कूड़े पर मिट्टी डालना मुहावरे का अर्थ क्या है।
- ((a))
इज्जत खराब होना
- ((b))
किसी के दोष को छिपाना
- ((c))
घर मिट्टी होना
- ((d))
छलनी कर डालना
Show Answer
किसी के दोष को छिपाना
सह उत्तर है - किसी के दोष को छिपाना
100 questions · 90 minutes · with answers · free
कूड़े पर मिट्टी डालना मुहावरे का अर्थ क्या है।
इज्जत खराब होना
किसी के दोष को छिपाना
घर मिट्टी होना
छलनी कर डालना
किसी के दोष को छिपाना
सह उत्तर है - किसी के दोष को छिपाना
जुगुप्सा का पर्यायवाची है-
घृणा
मीठा
तीखा
पसंदीदा
घृणा
जुगुप्सा का उचित पर्यायवाची 'घृणा' है। अन्य विकल्प असंगत हैं।

Key Points
अन्य विकल्प-

Additional Information
| शब्द | परिभाषा | उदाहरण |
|---|---|---|
| पर्यायवाची या समानार्थी | जिन शब्दों से समान अथवा आंशिक समान अर्थ का बोध होता है, उसे पर्यायवाची शब्द कहते है। 'पर्यायवाची' शब्द को 'समानार्थी' शब्द भी कहा जाता है। | यमुना-अर्कजा, रविजा, सूर्यजा दूध- अमृत, क्षीर, गोरस |
नीचे दिए गए शब्द का पर्यायवाची शब्द ज्ञात कीजिए।
ओज
अटल
वंश
उम्दा
शक्ति
शक्ति
ओज - तेज, शक्ति, बल, चमक, कांति, दीप्ति।

Key Points

Additional Information
| शब्द | परिभाषा | उदाहरण |
|---|---|---|
| पर्यायवाची | एक ही अर्थ में प्रयुक्त होने वाले शब्द, जो बनावट में भले ही अलग हों। 'पर्यायवाची-शब्द' को 'समानार्थी-शब्द' भी कहा जाता है| | ज्ञान-सूचना, विद्या, बोध झील- सरोवर, कूल |
माँ ने बाजार जाने के लिए ______ को बुलाया?
खिलौना
बच्चों
पैसा
सहारा
बच्चों
सही उत्तर है - बच्चों

Key Points
दिए गए गद्यांश को पढ़िए और उसके बाद आने वाले प्रश्नों के उत्तर दीजिए।
चीन विश्व का तीसरा सबसे बड़ा देश है। चीन की जनसंख्या भारत की जनसंख्या की तुलना में अधिक है। चीन हमारा पड़ोसी है। हिमालय भारत और चीन के बीच में स्थित है। चीन के पूर्व में प्रशांत महासागर और चीन के उत्तर में गोबी का विशाल रेगिस्तान है। चीन ने बिना किसी व्यवधान के पिछले 4000 वर्षों तक इस क्षेत्र पर शासन किया है।
पहली चीनी सभ्यता दो नदियों की महान नदी घाटी - उत्तर में ह्वांग हो और दक्षिण में यांग्त्ज़ी - में फली-फूली। यह सभ्यता भारत में सिंधु घाटी में हड़प्पा सभ्यता के समय में ही बढ़ी थी। आज भी, ये नदी घाटियां चीन के सबसे घनी आबादी वाले हिस्से हैं।
ज्यादातर चीनी किसानी के कार्य में लगे हैं। आधुनिक चीन में, किसानों के पास अपने खेतों का मालिकाना अधिकार नहीं है। प्रत्येक गांव की अपनी जमीन होती है। ग्रामीण एक साथ काम करते हैं और फसल उनके बीच साझा की जाती है। चीन में उगाई जाने वाली मुख्य फसलें दक्षिण में चावल और उत्तर में गेहूं और जौ हैं। सिल्क, चाय और कपास भी आधिक्य में उपजाया जाता है, और वहां मछली पकड़ने का एक बड़ा उद्योग भी है। चीन का रेशम पूरी दुनिया में प्रसिद्ध है। वास्तव में, चीन ने ही सबसे पहले रेशम बनाया था। उनके रेशम को प्राचीन सिल्क रूट के द्वारा दूर-दूर के स्थानों पर - यहाँ तक कि यूरोप - भी भेजा गया था।
चीन की महान दीवार, दुनिया के सात आश्रर्यों में से एक है और दुनिया की सबसे लंबी दीवार है। यह दीवार लगभग 2000 वर्ष पुरानी है और 6000 किलोमीटर से अधिक लंबी है। दीवार पत्थरों और ईंटों से बनी है। यह बाहरी अंतरिक्ष से दिखाई देने वाली एकमात्र मानव निर्मित संरचना है।
चीन व भारत के लिए निम्नलिखित कथनों में से क्या सत्य नहीं है?
दोनो की जनसंख्या विशाल है
उनकी सीमाएं साझी हैं।
सिल्क बनाने में ये दोनो पहले देश थे।
दोनो सभ्यताएं साथ-साथ पनपीं।
सिल्क बनाने में ये दोनो पहले देश थे।
चीन व भारत के लिए निम्नलिखित कथनों में से सिल्क बनाने में ये दोनो पहले देश थे यह कथन सत्य नहीं है।

Key Points

Additional Information
आधुनिक चीन में आम कृषि प्रथा क्या है?
किसान गांव में जमीन के अपने टुकड़े पर खेती करते हैं।
किसान संयुक्त रूप से गांव की भूमि पर खेती करते हैं।
किसान उपयोग के लिए अपनी व्यक्तिगत फसल इकट्ठा करते हैं।
किसान केवल ऐसी फसलें उगाते हैं जो लाभदायक हैं।
किसान संयुक्त रूप से गांव की भूमि पर खेती करते हैं।
आधुनिक चीन में आम कृषि प्रथा यह है कि किसान संयुक्त रूप से गांव की भूमि पर खेती करते हैं।

Key Points

Additional Information
चीनी रेशम यूरोप और अन्य देशों को _______ के माध्यम से पहुंचता था।
प्राचीन सिल्क रूट
गोबी रेगिस्तान
दो नदी घाटियां
चीन की महान दीवार
प्राचीन सिल्क रूट
चीनी रेशम यूरोप और अन्य देशों को प्राचीन सिल्क रूट के माध्यम से पहुंचता था।

Key Points

Additional Information
चीन की महान दीवार की कौन सी विशेषता बेहद विशिष्ट है?
यह दुनिया के अजूबों में से एक कहलाने वाली एकमात्र संरचना है।
यह चीनियों द्वारा बनाई जाने वाली ईंटों और पत्थरों से बनी पहली दीवार है।
यह मनुष्य द्वारा निर्मित एकमात्र संरचना है जिसे बाह्य अंतरिक्ष से देखा जा सकता है।
यह दुनिया की एकमात्र दीवार है जो 4000 साल से अधिक पुरानी है।
यह मनुष्य द्वारा निर्मित एकमात्र संरचना है जिसे बाह्य अंतरिक्ष से देखा जा सकता है।
चीन की महान दीवार की यह विशेषता बेहद विशिष्ट है कि यह "मनुष्य द्वारा निर्मित एकमात्र संरचना है जिसे बाह्य अंतरिक्ष से देखा जा सकता है।"

Key Points

Additional Information
विशाल गोबी रेगिस्तान पर चीन द्वारा __________ वर्षों तक शासन किया गया है।
2000
4000
400
200
4000
विशाल गोबी रेगिस्तान पर चीन द्वारा 4000 वर्षों तक शासन किया गया है।

