}\)

\(= -\theta cosec^2\theta + cot \theta - \frac{cos\theta}{sin\theta} \;\frac{d\theta}{dx}\)

\(= \frac{-\theta}{sin^2\theta} + \frac{-1}{sin\theta}\) \(\left(\because \frac{dx}{d\theta } = - sin\theta⇒\frac{d\theta}{dx } = \frac{-1}{sin\theta} \right)\)

\(= \frac{\theta}{sin^3\theta}\)

\(= \frac{cos^{-1}x}{(1-x^2)^{3/2}}\) \((\because sin \theta = \sqrt{1 - cos^2\theta} = \sqrt{1 - x^2})\)

Hence, \(\frac{dy}{dx} = \frac{cos^{-1}x}{(1 - x^2)^{3/2}}\).

Discussion

22.	If \( \sin \alpha=\frac{15}{53} \) and \( \sin \beta=\frac{33}{65} \), find the values of sin(α - β).
Answer» \(\because sin \,\alpha = \frac{15}{53}\) \(\therefore cos \,\alpha = \sqrt{1 - sin^2\alpha } \) \(= \sqrt{1 - \left(\frac{15}{53}\right)^2}\) \(=\frac{\sqrt{53^2 - 15^2}}{53}\) \(= \frac{\sqrt{2584}}{53}\) \(= \frac{2\sqrt{646}}{53}\) \(cos \beta = \sqrt{1 - sin^2\beta}\) \(= \sqrt{1 - \left(\frac{33}{65}\right)^2}\) \(= \frac{\sqrt{65^2 - 33^2}}{65}\) \(= \frac{\sqrt{3136}}{65}\) \(= \frac{56}{65}\) \(\therefore sin(\alpha - \beta) = sin\,\alpha \;cos\beta - cos\,\alpha\; sin\beta \) \(= \frac{15}{53} \times \frac{56}{65} -\frac{2\sqrt{646}}{53} \times \frac{33}{65}\) \(= \frac1{65\times 53} (840 - 66\sqrt{646})\)

22.

If \( \sin \alpha=\frac{15}{53} \) and \( \sin \beta=\frac{33}{65} \), find the values of sin(α - β).

Answer»

\(\because sin \,\alpha = \frac{15}{53}\)

\(\therefore cos \,\alpha = \sqrt{1 - sin^2\alpha } \)

\(= \sqrt{1 - \left(\frac{15}{53}\right)^2}\)

\(=\frac{\sqrt{53^2 - 15^2}}{53}\)

\(= \frac{\sqrt{2584}}{53}\)

\(= \frac{2\sqrt{646}}{53}\)

\(cos \beta = \sqrt{1 - sin^2\beta}\)

\(= \sqrt{1 - \left(\frac{33}{65}\right)^2}\)

\(= \frac{\sqrt{65^2 - 33^2}}{65}\)

\(= \frac{\sqrt{3136}}{65}\)

\(= \frac{56}{65}\)

\(\therefore sin(\alpha - \beta) = sin\,\alpha \;cos\beta - cos\,\alpha\; sin\beta \)

\(= \frac{15}{53} \times \frac{56}{65} -\frac{2\sqrt{646}}{53} \times \frac{33}{65}\)

\(= \frac1{65\times 53} (840 - 66\sqrt{646})\)

Discussion

23.

Write the SQL command for the following

Answer» 1). create table ( Roll_No int, NAME varchar (20), CLASS int, FEES int);

2). insert into

values (03, "ANIL", 10, 2000);

3).insert into

(Roll_No, NAME, FEES) values (04, "ASHISH", 2000);

4). select*from

;

5). select NAME from

order by FEES;

Discussion

24.

Q.8. Find the number of words with or without meaning which can be made using all the letters of the word AGAIN .If these words are written as in a dictionary, what will be the 47word?

Answer»

Number of A's in AGAIN = 2

Number of G, I \(\&\) N in AGAIN = 1 (each).

∴ Total words formed by AGAIN \(= \frac{5!}{2! \, 1! \, 1! \,1!}\) \(= \frac{120}{2} = 60.\)

Total number of words starting with \(A = 4! = 24\)

Total number of words starting with \(G = \frac{4!}{2!} = \frac{24}{2} = 12\)

Total number of words starting with \(I = \frac{4!}{2!} = \frac{24}{2} = 12\)

Last word which starts by I is

48^th word = INGAA

∴ 47^th word = INAGA.

Discussion

25.	Two identical dice are rolled. The probability that same number will appear on each of them will be______________.
Answer» total no of events in sample space- 6²=36 since both of the dice should have same number thus it can be E= {11,22,33,44,55,66} therefore, total no of required events=6 thus probability of getting the event P(E)=no of elements in E ____________________ no of elements in sample space =6/36=1/6

Discussion

26.	tan y sec^2x dx + tan x sec^y dy +0
Answer» sec2xtanydx+sec2ytanxdy=0 On separating the variables (dividing the equation by \tan x \tan y) ⇒tanxsec2xdx=−tanysec2ydy On integrating both sides, we get ∫tanxsec2xdx=−∫tanysec2ydy Put tanx=u⇒sec2x.dx=du and tany=v⇒sec2y.dy=dv ∴∫udu=−∫vdv ⇒logu=−logv+logc ⇒u=vc⇒u.v=c ∴tanx.tany=c

Discussion

27.	The wavelength of the photo-electric threshold for silver is 3.25×10^-7m. Find the velocity of electrons ejected from the surface by a ultra Violet light of wavelength= 2.536× 10^7m.
Answer» *The phenomenon in which electrons emitted from the metal surface by illuminated (incident) electromagnetic radiation (light energy)on the metal surface is called photoelectric effect*

Discussion

28.	{φ} or {phi} is a(a) Null set(b) Singleton set(c) Not a set(d) None of these
Answer» ϕ is a null set.

Discussion

29.	Which of the following equations has no solution?A. sec`theta`= 23B. `costheta=sqrt2`C. `tantheta=1/7`D. `sintheta=-1/5`
Answer» Correct Answer - B We know that, range of cos`theta` is [-1,1]. Therefore cos`theta=sqrt2` is not possible.

Discussion

30.	If p,q and r are non-zero, non-coplanar vectors then [p+q-r p-q q-r]= . . .A. 3[p q r]B. 0C. [p q r]D. 2[p q r]
Answer» Correct Answer - C Given, p, q and r are non-zero coplaner vectors. `therefore[p+q-r p-qq-r]` `=(p+q-r)dot[(p-q)xx(q-r)]` `=(p+q-r)dot[pxxq-pxxr-qxxq+qxxr]` `=(p+q-r).[pxxq-pxxr+qxxr](becauseqxxq=0)` `=p.(pxxq)-p.(pxxr)+pdot(qxxr)+qdot(pxxq)-rdot(pxxq)-rdot(pxxr)+rdot(qxxr)` `=[pqr]-[qpr]-[rpq]` `=[pqr]+[pqr]-[pqr]` `=2[pqr]-[pqr]=[pqr]`

Discussion

31.	The dimension of the physical quantity `alpha` in the equation. `E = V alpha`. Where E is the energy and V is voulume has same dimesion as ofA. ImpulseB. PowerC. Linear MomentumD. Pressure
Answer» Correct Answer - D `alpha = E//V` `[alpha] = (M^(1)L^(2)T^(-2))/(L^(3)) = M^(1) L^(-1) T^(-2)`

Discussion

32.	The displacement of a body is given by `2 s= g t^(2)` where g is a constant. The velocity of the body at any time t is :A. `g t`B. `g t//2`C. `g t^(2)//2`D. `g t^(3)//6`
Answer» Correct Answer - A `2S = g t^(2)` `2(dS)/(dt) = g 2t` `v = g t`

Discussion

33.	The number of solutions of `sin^(2)theta=1/2`in `[0,pi]` is ……A. threeB. fourC. twoD. one
Answer» Correct Answer - C We have, `sin^(2)theta=1/2!sintheta=pm1/(sqrt2)` We know, `thetain[0,pi]sintheta` is positive `thereforesintheta=sin45^(@),sin(180^(@)-45^(@))`i.e.. `sin135^(@)`

Discussion

34.	In case of an ideal spring, we take the reference point (where potential energy is assumed to be zero) at extension of `x_(0)` instead of taking at natural length. Then potential energy when spring is extended by `x` is `:`A. `(1)/(2)k(x-x_(0))^(2)`B. `(1)/(2)k(x^(2)-x_(0)^(2))`C. `(1)/(2)k(x^(2)-2x x_(0))`D. `(1)/(2)k(2x x_(0)-x^(2))`
Answer» Correct Answer - B `DeltaU=U_(x)=U_(x_(0))=(1)/(2)kx^(2)-(1)/(2)kx_(0)^(2)`

Discussion

35.