Key Points

Additional Information

Important Points
| शब्द | परिभाषा | उदाहरण |
|---|---|---|
| विलोम | जिस शब्द का दूसरे शब्द के ठीक विपरीत अर्थ होता है, वह उसका विलोम शब्द होता है। | दिन-रात काला-गोरा आदि |
प्रश्न में दिए गए विलोम शब्द का चयन उसके नीचे दिए गए विकल्पों में से कीजिये
विरक्ति
आसक्त
अनुरक्ति
उक्त
विरत
अनुरक्ति
सही उत्तर अनुरक्ति है|

Key Points
किस विकल्प में सम्प्रदान कारक का सही हुआ है ?
आसमान का रंग नीला है।
हिमालय से नदी निकलती है।
हाथ से घड़ी गिर गयी।
बच्चों के लिए मिठाई लाओ।
बच्चों के लिए मिठाई लाओ।
सही उत्तर है - "बच्चों के लिए मिठाई लाओ।"

Key Points
अन्य विकल्पों का विश्लेषण:-

Additional Information
पर्याय की दृष्टि से कौन सा युग्म सुमेलित नहीं है?
तालाब - पुष्कर
कष्ट - व्यथा
पत्नी - कलत्र
नदी - तरिणी
नदी - तरिणी
पर्याय की दृष्टि से कौन सा युग्म सुमेलित नहीं है- 'नदी - तरिणी'।
नदी के पर्यायवाची शब्द- तरनी, तटनी, लहरी आदि।

Key Pointsसमान अर्थ देने वाले शब्दों को पर्यायवाची शब्द कहते है।
अन्य पर्यायवाची युग्म सुमेलित है-

Additional Informationकुछ महत्वपूर्ण पर्यायवाची शब्द-
| शब्द | पर्यायवाची |
|---|---|
| असुर | तमीचर, यातुधान, रजनीचर |
| आकाश | व्योम, शून्य, गगन, अम्बर, नभ। |
| नाव | तरिणी, बेड़ा, तरी |
| आँगन | आजिरा, अँगना, प्रांगण |
| गेह | मंदिर, आलय, धाम |
| चोर | साहसिक, दस्यु, रजनीचर |
| सिंह | केहरी, मृगराज, केशरी |
| हंस | कलकंठ, मराल, सिपपक्ष |

Mistake Pointsनदी का पर्यायवाची शब्द 'तटनी' है 'तरिणी' नहीं**।**
'तरिणी' नाव का पर्यायवाची है।
दिये गये वाक्यांश के लिए एक शब्द दीजिये |
जो सप्ताह में एक बार होता हो
वार्षिक
साप्ताहिक
मासिक
पाक्षिक
साप्ताहिक
जो सप्ताह में एक बार होता हो वाक्यांश के लिए एक शब्द साप्ताहिक होता है । अन्य विकल्प असंगत है। अतः सही उत्तर विकल्प 2) साप्ताहिक होगा ।

Key Points
| कम से कम शब्दोँ मेँ अधिकाधिक अर्थ को प्रकट करना एक कला है जोकि एक अच्छी रचना के लिए आवश्यक है। ऐसे शब्दोँ के प्रयोग से वाक्य–रचना मेँ संक्षिप्तता, सुन्दरता व गंभीरता आती है। | |
|---|---|
| कुछ अन्य उदाहरण: | |
| जिसके समान कोई दूसरा न हो | अद्वितीय |
| धन की इच्छा रखने वाला | धनेच्छु |
| जिसका कोई आसरा न हो | निराश्रित |
| शोभा देने वाला | शोभनीय |

Additional Information
| वार्षिक | जो वर्ष में एक बार होता हो |
|---|---|
| मासिक | जो माह में एक बार होता हो |
| पाक्षिक | जो एक पक्ष में एक बार होता हो |
सही वर्तनी वाला शब्द कौन-सा है?
उपर्युक्त
ऊपयुक्त
उपर्युत्त
उपरिक्त
उपर्युक्त
सही वर्तनी वाला शब्द है - 'उपर्युक्त'

Mistake Points

Key Points

Additional Information कुछ अशुद्ध से शुद्ध शब्द:-
देश को ________ से बचाना चाहिए
पानी
गद्दारों
बाजारों
धर्म
गद्दारों
देश को गद्दारों से बचाना चाहिए।

Key Points
अन्य विकल्प -

Additional Information
विकल्पों में दिए गए अन्य शब्दों का वाक्य प्रयोग -
‘अंधे के हाथ बटेर लगना’ मुहावरे का क्या अर्थ है?
लाभ होना
बटेर का जाल में फँसना
अंधे के पास बटेर का आना
बिना परिश्रम के अच्छी वस्तु हाथ लगना
बिना परिश्रम के अच्छी वस्तु हाथ लगना
‘अंधे के हाथ बटेर लगना’ का अर्थ ‘बिना परिश्रम के अच्छी वस्तु हाथ लगना’ है। शेष विकल्प त्रुटिपूर्ण हैं। अतः सही विकल्प ‘बिना परिश्रम के अच्छी वस्तु हाथ लगना’ है।
विशेष
| मुहावरा | अर्थ | वाक्य प्रयोग |
|---|---|---|
| अंधे के हाथ बटेर लगना | बिना परिश्रम के अच्छी वस्तु हाथ लगना | विजय मात्र आठवीं पास है फिर भी उसकी सरकारी नौकरी लग गई। इसी को कहते हैं - अंधे के हाथ बटेर लगना। |
हिन्दी दिवस मनाया जाता है
14 सितम्बर को
05 सितम्बर को
02 अक्टूबर को
26 जनवरी को
14 सितम्बर को
हिंदी दिवस - हर साल हम 14 सितंबर को हिंदी दिवस के रूप में मनाते हैं। क्योंकि इसी दिन भारत की संविधान सभा ने देवनागरी लिपि में लिखी गई हिंदी भाषा को भारतीय गणराज्य की राजभाषा घोषित किया था। हिंदी के प्रचार और प्रसार के लिए तत्कालीन भारतीय सरकार ने 14 सितंबर 1949 से प्रतिवर्ष 14 सितम्बर को हिंदी दिवस के रूप में मनाने अनुरोध किया था। संविधान द्वारा हिंदी को भारत की राजभाषा का दर्जा दिये जाने की खुशी में हम हिंदी दिवस मनाते हैं। संविधान के अनुच्छेद 343 में हिंदी भाषा को राजभाषा के तौर पर अपनाने का उल्लेख मिलता है।

Additional Information
भाषा - भाषा वह साधन है जिसके द्वारा हम अपने विचारों को व्यक्त कर सकते हैं और इसके लिये हम वाचिक ध्वनियों का प्रयोग करते हैं। भाषा, मुख से उच्चारित होने वाले शब्दों और वाक्यों आदि का वह समूह है जिनके द्वारा मन की बात बताई जाती है।
बोली - भाषा की छोटी इकाई को बोली कहा जाता है। इसका क्षेत्र सीमित होता है। इसमें व्यक्तिगत बोलचाल ही माध्यम होता है और देशज तथा घरेलू शब्दावली का प्रयोग होता है। यह बोलचाल की भाषा मानी जाती है। उदाहरण : बिहारी, बघेली, छत्तीसगढ़ी, अवधी आदि
संदिग्ध वर्तमान काल का उदाहरण है -
यह पढ़ा जाता था।
यह पढ़ा जाता होगा।
यह पढ़ा जाएगा।
यह पढ़ा जाता है।
यह पढ़ा जाता होगा।
विकल्प (2) संदिग्ध वर्तमान काल का सही उदाहरण है- यह पढ़ा जाता होगा। अन्य विकल्प असंगत है।
यह पढ़ा जाता था | यह वाक्य सामान्य भूतकाल का उदहारण है।
यह पढ़ा जायेगा। यह वाक्य सामान्य भविष्यकाल का उदहारण है।
यह पढ़ा जाता है। यह वाक्य सामान्य वर्तमानकल का उदहारण है।