_______, a member of the 1967 batch, made it to the position of Financial Commissioner of the Indian Railways Board.1. Kiran Devi2. Vijaylakshmi Viswanathan3. Smita Jena4. Lalita Suryawanshi

Answer» Correct Answer - Option 2 : Vijaylakshmi Viswanathan

The correct answer is Vijaylakshmi Viswanathan.

In 2002 Vijaylakshmi Viswanathan, a member of the 1967 batch, made it to the position of Financial Commissioner of the Indian Railways Board.
Vijaylakshmi was also the first woman Divisional Rail Manager on the Indian Railways in the late 1990s.
She was the additional manager general of the southern railway.
She got promoted to the GM cadre and posted as an additional member of the railway board.

Financial Commissioner for Railways:
- The Financial Commissioner for Railways was appointed in April 1923.
- This was followed by the Separation Convention of 1924 in which the Railway finances were separated from the General Finances of the Government of India.
- The process of the separation of the Accounting and Auditing functions on the Railways was completed in 1929.
- The Financial Commissioner for Railways represents the Ministry of Finance on the Railway Board.
- And also functions ex-officio as Secretary to the Government of India in the Ministry of Railways in financial matters.

Discussion

36.	`int_(0)^(4)1/(1+sqrtx)dx`=…..A. `log((e^(4))/6)`B. `log((e^(4))/9)`C. `log((e^(4))/9)`D. `log((e^(4))/4)`
Answer» Correct Answer - C Let `I=int_(0)^(4)1/(1+sqrtx)dx` Putting, `1+sqrtx=t!1/(2sqrtx)dx=dt` `!dx=2sqrtxdt!dx=2(t-1)dt` at `x=0,t=1` and x=4,t=3 Now, `I=int_(1)^(3)(2(t-1)dt)/t=2int_(1)^(3)(1-1/t)dt` `=2[t-logabst]_(1)^(3)` `=2[(3-log3)-(1-log1)]` `=2[2-log3](becauselog1=0)` `=4+2log(1/3)=4loge+log(1/9)` `=loge^(4)+log(1/9)=log(e^(4)/9)`

Discussion

37.	`int(sqrt(x^(2)-a^(2)))/xdx`=…… .A. `sqrt(x^(2)-a^(2))-acos^(-1)(a/x)+c`B. `xsqrt(x^(2)-a^(2))-1/atan^(-1)(x/a)+c`C. `sqrt(x^(2)-a^(2))+asec^(-1)(x/a)+c`D. `sqrt(x^(2)-a^(2))+1/xsec^(-1)(x)+c`
Answer» Correct Answer - A Let `I=int(sqrt(x^(2)-a^(2)))/x`dx Putting x=a sec`theta!theta=sec^(-1)(x/a)` `!dx=asecthetatanthetadtheta` `thereforeI=int(sqrt(asec^(2)theta-a^(2)))/(asectheta)(asecthetatanthetadtheta)` `=intatanthetadottanthetadtheta=intatan^(2)thetadtheta` `=aint(sec^(2)theta-1)dtheta=a[tantheta-theta]+C` `=a[sqrt(sec^(2)theta-1)-theta]+C` `=a[sqrt((x^(2))/(a^(2))-1)sec^(-1)(x/a)]+C` `!sqrt(x^(2)-a^(2))-acos^(-1)(a/x)+C`

Discussion

38.	In which one of the following countries, the rate of Income Tax is highest?(1) US (2) China (3) Japan (4) UK (5) France
Answer» In Japan countries, the rate of Income Tax is highest.