Key Points
संदिग्ध वर्तमान काल:-

Additional Informationसामान्य वर्तमान:-
सामान्य भविष्यकाल:-
सामान्य भूतकाल:-
जीवनभर मैं सत्य का पालन करुँगा।
रेखांकित शब्द के स्थान उचित शब्द लिखिए।
कभी कभी
एक साल तक
कभी भी
आजीवन
आजीवन
विकल्प 4, ‘आजीवन’ सही है।

Key Points

Additional Information
दिए गए वाक्य में रेखांकित खंड को प्रतिस्थापित करने के लिए उपयुक्त विकल्प का चयन करें।
मौर्यकालीन समय में लोग सुखी थे।
मौर्यकाल के समय
मौर्ययुग के समय में
मौर्यकाल में
मौर्यकाल के युग में
मौर्यकाल में
सही उत्तर - मौर्यकाल में

Key Points

Additional Information
दिए गए अनुच्छेद में कुछ शब्द हटा दिए गए हैं। दिए गए विकल्पों की सहायता से रिक्त स्थान भरें। प्रत्येक प्रश्न संख्या के लिए सबसे उपयुक्त विकल्प का चयन कीजिए।
वर्तमान समय में अपनी व्यस्त जीवन शैली के कारण लोग (1)______ पाने के लिए योग करते हैं। योग से न केवल व्यक्ति का (2)______ दूर होता है बल्कि मन और मस्तिष्क को भी शांति मिलती है योग बहुत ही (3)______ है। योग न केवल हमारे मस्तिष्क को ही ताकत पहुंचाता है बल्कि हमारी आत्मा को भी (4)______ करता है। जिस वजह से आज (5)______ विदेशों में भी प्रसिद्ध है।
गद्यांश के रिक्त स्थान (5) के लिए सर्वाधिक उपयुक्त शब्द होगा-
याम
याग
योग
वियोग
योग
सही उत्तर है - ‘योग’।

Key Pointsसंपूर्ण वाक्य:
योग का अर्थ :
अन्य विकल्प:
गद्यांश के रिक्त स्थान (4) के लिए सर्वाधिक उपयुक्त शब्द होगा-
दूषित
अशुचि
शुद्ध
अशुद्ध
शुद्ध
सही उत्तर है - ‘शुद्ध’।

Key Pointsसंपूर्ण वाक्य :
शुद्ध का अर्थ :
अन्य विकल्प :
दिए गए अनुच्छेद में कुछ शब्द हटा दिए गए हैं। दिए गए विकल्पों की सहायता से रिक्त स्थान भरें। प्रत्येक प��रश्न संख्या के लिए सबसे उपयुक्त विकल्प का चयन कीजिए।
वर्तमान समय में अपनी व्यस्त जीवन शैली के कारण लोग (1)______ पाने के लिए योग करते हैं। योग से न केवल व्यक्ति का (2)______ दूर होता है बल्कि मन और मस्तिष्क को भी शांति मिलती है योग बहुत ही (3)______ है। योग न केवल हमारे मस्तिष्क को ही ताकत पहुंचाता है बल्कि हमारी आत्मा को भी (4)______ करता है। जिस वजह से आज (5)______ विदेशों में भी प्रसिद्ध है।
गद्यांश के रिक्त स्थान (3) के लिए सर्वाधिक उपयुक्त शब्द होगा-
हानिकारक
लाभकारी
अहितकर
शुभंकर
लाभकारी
सही उत्तर है - ‘लाभकारी’।

Key Pointsसंपूर्ण वाक्य :
लाभकारी का अर्थ :
अन्य विकल्प :
गद्यांश के रिक्त स्थान (2) के लिए सर्वाधिक उपयुक्त शब्द होगा-
विश्वास
आचरण
तनाव
आशंका
तनाव
सही उत्तर है - ‘तनाव’।

Key Pointsसंपूर्ण वाक्य :
तनाव का अर्थ :
अन्य विकल्प :
गद्यांश के रिक्त स्थान (1) के लिए सर्वाधिक उपयुक्त शब्द होगा-
संतोष
असंतोष
रोजगार
पैसा
संतोष
सही उत्तर है - ‘संतोष’।

Key Pointsसंपूर्ण वाक्य :
संतोष का अर्थ :
अन्य विकल्प :
Which of the following has became the first State in India to start the Caste based census in 2023?
Odisha
Bihar
Chhattisgarh
Jharkhand
Bihar
The correct answer is Bihar.

Key Points
Under which Article of the Constitution of India, the Supreme Court has been given place as the ‘Court of Records’?
129
130
137
143
129
The Supreme Court of India is the highest judicial court and the final court of appeal under the Constitution of India, the highest constitutional court, with the power of judicial review.

Important Points A court of record is a court whose acts and proceedings are enrolled for perpetual memory and testimony.
Thus, we can say that Article 129 of the Constitution empowers the Supreme Court to be a Court of Records.

Additional Information
Surya Kumar Yadav is related to which of the following sports?
Cricket
Football
Hockey
Shooting
Cricket
The correct answer is Cricket.

Key Points

Additional Information
Sania Mirza is related to which sport?
Badminton
Table Tennis
Cricket
Tennis
Tennis
The correct answer is Tennis.

Key Points

Important Points
Who was the Sultan of Delhi when Mongols attacked during 1299-1301?
Alauddin Khilji
Muhammad Tughlaq
Jalal-ud-din Khalji
Firoz Shah Tughlaq
Alauddin Khilji
The correct answer is Allaudin Khilji.
The Mongols attacked Delhi twice during the reign of Allaudin Khilji.
The Sultan of Delhi, who is reputed to have built the biggest network of canals in India was ________.
Iltutmish
Ghiyas-ud- din - Tughlaq
Firoz Shah Tughlaq
Sikandar Lodi
Firoz Shah Tughlaq
The correct answer is Firoz Shah Tughlaq.

Key Points

Additional Information
Tughlaq Rulers with their timeline:
| Rulers | Timeline |
|---|---|
| Ghiyasuddin Tughlaq | 1320-25 |
| Muhammad bin Tughlaq | 1325-51 |
| Firuz Shah Tughlaq | 1351-88 |
| Nasiruddin Muhammad | 1390-94 |
| Humayun | 1394-95 |
| Nasiruddin Mahmud | 1395-1412 |
To which of the following states does the folk song 'Bhawaiya' belong?
Chhattisgarh
Jharkhand
Odisha
West Bengal
West Bengal
The correct answer is option 4, i.e. West Bengal
Atomic Number 117 belongs to which of the following group in modern periodic table?
Group 15
Group 16
Group 17
Group 18
Group 17
The correct answer is Group 17.

Key Points
Tennessine:

Additional Information
When was “Protection of Children from Sexual Offences Act (POCSO)” came in force in India?
2008
2010
2011
2012
2012
The correct answer is 2012.

Key Points
Thus, we can say that POCSO Act came into force in 2012.
Who among the following has been awarded the Sahitya Akademi Awards 2022 in the Hindi language?
Anis Ashfaq
Badri Narayan
Praveen Bandekar
Manoj Kumar Goswami
Badri Narayan
The correct answer is Badri Narayan.

Key Points

Additional Information
The First Employment Working Group meeting of the G20 summit was held in which city from 2 to 4 February 2023?
New Delhi
Patna
Jodhpur
Agra
Jodhpur
The correct answer is Jodhpur.

In News

Key Points

Additional Information
Jhaveri sisters related to which of the following dance form?
Odissi
Manipuri
Kathak
Kuchipudi
Manipuri
The correct answer is Manipuri.

Key Points

Additional Information
Which of the following is India's longest freight train?
Super Vasuki
Super Vasudha
Vande Bharat
Super Rajdhani
Super Vasuki
The correct answer is option 1.

In News

Key PointsAbout Super Vasuki
According to the latest update, the Centre is likely to cut its 2023-24 (FY24) fiscal deficit in the range of 5.8-5.9% of the GDP from _______ in FY23.
6.4%
7.6%
6.2%
7.2%
6.4%
The correct answer is 6.4%.

In News

Key Points

Additional Information
In which state first Khelo India university games 2020 were organized?
Punjab
Odisha
Bihar
Gujrat
Odisha
The correct answer is Orissa.

Key Points

Additional Information
What is the full form of K-FON?
Kerala Fiber Optic Network
Kerala Future Optic Network
Kerala Future Open Networking
None of the above
Kerala Fiber Optic Network
The correct answer is option 1.

Key Points
Which of the following rivers originates in Maharashtra flows through Karnataka and Andhra Pradesh to meet the Bay of Bengal in Andhra Coast?
Cauvery
Mahanadi
Godavari
Krishna
Krishna
The correct answer is Krishna.

Key Points

Additional Information
Who has been appointed as the first woman Director General of the Council of Scientific & Industrial Research (CSIR) in August 2022?
Ritu Karidhal
Chandrima Shaha
Mangala Mani
Nallathamby Kalaiselvi
Nallathamby Kalaiselvi
The correct answer is Nallathamby Kalaiselvi.

Key Points


Additional Information
Khalsa Panth was founded by
Guru Gobind Singh
Guru Ramdas
Guru Nanak
Arjun Dev
Guru Gobind Singh
The correct answer is Guru Gobind Singh.

Key Points

Important Points

Additional Information
Which city hosted India’s first ever Formula E-race?
Noida
Indore
Lucknow
Hyderabad
Hyderabad
The correct answer is Hyderabad.

In News

Additional Information
Mahatma Gandhi return to India from South Africa in 1915. At that time what was the age of Mahatma Gandhi?
44
45
50
52
45
The correct answer is 45.

Key Points

Important Points

Additional Information
Mahatma Gandhi:
Who formulated the wave theory of light?
Isaac Newton
Galileo Galilei
Michael Faraday
Christiaan Huygens
Christiaan Huygens
The correct answer is Christiaan Huygens.

Key Points
Where was the second Buddhist Council held?
Kundalvana
Vaishali
Rajgriha
Pataliputra
Vaishali
The correct answer is Vaishali.

Key Points
Thus, we can say that the Second Buddhist Council was held at Vaishali.

Additional Information
The Tropic of Cancer does NOT pass through which of the following Indian states?
Madhya Pradesh
West Bengal
Gujarat
Andhra Pradesh
Andhra Pradesh
The correct answer is Andhra Pradesh.

Key Points

Additional Information
According to which of the following Articles shall the Supreme Court of India have power to review any judgement pronounced or order made by the Parliament?
Article 135
Article 143
Article 137
Article 235
Article 137
The correct answer is Article 137.

Key Points
| Article | Subject Matter |
|---|---|
| Article 135 | Jurisdiction and powers of the Federal Court under existing law to be exercisable by the Supreme Court. |
| Article 143 | Power of President to consult Supreme Court. |
| Article 235 | Control over subordinate courts. |
What will come in place of (-)?
1, 4, 3, 8, 7, 12, _, 16, 21
13
19
14
15
13
The logic followed here is:
Given series is 1, 4, 3, 8, 7, 12, _, 16, 21

Therefore, '13' is the required number.
Hence, "Option (1)" is the correct answer.
In a certain code language, 'PLANNED' is written as 'RNCNPGF' and 'PROMOTE' is written as 'RTQMQVG'. How will 'IMPROVE' be written in that language?
KORTQXG
KORRQXG
KOQRQXG
KORTOXG
KORRQXG
The position of the letters according to the English alphabet series:

The logic that follows here is as follows:
The word PLANNED is written as RNCNPGF

Similarly, the word PROMOTE will be written as RTQMQVG

In the same way, IMPROVE will be written as

IMPROVE is written as KORRQXG
Hence, the correct answer is "KORRQXG".
Read the given statements and conclusions carefully. Assuming that the information in the statements is true, even if they appear to be at variance with commonly known facts, select which of the conclusions logically follow(s) from the statements beyond reasonable doubt.
Statement:
I. All pets are birds.
II. Some birds are fishes.
Conclusion:
I. Some fishes are pets.
II. All birds are fishes.
Only conclusion I follows.
Only conclusion II follows.
Neither conclusion follows.
Both the conclusions follow.
Neither conclusion follows.
he logic followed here is:
Draw the Venn diagram:

Conclusions:
I. Some fishes are pets → False (No direct relationship given between fishes and pet it may be possible but not defined)
II. All birds are fishes → False (It may be true but not definitely, Some birds are fishes)
Therefore, the correct answer is "Neither conclusion follows.".
Hence, the correct answer is "Option (3)".

Additional Information

If 15378 : 24 :: 20654 : ?
21
34
17
26
17
The logic followed here is:
15378 = 1 + 5 + 3 + 7 + 8 = 24
similarly,
20654 = 2 + 0 + 6 + 5 + 4 = 17
Hence, the correct answer is "Option (3)".
A cyclist is riding from West to East and then takes a sharp left and goes about on a U - turn and then takes a right turn. In which direction is he heading towards?
East
South
North
West
West
We can understand the journey of cyclists by following figure given below:

We can see that he is going in the 'West' direction.
Hence, the correct answer is "West".
In the following question, select the odd word pair from the given alternatives.
Computer - Mouse
Boat - Oar
Car - Engine
Car - Windshield
Car - Windshield
The logic followed in the given pair:
The first item in each pair is operated by the second item of the pair.
Laptop is operated by a Mouse.
Boat is operated by an Oar
Car is operated by an Engine.
However,
Car - Windshield is the only option that doesn't follow the logic as a Car is not operated by a windshield.
Hence, ‘Car - Windshield’ is the correct pair.
I, J, K, L, M, N and O are sitting along a circle facing at the centre and are playing cards. M is the immediate neighbour of I and L. J is second to the left of O. N is on the immediate right of I. What is the position of N?
2nd to the left of L
3rd to the right of O
To the immediate left of J
2nd to the right of K
To the immediate left of J
I, J, K, L, M, N and O are sitting along a circle facing at the centre.

M is the immediate neighbour of I and L.
N is on the immediate right of I.

N is to the immediate left of J.
Hence, the correct answer is "To the immediate left of J "
Select the option that is related to the third letter-cluster in the same way as the second letter-cluster is related to the first letter-cluster.
FRIED : TRHJF :: FACET : ?
VFLGC
VFGCL
VHJEB
VLFCG
VHJEB

Logic:
1) Given word is arranged according to descending order.
2) Vowels are coded as multiplied by 2.
3) Consonants are coded as + 2.
The logic followed here is :-

Similarly,

Hence, the correct answer is "VHJEB".
The sequence of folding a piece of paper and the manner in which the folded paper has been cut is shown in the following figures. How would this paper look when unfolded?