Discussion

39.	The per capital food grains consumption: (a) has fallen steadily over the years (b) has fluctuated (c) has remained stagnant (d) has risen very slowly
Answer» (d) has risen very slowly

Discussion

40.	The co-ordinates of the foot of perpendicular drawn from origin to the plane 2x - y + 5z - 3 = 0 are .....A. `(2/(sqrt(30)),(-1)/(sqrt(30)),5/(sqrt(30)))`B. `(2,-1,5)`C. `(2/3,(-1)/3,5/3)`D. `(1/5,(-1)/10,1/2)`
Answer» Correct Answer - D Given equation of plane is 2x-y+5z-3=0. `therefore` Foot of perpendicular drawn from origin to the given plane `!(x-0)/2=(y-0)/(-1)=(z-0)/5` `=(-(0+0+0-3))/((2)^(2)+(-1)^(2)+(5)^(2))` `!x/2=y/(-1)=z/5=3/30=1/10` `thereforex/2=1/10,y/(-1)=1/10,z/5=1/10` `!x=1/5,y=-1/10,z=1/2`

Discussion

41.	If `vec(A)` makes an angle `alpha, beta` and `gamma` from x,y and z axis respectively then `sin^(2)alpha+sin^(2) beta+sin^(2) gamma=`
Answer» Correct Answer - 3 `cos^(2) alpha+cos^(2) beta+cos^(2)gamma=1` `1-sin^(2) alpha+1-sin^(2) beta+1-sin^(2) gamma=1` `sin^(2) alpha+sin^(2) beta +sin^(2) gamma=2`

Discussion

42.	2times3+2-:2times3
Answer» Simplify Fraction `2 * 3 * 1 * 3` Remove Multiplying By One `2 * 3 * 3` Simplify Arithmetic `18`

Discussion

43.	Highest milk producer in India is : (a) U.P. (b) Gujarat (c) Punjab (d) Haryana
Answer» Highest milk producer in India is U.P.

Discussion

44.	If `A={x in R//x^(2)+5\|x\|+6=0}` then n(A)= . . .A. 2B. 0C. 1D. 4
Answer» Correct Answer - D We have, `x^(2)-5absx+6=0` `!x^(2)-3absx-2absx+6=0` `!absx(absx-3)-2(absx-3)=0` `!(absx-2)(absx-3)=0` `!absx-2=0` or `absx-3=0` `!x=-2,2` or `x=-3,3` `therefore` n(A)=4

Discussion

45.	The displacement of a particle is given by `x=At^(3)+Bt^(2)+Ct+D`. The dimension of L in `(AD)/(BC)` will beA. 3B. 2C. 1D. 0
Answer» Correct Answer - 4 `[At^(3)]=L` [D]=L `[Bt^(2)]=L` [Ct]=L

Discussion

46.	GDR means:(a) 'gross domestic ratio' which is a macro aggregate (b) 'global depository receipt' which is the mechanism to raise funds from international market (c) 'global development range' which has been set up by UNO for developing countries (d) 'geographically developed regions' as defined by the UNDP
Answer» b) 'global depository receipt' which is the mechanism to raise funds from international market

Discussion

47.	(1)/(2)+(3)/(5)
Answer» Add Fractions `11 / 10` 1.1

Discussion

48.	1(2)/(3)-:(2)/(7)times(x)/(7)=1(1)/(4)times(2)/(3)-:(1)/(6)
Answer» Simplify Left Side `1/147 x = 1 * 1/4 * 2/3 / 1 / 6` Simplify Right Side `1/147 x = 1/36` Multiply Both Sides By Inverse Fraction `1/147 x * 147/1 = (1/36) * 147/1` Simplify Left Side `x = (1/36) * 147/1` Simplify Right Side `x = 49/12` x=4.083333333333333

Discussion

49.	The equivalent for of the statement `~(p to ~ q)` isA. `pwedgeq`B. `pwedge~q`C. `pvee~q`D. `~pveeq`
Answer» Correct Answer - A Given statement ~(`pto~q)equiv~(~pvee~q)equivpwedgeq`

Discussion

50.	`3845xx5xx782+769xx25xx218`
Answer» Collect And Combine Like Terms `15033950 d + 769 * 25 * 218` Simplify Arithmetic `15033950 d + 4191050`

Discussion

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​​​​​​Who was M Hamel

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If \( x^{2}-a x+a-1=0 \) and \( x^{2}-4 x+a=0 \) have a common root then find the sum of all possible value(s) of a

a lottery of 60 tickets numbered 1 to 60, two tickets are drawn simultaneously. Find the probability that (i) both the tickets drawn have prime numbers: (ii) none of the tickets drawn has prime number.