The paper when unfolded will appear as shown below:

Hence, 'option 3' is the correct answer.
'A × B' means A is the father of B.
'A - B' means A is the sister of B.
'A + B' means A is the mother of B.
'A ÷ B' means A is the brother of B.
In the expression O + S × P ÷ T, how is P related to O?
Sister
Father
Brother
Grandson
Grandson
By using the symbols in the table given below, we can draw the following family tree:

| Sign | Relation |
|---|---|
| × | Father |
| - | Sister |
| + | Mother |
| ÷ | Brother |
Given: O + S × P ÷ T

Clearly, P is the Grandson of O.
Hence, the correct answer is "Grandson".
Three of the following letter-clusters are alike in some manner and hence form a group. Which letter-cluster does not belong to that group?
FKA
CJZ
PUK
CHX
CJZ
According to the English alphabets & their positional values:

The pattern followed in the given options is:
Option 1) FKA :

Option 2) CJZ :

Option 3) PUK :

Option 4). CHX :

So, CJZ is the odd one.
Hence, the correct answer is "Option 2".
Seven friends K, L, M, N, O, P and Q are sitting on a straight bench facing north. M and Q are not sitting at any of the extreme ends. K is sitting exactly at the middle position. Only P is sitting between Q and N. L is sitting third to the right of K. K is sitting to the immediate left of O.
Who is sitting at the extreme left end?
O
Q
N
L
N
Seven friends K, L, M, N, O, P and Q are sitting on a straight bench facing north.
K is sitting exactly at the middle position.
L is sitting third to the right of K.
K is sitting to the immediate left of O.

Only P is sitting between Q and N.
M and Q are not sitting at any of the extreme ends.


So, "N" is sitting at the extreme left end.
Hence, the correct answer is "N".
Select the figure that will come next in the following figure series.






The pattern followed here is:

Hence, the correct answer is "Option 2".
Select the letter-cluster that can replace the question mark (?) in the following series.
KCZ, MEY, OGX, QIW, ?
JKU
SKV
JKL
JKT
SKV
Position values of the letters, according to the English alphabet series is:

The logic of the above series is mentioned below-

Hence, SKV is correct answer.
Suppose the first and the second letters of the English alphabet series changed places, also the third and the fourth, the fifth and the sixth, and so formed, which letter would be the 15th from the left?
T
P
R
O
P
As per the given information:
B A D C F E H G J I L K N M P O R Q T S V U X W Z Y
Here, the letter 'P' is 15th from the left.
Hence, the correct answer is "Option (2)".
In the following question, choose the correct mirror image of the figure (x) from the four alternatives given along with.






If a mirror is placed along MN line, then, we will get the following mirror image-

Hence, the correct answer is option 2.
Seven persons – G, M, R, K, L, P and C – are sitting around a circular table facing the centre. The following information is known about them. G is to the immediate right of K, who is third to the left of C. R is adjacent to both C and P. M is not adjacent to G. Who is third to the left of M ?
C
L
R
G
C
Given: Seven persons – G, M, R, K, L, P and C.
G is to the immediate right of K, who is third to the left of C.
R is adjacent to both C and P.


And, L will sit on the remaining place.

So, 'C' is the third to the left of M.
Hence, the correct answer is "C".
Brick is related to ________ in the same way as Chapati is related to Wheat.
Paint
House
Cement
Clay soil
Clay soil
Given:
Chapati is related to Wheat → Chapati is made from wheat.
Similarly,
Brick is related to clay soil → Brick is made from clay soil.
Hence, the correct answer is "Option (4)".
Three different positions of the same dice are shown (Figures 1-3). Find the number on the face opposite to the face having ‘2’.

1
4
6
5
6
When we compare figure 1 and figure 2:

We can see that 3 is opposite to 4.
When we compare figure 1 and figure 3:

We can see that 5 is opposite to 1.
Now we only have two faces left i.e., 2 and 6 which means 2 and 6 are opposite to each other.
Hence, the correct answer is Option 3.
Four numbers are given, out of which three are alike in some way and one is different. Select the odd number.
224
362
168
288
362
The logic followed here is:
Check all options:
Option (1) : 224 → 152 – 1 = 225 – 1 = 224
Option (2) : 362 → 192 + 1 = 361 + 1 = 362
Option (3) : 168 → 132 – 1 = 169 – 1 = 168
Option (4) : 288 → 172 – 1 = 289 – 1 = 288
Therefore, '362' is odd.
Hence, "Option (2)" is the correct answer.
Six friends, A, B, C, D, E, and F are seated in a row facing north. There are exactly two seats to the left of B. F is an immediate neighbour of both B and D. E is not at either of the extreme seats of the row. A is sitting at the leftmost end. C is not an immediate neighbour of E. If A and D decide to swap their positions, what will be the new position of A?
Third to the right of E
Second to the left of F
Third from the right end
Extreme right of the row
Third to the right of E
Six friends, A, B, C, D, E, and F are seated in a row facing north.

OR


OR

According to given information exact position of E is not given and C will not sit with E. A is sitting at the leftmost end. So, the first arrangement is rejected.
Now, We will go with the second arrangement.
So, the final arrangement will be,

According to the condition, A and D decide to swap their positions then it will become:

The new position of A will be Third to the right of E.
Hence, the correct answer is "Third to the right of E".
How many such pairs of letters are there in the word 'CLAVICLE' (in both forward and backward direction) which have as many letters between them as in the sequence in the English alphabet?
Five
Four
Three
Two
Three
Given:
CLAVICLE

As per the given information:

Here, three pairs are shown in the above figure.
Hence, the correct answer is "Option (3)".
How many triangles are there in the given figure?

18
19
21
17
21
We count the triangles in the given figure:

:

Total triangles = 21
Hence, the correct answer is option (3).
If the first half of the English alphabet series is reversed, which of the following will be the twelfth to the right of the seventh letter from the left end?
P
O
S
N
S
We solve the given statement with the help of the following table:

Step 1: We reverse the first half of the alphabets series,
M L K J I H G F E D C B A N O P Q R S T U V W X Y Z
Step 2: Seventh letter from the left end.
M L K J I H G F E D C B A N O P Q R S T U V W X Y Z
G is the seventh letter from the left end.
Step 3: The twelfth to the right of the seventh letter from the left end.
M L K J I H G F E D C B A N O P Q R S T U V W X Y Z
S is twelfth to the right of the seventh letter from the left end
Hence the correct answer is option (3).
Select the option in which the given figure is embedded (rotation is NOT allowed).






We consider the given options and see whether the given figure can be embedded:

Hence, the correct answer is option 3).
5 men and 3 women together or 9 men can cultivate a land in 60 days. Then how many days 8 men and 9 women together cultivate the same land.
23
27
25
26
27
Given:
5 men and 3 women together or 9 men can cultivate a land in 60 days
Calculation:
According to the question,
(5m + 3w) = 9m
⇒ 3w = 4m
So, (8m + 9w) = 8m + 12m = 20m
9m can cultivate a land in 60 days
1m can cultivate a land in 60 × 9 days
20m can cultivate a land in (60 × 9)/20 days = 27 days.

Alternate Method(5m + 3w) × 60 = 9m × 60
⇒ m/w = 3/4
Total work = (5 × 3 + 3 × 4) × 60 = 27 × 60 =1620
Total efficiently of (8m + 9w) = 8 × 3 + 9 × 4 = 24 + 36 = 60
Required no of days = 1620/60 = 27 days
Find the value of
0.3
1.9
2.4
2.7
2.4
Given:
Formula used:
a3 - b3 = (a - b)(a2 + b2 + ab)
Calculation:
Here, 0.027 = 0.3 × 0.3 × 0.3 = 0.33
⇒ 2.7 x 2.7 x 2.7 = 2.73
⇒ 7.29 = 2.72
⇒ 0.81 = 2.7 × .3
⇒ 0.09 = 0.32
we can assume a = 2.7 and b = 0.3
apply the formula a3 - b3 = (a - b)(a2 + b2 + ab)
=
=
= (2.7 - 0.3) = 2.4
∴ The correct answer is "2.4"
A circle circumscribes a triangle ABC. Find the angle subtended by arc BC at the circumcentre of Δ ABC, If ∠BAC 40°.
30°
60°
40°
80°
80°
Given-
∠BAC = 40°
Concept Used:
Circumcentre: The intersection point of two perpendicular bisectors of a triangle is the circumcentre of the triangle.
The circumcenter is also the center of the circle passing through the
three vertices, which circumscribes the triangle.
Theorem: The angle subtended by an arc at the center is double the
angle subtended by it at any point on the remaining part of the circle.
Calculation:

We know that the intersection point of two perpendicular bisectors of a triangle is the circumcentre of the triangle.
Let that point be O.
Using the theorem discussed above
∠BOC = 2 × ∠BAC
⇒ ∠BOC = 2 × 40°
⇒ ∠BOC = 80°
∴ The angle subtended by the intersection point of two of its perpendicular bisector on the arc BC is 80°

Additional InformationIncenter:
The incenter of a triangle is the point of intersection of all the three
interior angle bisectors of the triangle.

An amount invested in simple interest gives Rs 4200 interest at a rate of 15% in 4 years. What is the principal (in Rs)?
7000
6000
8000
9000
7000
⇒ Interest = Rs. 4200, Rate = 15% and T = 4 years, Let Principal be p
⇒ S.I = (P × R × T) / 100, where P is the principal, r is the rate of interest and t is the time period.
⇒ 4200 = (p × 15 × 4)/100
⇒ 4200 × 100 = 60p
⇒ p = (4200 × 100)/60
∴ Principal = Rs. 7000
A certain sum amounts to ₹17,925 in 3 years and to ₹21,825 in 7 years at the same rate per cent per annum at simple interest. What will be the simple interest (in ₹) on a sum of ₹18,500 for 4 years at double the earlier rate?
10,582
8,245
9,876
7,625
10,582
Given:
Amount in 3 year = ₹17,925
Amount in 7 year = ₹21,825
Formula used:
1. SI = (PRT)/100
2. Amount = P + SI
Where, P = Principal, R = Rate, T = Time(in years)
Calculation:
SI in (7 - 3) year = 21825 - 17925
⇒ SI in 4 year = ₹3900
⇒ SI in 3 year = 3900 x 3/4 = ₹2925
Now, P = 17925 - 2925 = ₹15000
⇒ 2925 = (15000 × 3 × R)/100
⇒ R = 6.5%
⇒ 2R = 13%
According to the question,
SI = (18500 x 22 x 13)/(5 x 100)
⇒ SI = ₹10,582
∴ The required SI is ₹10,582.
Which one among the following is the largest?
7/9
11/14
3/4
10/13
11/14

Shortcut Trick


Alternate Method
Converting the fractions into decimals;
7/9 = 0.77
11/14 = 0.78
3/4 = 0.75
10/13 = 0.76
⇒ 0.78 > 0.77 > 0.76 > 0.75
⇒ 11/14 > 7/9 > 10/13 > 3/4
∴ The correct answer is (11/14).
A person travels from A to B at 75 kmph in a Car and in the return journey the speed is reduced by 15 kmph. If the total time taken is four-and-half hours then the distance (in kms) between A and B is:
100
120
140
150
150
Given:
Speed during going = 75 kmph
Speed is reduced while returning
Total time taken = 4.5 hours = 9/2 hours
Formula used:
Time taken = Distance/Speed
Calculation:
Let the distance from A and B is x km
Speed while returning = (75 – 15) kmph = 60 kmph
Time taken while going = x/75 hr
Time taken while returning = x/60 hr
According to the question,
(x/75) + (x/60) = 4.5
⇒ 9x/300 = 4.5
⇒ x = 0.5 × 300 = 150 km
∴ The distance between A and B is 150 km
What is the greatest number which divided by 1356, 1868, and 2764 leaves a remainder of 12 in each case?
74
64
54
44
64

Shortcut Trick
Required number = HCF of (1356 − 12), (1868 − 12) and (2764 − 12).
Required number = HCF of 1344, 1856 and 2752.
The difference between the first two numbers (1856 − 1344) is 512.
The required HCF must be a factor of 512. From the given options (74, 64, 54, 44), only 64 is a perfect factor of 512.
∴ The correct answer is 64.

Alternate Method
Given:
Numbers given are 1356, 1868 and 2764.
The remainder in each case is 12.
Formula Used:
Required greatest number = HCF of (a − r), (b − r) and (c − r)
Calculations:
⇒ First number = 1356 − 12 = 1344
⇒ Second number = 1868 − 12 = 1856
⇒ Third number = 2764 − 12 = 2752
⇒ Prime factorization of 1344 = 26 × 3 × 7
⇒ Prime factorization of 1856 = 26 × 29
⇒ Prime factorization of 2752 = 26 × 43
⇒ HCF of (1344, 1856, 2752) = 26 = 64
∴ The correct answer is 64.

Additional Information
Case 1: Same Remainder Given
The greatest number that divides a, b, and c leaving a remainder r in each case is the HCF of (a − r), (b − r), and (c − r).
Case 2: Same Remainder Not Given
The greatest number that divides a, b, and c leaving the same remainder in each case is the HCF of |a − b|, |b − c|, and |c − a|.
Case 3: LCM Remainder Concept
The least number which when divided by a, b, and c leaves a remainder r in each case is [LCM of (a, b, c)] + r.
Find the sum of unit and tenth digit of 7181.
3
9
7
1
7
Last two digit of 7n,
71 = 07
72 = 49
73 = 43
74 = 01
⇒ Cyclicity of 7n is 4,
⇒ 7181 = 74 × 45 + 1 = 71 = 07
⇒ Last two digits of 7181 is 07.
∴ Required sum = 0 + 7 = 7.
The respective ratio between the present ages of Rani and Moni is 6 ∶ 7. If Moni is 4 years older than Rani, then what will be the respective ratio of the ages of Rani and Moni after 4 years?
4 ∶ 3
7 ∶ 8
3 ∶ 4
3 ∶ 5
7 ∶ 8
Given
The ratio of the present age of Rani and Moni = 6 : 7
Calculation
Let the ratio be x
So, the difference in ages of Rani and Moni = 4
⇒ 7x - 6x = 4
⇒ x = 4
So, Age of Rani and Moni after 4 years
Age of Moni = 7x + 4 = 7 × 4 + 4 = 28 + 4 = 32
Age of Rani = 6x + 4 = 6 × 4 + 4 = 24 + 4 = 28
Ratio of Age of Rani and Moni after 4 years = 28 : 32 = 7 : 8
∴ The correct answer is 7 : 8
If 9cotθ = 4, then = ?
1
0

Shortcut Trick
Given 9cotθ = 4 ⇒ cotθ = 4/9.
Divide the numerator and denominator of the fractional part by sinθ to convert it into cotθ:
⇒ [(4 − cotθ) / (4 + cotθ)] + 3
⇒ [(4 − 4/9) / (4 + 4/9)] + 3
⇒ (32/9) ÷ (40/9) + 3 ⇒ 32/40 + 3
⇒ 4/5 + 3 = 19/5
∴ The correct answer is 19/5.