\(y = \frac{x \,cos^{-1} x}{\sqrt{1- x^2}} - log(\sqrt{1 - x^2})\)Find dy/dx?

If \( \sin \alpha=\frac{15}{53} \) and \( \sin \beta=\frac{33}{65} \), find the values of sin(α - β).

Write the SQL command for the following

Q.8. Find the number of words with or without meaning which can be made using all the letters of the word AGAIN .If these words are written as in a dictionary, what will be the 47word?

Two identical dice are rolled. The probability that same number will appear on each of them will be______________.

tan y sec^2x dx + tan x sec^y dy +0

The wavelength of the photo-electric threshold for silver is 3.25×10^-7m. Find the velocity of electrons ejected from the surface by a ultra Violet light of wavelength= 2.536× 10^7m.

{φ} or {phi} is a(a) Null set(b) Singleton set(c) Not a set(d) None of these

Which of the following equations has no solution?A. sec`theta`= 23B. `costheta=sqrt2`C. `tantheta=1/7`D. `sintheta=-1/5`

If p,q and r are non-zero, non-coplanar vectors then [p+q-r p-q q-r]= . . .A. 3[p q r]B. 0C. [p q r]D. 2[p q r]

The dimension of the physical quantity `alpha` in the equation. `E = V alpha`. Where E is the energy and V is voulume has same dimesion as ofA. ImpulseB. PowerC. Linear MomentumD. Pressure

The displacement of a body is given by `2 s= g t^(2)` where g is a constant. The velocity of the body at any time t is :A. `g t`B. `g t//2`C. `g t^(2)//2`D. `g t^(3)//6`

The number of solutions of `sin^(2)theta=1/2`in `[0,pi]` is ……A. threeB. fourC. twoD. one

_______, a member of the 1967 batch, made it to the position of Financial Commissioner of the Indian Railways Board.1. Kiran Devi2. Vijaylakshmi Viswanathan3. Smita Jena4. Lalita Suryawanshi

`int_(0)^(4)1/(1+sqrtx)dx`=…..A. `log((e^(4))/6)`B. `log((e^(4))/9)`C. `log((e^(4))/9)`D. `log((e^(4))/4)`

`int(sqrt(x^(2)-a^(2)))/xdx`=…… .A. `sqrt(x^(2)-a^(2))-acos^(-1)(a/x)+c`B. `xsqrt(x^(2)-a^(2))-1/atan^(-1)(x/a)+c`C. `sqrt(x^(2)-a^(2))+asec^(-1)(x/a)+c`D. `sqrt(x^(2)-a^(2))+1/xsec^(-1)(x)+c`

In which one of the following countries, the rate of Income Tax is highest?(1) US (2) China (3) Japan (4) UK (5) France

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The co-ordinates of the foot of perpendicular drawn from origin to the plane 2x - y + 5z - 3 = 0 are .....A. `(2/(sqrt(30)),(-1)/(sqrt(30)),5/(sqrt(30)))`B. `(2,-1,5)`C. `(2/3,(-1)/3,5/3)`D. `(1/5,(-1)/10,1/2)`

If `vec(A)` makes an angle `alpha, beta` and `gamma` from x,y and z axis respectively then `sin^(2)alpha+sin^(2) beta+sin^(2) gamma=`

2times3+2-:2times3

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If `A={x in R//x^(2)+5|x|+6=0}` then n(A)= . . .A. 2B. 0C. 1D. 4

The displacement of a particle is given by `x=At^(3)+Bt^(2)+Ct+D`. The dimension of L in `(AD)/(BC)` will beA. 3B. 2C. 1D. 0

(1)/(2)+(3)/(5)

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The equivalent for of the statement `~(p to ~ q)` isA. `pwedgeq`B. `pwedge~q`C. `pvee~q`D. `~pveeq`

`3845xx5xx782+769xx25xx218`

Who was M Hamel