Alternate Method
Given:
⇒ 9cotθ = 4 ⇒ cotθ = 4/9

Calculations:
⇒ By Pythagoras theorem, Hypotenuse = √(Base2 + Perpendicular2)
⇒ Hypotenuse = √(42 + 92) = √(16 + 81) = √97
⇒ sinθ = Perpendicular ÷ Hypotenuse = 9/√97
⇒ cosθ = Base ÷ Hypotenuse = 4/√97
⇒ Numerator = 4sinθ − cosθ = 4 × (9/√97) − (4/√97) = 36/√97 − 4/√97 = 32/√97
⇒ Denominator = 4sinθ + cosθ = 4 × (9/√97) + (4/√97) = 36/√97 + 4/√97 = 40/√97
⇒ Fraction value = (32/√97) ÷ (40/√97) = 32/40 = 4/5
⇒ Total Expression = 4/5 + 3 = 19/5
∴ The correct answer is 19/5.

Additional Information
Trigonometric Ratios
In a right-angled triangle, sinθ = Perpendicular ÷ Hypotenuse, cosθ = Base ÷ Hypotenuse, and tanθ = Perpendicular ÷ Base.
Basic Trigonometric Identities
The three fundamental identities are: sin2θ + cos2θ = 1, 1 + tan2θ = sec2θ, and 1 + cot2θ = cosec2θ.
Pythagorean Theorem
For any right-angled triangle, the square of the hypotenuse is strictly equal to the sum of the squares of its other two sides: H2 = P2 + B2.
A takes twice as much time as B or thrice as much as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in
4 days
6 days
8 days
12 days
6 days

Shortcut Trick
Time ratio of A : B : C = 6 : 3 : 2
Efficiency ratio of A : B : C = 1/6 : 1/3 : 1/2 = 1 : 2 : 3
Total efficiency of A + B + C = 1 + 2 + 3 = 6 units/day
Total work = Combined efficiency × Total days = 6 × 2 = 12 units
Time taken by B alone = Total work ÷ B's efficiency = 12 ÷ 2 = 6 days
∴ The correct answer is 6 days.

Alternate Method
Given:
Time taken by A = 2 × Time taken by B = 3 × Time taken by C
Let Time taken by A = 6x days.
Time taken by B = 3x days.
Time taken by C = 2x days.
| Person | Days | Total Work | Efficiency |
|---|---|---|---|
| A | 6x | 6x | 1 |
| B | 3x | 2 | |
| C | 2x | 3 |
Calculations:
⇒ Total efficiency of A, B and C = 1 + 2 + 3 = 6
⇒ Time taken by A, B and C together = Total Work ÷ Total Efficiency
⇒ 2 = 6x ÷ 6
⇒ x = 2
⇒ Time taken by B alone = 3x = 3 × 2 = 6 days
∴ The correct answer is 6 days.

Additional Information
Pipes & Cisterns
Similar to Time & Work, an inlet pipe does positive work while an outlet pipe does negative work. Net efficiency = Inlet efficiency − Outlet efficiency.
Work & Wages
Wages are always distributed in the ratio of the total work done by each individual. If they work for the same number of days, the ratio of wages equals their ratio of efficiencies.
Alternate Day Work
When persons work on alternate days, calculate the total work done in a complete cycle (e.g., 2 days for 2 people) and multiply to reach as close to total work as possible before adjusting.
The bar graph given below shows the number of students (in thousands) of two universities in six different years. What is the difference between the number of students in University 1 in the year 2017 and the number of students in University 2 in the year 2019?
2000
1500
1000
0
0
Solution:
Number of students in University 1 in the year 2017 is 20,000.
Number of students in University 2 in the year 2019 is 20,000.
Hence, the difference between both the university is 0.
Refer the below data table and answer the following Question.
| Year वर्ष | Ratio Import / Export अनुपात आयात / निर्यात |
|---|---|
| 2011 | 0.7 |
| 2012 | 1.1 |
| 2013 | 0.9 |
| 2014 | 1.5 |
| 2015 | 1.2 |
If the imports in 2012 was Rs. 1000 crores and the total exports in the years 2012 and 2013 together was Rs.3200 crores, then the imports in 2013 was?
2062
2291
909
2545
2062
Exports in the year 2012 = 1000/1.1 ≈ 909 crores
Exports in the year 2013 = 3200 - 909 = Rs. 2291 crores
∴ Imports in 2013 = 2291 × 0.9 ≈ Rs. 2062 crores
If a, b, c are real numbers and a2 + b2 + c2 = 2(a - b - c) - 3, then the value of a + b + c is
-1
1
3
0
-1
Given:
a2 + b2 + c2 = 2(a - b - c) - 3
Concept used:
Calculation:
a2 + b2 + c2 = 2(a - b - c) - 3
⇒ (a2 - 2a + 1) + (b2 + 2b + 1) + (c2 + 2c + 1) = 0
⇒ (a - 1)2 + (b + 1)2 + (c + 1)2 = 0
According to the concept,
(a - 1)2 = 0
⇒ a = 1
(b + 1)2 = 0
⇒ b = -1
(c + 1)2 = 0
⇒ c = -1
Now, a + b + c
⇒ 1 - 1 - 1 = -1
∴ The required value of a + b + c is -1.

Alternate MethodGiven:
a, b, c are real numbers and a2 + b2 + c2 = 2(a - b - c) - 3
Calculations:
Rearrange the equation:
a2 + b2 + c2 = 2a - 2b - 2c - 3
⇒ a2 - 2a + b2 + 2b + c2 + 2c + 3 = 0
Group terms to form perfect squares:
⇒ (a2 - 2a + 1) + (b2 + 2b + 1) + (c2 + 2c + 1) = 0
⇒ (a - 1)2 + (b + 1)2 + (c + 1)2 = 0
Since a, b, c are real numbers, each squared term must be zero for their sum to be zero:
a - 1 = 0 ⇒ a = 1
b + 1 = 0 ⇒ b = -1
c + 1 = 0 ⇒ c = -1
Find a + b + c:
a + b + c = 1 + (-1) + (-1)
⇒ a + b + c = 1 - 1 - 1
⇒ a + b + c = -1
∴ The value of a + b + c is -1.
The length of a rectangular field is increased by 30% and breadth is decreased by 30%. What is the per cent increase or decrease in its area?
9% decrease
21% decrease
21% increase
19% increase
9% decrease

Shortcut TrickLet the length and breadth be 10 units each
So, Area of rectangle = 10 × 10 = 100 sq. unit
New length = 130% of 10 = 13
New breadth = 70% of 10 = 7
So, New area of rectangle = 13 × 7 = 91 sq. unit
Percentage decrease in area = %
∴ Decrease percent is 9%

Alternate Method
Given:
Length of rectangular Field increased by 30%
Breadth of the Rectangular Field decreased by 30%
Formula Used:
Area of rectangle = Length × Breadth
Calculation:
Let the Length of rectangular field be x
and the breadth of the field be y
Initial area of the field = x × y = xy units2
New length after increase of 30% = [x + (30x/100)]
⇒ 13x/10 units
New breadth after decrease of 30% = [y – (30y/100)
⇒ 7y/10 Units
New area of Rectangular Field = (13x/10) × (7y/10)
⇒ 91xy/100 Units2
Decrease in the area = xy – (91xy/100)
⇒ 9xy/100 Units2
Percentage change in area = [(9xy/100)/xy] × 100
⇒ 9%
∴ Decrease in the area of rectangular field is 9%.
The diameter of the driving wheel of a bus is 140 cm. How many revolutions per minute must the wheel make to keep a speed of 66 km/h?
200
2220
240
250
250
Let, revolution per minute be x
Diameter of the driving wheel = 140 cm
⇒ Radius of the driving wheel = (140/2) = 70 cm
⇒ Circumference of the driving wheel = 2 × 22/7 × 70 = 440 cm = 4.4 m
Now, 66 km/h = 66 × (5/18) m/s = 66 × (5/18) × 60 m/min = 1100 m/min
According to the the question,
4.4x = 1100
⇒ x = 1100/4.4 = 250
∴ The wheel must make 250 revolutions per second.
A man undertakes to do a work in 150 days. He employs 200 men. He finds that only a quarter of the work is done in 50 days. How many additional men should he employ so that the whole work is finished in time?
75
85
100
120
100
200 men can complete the quarter of work in 50 days
If they continue the work, time taken to complete the remaining work = 3 × 50 = 150 days
[∵ ¾ th of the work is remaining]
But they have to complete in 100 days to finish in time
Time ∝ 1/Number of employees
Let the number of extra employees required to complete the work in time be x
∴ 150/100 = (200 + x)/200
300 = 200 + x
∴ x = 100
One side of the triangle is 15 cm and the corresponding height is 6 cm, then area of the triangle is:
46 sq.cm
45 sq.cm
47 sq.cm
48 sq.cm
45 sq.cm
Given:
Side of triangle = 15 cm
Height of triangle = 6 cm
Concept Used:
Area of triangle = × Base × Height
Calculation:
⇒ Putting the values in formula, we get
⇒ Area of triangle = × 6 × 15
⇒ Area of triangle = 3 × 15 = 45 cm2
Therefore, the area of triangle is 45 cm2.
The difference between the two parallel sides of a trapezium is 4 cm. The perpendicular distance between them is 19 cm. If the area of the trapezium is 475 cm2, find the length of the parallel side.
24 cm & 28 cm
23 cm & 27 cm
20 cm & 24 cm
16 cm & 20 cm
23 cm & 27 cm
GIVEN:
The difference between the two parallel sides of a trapezium = 4 cm and the perpendicular distance between them = 19 cm
The area of the trapezium = 475 cm2
FORMULA USED:
The area of the trapezium = 1/2 × (sum of parallel side) × (perpendicular distance between them) sq. unit
CALCULATION:
Let the two parallel sides of a trapezium be a cm and b cm
⇒ a - b = 4 ----(1)
⇒ The area of the trapezium = 1/2 × (sum of parallel side) × (perpendicular distance between them) sq. unit
⇒ 475 = 1/2 × (a + b) × 19
⇒ a + b = 50 ----(2)
⇒ on solving equation (1) & (2)
⇒ a = 27 and b = 23
∴ two parallel sides of the trapezium are 27 cm and 23 cm
Which of the following fraction is the largest?
7/8
13/16
63/80
31/40
7/8
Calculation:
7/8 = 0.875
13/16 = 0.8125
63/80 = 0.7875
31/40 = 0.775
So, 7/8 is the largest
∴ The required answer is 7/8.

Alternate MethodLCM of 8, 16, 80, 40 is 80
So,
7/8 = 80 × 7/8 = 70
13/16 = 80 × 13/16 = 65
63/80 × 80 = 63
31/40 × 80 = 62
So, 7/8 is the largest among them
The third proportional to (x2 – y2) and (x + y) is:
Given:
(x2 – y2) and (x + y)
Formula used:
(x2 – y2) = (x + y)(x - y)
Calculation:
let A be the third proportion,
A =
Answer is .
The average age of 7 members of a family is 25. If one of the members whose age is 28 years, is excluded, then others are in the ratio 1 : 2 : 3 : 4 : 5 : 6. Find the age of the eldest member of the family.
46
44
48
42
42
FORMULAE USED:
Average = Sum of all/total number of terms
CALCULATION:
25 = Sum of all/7
⇒ Sum = 175
Let the ratio be k
Then, sum of remaining six people will be 21k
⇒ 175 – 28 = 21k
⇒ k = 7
Age of oldest member will be = 6 × k = 6 × 7 = 42
∴ So, the age of the eldest member of the family is 42 years
A shopkeeper sold two items, one at 25% profit and another at 15% loss and got a profit of Rs. 35. If the cost price of the item sold at 25% profit is twice than that of the item sold at 15% loss, find the sum of the cost price of both items.
Rs. 300
Rs. 200
Rs. 100
Rs. 400
Rs. 300

Shortcut Trick
Let the Cost Price of the second item be 100 units. Then the Cost Price of the first item is 200 units.
Profit from first item = 200 × 25% = 50 units. Loss from second item = 100 × 15% = 15 units.
Net profit = 50 − 15 = 35 units. Given net profit = Rs. 35.
∴ 35 units = Rs. 35 ⇒ 1 unit = Rs. 1.
Sum of Cost Price = 200 + 100 = 300 units = 300 × 1 = Rs. 300.
∴ The correct answer is Rs. 300.

Alternate Method
Given: CP1 = 2 × CP2, Profit%1 = 25%, Loss%2 = 15%, Net Profit = Rs. 35.
Formulas: Profit = CP × Profit%, Loss = CP × Loss%, Total CP = CP1 + CP2.

⇒ Let Cost Price of item 2 be x. Then Cost Price of item 1 is 2x.
⇒ Profit from item 1 = 2x × (25/100) = 0.5x.
⇒ Loss from item 2 = x × (15/100) = 0.15x.
⇒ Net Profit = 0.5x − 0.15x = 0.35x.
⇒ 0.35x = 35 ⇒ x = 35 ÷ 0.35 = 100.
⇒ Sum of Cost Price = 2x + x = 3x = 3 × 100 = 300.
∴ The correct answer is Rs. 300.

Additional Information
Net Profit and Loss
When multiple transactions occur, the overall profit or loss is the algebraic sum of individual profits (positive) and losses (negative).
Cost Price Calculation
Total Cost Price is the sum of the individual cost prices of all articles purchased: Total CP = CP1 + CP2 + ... + CPn.
Five years ago the sum of the ages of A and B was 58 years. The difference between B's age 8 years ago and A's age 8 years hence is 16 years. The ratio of the present ages of A and B is:
9 ∶ 25
25 ∶ 9
5 ∶ 13
36 ∶ 52
9 ∶ 25

Shortcut Trick
Sum of present ages = 58 + 5 + 5 = 68 years.
Difference (B − 8) − (A + 8) = 16 ⇒ B − A = 32 years.
A = (Sum − Diff) ÷ 2 = (68 − 32) ÷ 2 = 18 years.
B = (Sum + Diff) ÷ 2 = (68 + 32) ÷ 2 = 50 years.
Ratio A : B = 18 : 50 = 9 : 25.
∴ The correct answer is 9 : 25.

Alternate Method

Let the present ages of A and B be A and B respectively.
According to first condition:
⇒ (A − 5) + (B − 5) = 58
⇒ A + B − 10 = 58
⇒ A + B = 68 --- (eq i)
According to second condition:
⇒ (B − 8) − (A + 8) = 16
⇒ B − 8 − A − 8 = 16
⇒ B − A = 32 --- (eq ii)
Adding (eq i) and (eq ii):
⇒ 2B = 100 ⇒ B = 50
Subtracting (eq ii) from (eq i):
⇒ 2A = 36 ⇒ A = 18
⇒ Ratio A : B = 18 : 50 = 9 : 25
∴ The correct answer is 9 : 25.

Additional Information
Age Sum Property
If the sum of ages of 'n' people is S now, then 'x' years ago the sum was S − (n × x).
Age Difference Constant
The difference between the ages of two individuals remains constant at any point in time.
Ratio and Proportion
To find the ratio of two quantities, they must be in the same unit and simplified to their lowest terms.
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