RRB NTPC CBT 1 2020: উত্তরসহ প্রশ্ন

With ∠C = 90° in an isosceles triangle, AC = BC = 8 cm and AB is the hypotenuse: √(8² + 8²) = 8√2 cm.

Third column = (first)³ + (second)²: 5³ + 4² = 141 and 6³ + 2² = 220. So 7³ + 3² = 343 + 9 = 352.

The only child of Supriya's grandmother is Supriya's parent. That parent's daughter is Supriya's sister.

The Swachh Bharat Mission was launched on 2 October 2014, Gandhi Jayanti.

By alligation, officers : non-officers = (3560 − 2600) : (5400 − 3560) = 960 : 1840 = 12 : 23. With 12 officers there are 23 non-officers.

Let the larger number be x: x + 24 = 5(x − 24), so 4x = 144 and x = 36.

Shah Jahan began building the Taj Mahal complex in about 1632 in memory of Mumtaz Mahal.

9 m south-east followed by 9 m north-west cancel each other. The remaining moves are 15 m west and 6 m east, a net 9 m west, so she is 9 m from the start.

Among the options, Kudankulam in Tamil Nadu (units commissioned from 2013) is the newest nuclear power plant; Tarapur, Kalpakkam and Kaiga are much older.

Part III of the Constitution (Articles 12–35) contains the Fundamental Rights.

Kuchipudi, named after a village in Krishna district, is the classical dance of Andhra Pradesh.

Only the number 4 lies inside the triangle, the rectangle and the circle at the same time.

Kolleru Lake, a large freshwater lake between the Godavari and Krishna deltas, is in Andhra Pradesh.

In each column, bottom = first × second − second × third: 7×6 − 6×5 = 12, 8×5 − 5×2 = 30, 5×4 − 4×2 = 12. So 8×7 − 7×3 = 56 − 21 = 35.

LCM(6, 14, 28) = 84. The largest multiple below 500 is 84 × 5 = 420.

Beti Bachao, Beti Padhao was launched on 22 January 2015 at Panipat, Haryana.

x⁴ + 1/x⁴ = 194 gives x² + 1/x² = √196 = 14, and x + 1/x = √16 = 4. Then x³ + 1/x³ = 4³ − 3 × 4 = 52.

At a 10% loss, CP = 45000/0.9 = Rs 50,000. For a 15% gain, SP = Rs 57,500.

Decoding option 1: 36 × 6 ÷ 3 + 5 − 3 = 72 + 2 = 74, which is correct. For example option 4 becomes 36 ÷ 6 × 3 + 7 − 3 = 22, not 24.

The multipliers increase by 1: 8 × 1.5 = 12, 12 × 2.5 = 30, 30 × 3.5 = 105, 105 × 4.5 = 472.5.

First = 2 × second = 3 × third, so the numbers are in the ratio 6 : 3 : 2. Their sum = 3 × 880 = 2640, so one part = 240 and the smallest = 2 × 240 = 480.

With rate r% for r years: 24000 × r × r/100 = 19440, so r² = 81 and r = 9%.

Circumference = 700 × 0.44 m = 308 m, so r = 308/(2 × 22/7) = 49 m. Area = 22/7 × 49² = 7546 m².

The first digit of the result is the sum of the second number's digits and the second digit is the difference of the first number's digits: 15 × 17 → (1+7)(5−1) = 84; 92 × 23 → (2+3)(9−2) = 57. So 54 × 32 → (3+2)(5−4) = 51.

The word is reversed and each letter written as its position: FRENCH → H C N E R F = 8 3 14 5 18 6. GERMAN → N A M R E G = 14 1 13 18 5 7 = 141131857.

50 = 7² + 1, 82 = 9² + 1 and 170 = 13² + 1. 59 is not a square plus 1, so it is different.

The Golden Quadrilateral highway project linking Delhi, Mumbai, Chennai and Kolkata was launched in 2001 by PM Atal Bihari Vajpayee.

SAARC has 8 members: Afghanistan, Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan and Sri Lanka.

Facebook was founded in 2004 by Mark Zuckerberg with fellow Harvard students.

The banyan, India's national tree, is Ficus benghalensis. Ficus religiosa is the peepal and Azadirachta indica the neem.

Robert Hooke discovered the cell in 1665 while observing cork under a microscope.

Sardar Vallabhbhai Patel presided over the Karachi session of the Congress in March 1931, which passed the resolution on Fundamental Rights.

The Tokyo Summer Olympics, postponed from 2020 because of COVID-19, were held in 2021.

Lord Dalhousie (Governor-General 1848–1856) applied the Doctrine of Lapse to annex states such as Satara, Jhansi and Nagpur.

In dictionary order: Dance, Dare, Dear, Degree, Development. The middle word is Dear.

The SI unit of force is the newton (1 N = 1 kg m/s²). The dyne is the CGS unit.

4x/5 − 3x/4 = x/20 = 12, so x = 240.

OLE stands for Object Linking and Embedding, a Microsoft technology for placing objects from one application into documents of another.

Numerator: 12.25 + 7/8 × 56 − 9 = 12.25 + 49 − 9 = 52.25. Denominator: 25 ÷ 5 × 10.25 + 10/9 × 2.7 − 2 = 51.25 + 3 − 2 = 52.25. The value is 1.

Chalk is calcium carbonate. Hydrochloric acid reacts with it to give carbon dioxide, which turns lime-water milky.

New area = 1.10 × 1.08 = 1.188 times the old area – an 18.8% increase.

The Bharat Ratna, India's highest civilian award, was instituted in 1954.

SP = 500 × 1.08 = Rs 540. After a 20% discount SP = 0.8 × MP, so MP = 540/0.8 = Rs 675.

In May 2019 the WHO certified Algeria and Argentina as malaria-free.

The five permanent members of the UN Security Council – China, France, Russia, the UK and the USA – have veto power.

INCOSPAR (Indian National Committee for Space Research) was formed in 1962 under Vikram Sarabhai; it became ISRO in 1969.

The India State of Forest Report 2019 put forest cover at 21.67% of India's geographical area.

Kudumbashree, a women-led community poverty-alleviation programme, was launched by the Kerala government in 1998.

Buying and selling goods and services over the internet is e-commerce.

Write the numbers as 24a and 24b with a, b co-prime: a + b = 384/24 = 16. Co-prime pairs: (1, 15), (3, 13), (5, 11), (7, 9) – 4 pairs.

Number of 3 cm cubes = (27/3) × (18/3) × (21/3) = 9 × 6 × 7 = 378.

The increases alternate +2, +6: 70, 72, 78, 80, 86, 88, 94.

Let males = 4k, females = 7k. (4k − 50)/(7k − 100) = 7/12 gives 48k − 600 = 49k − 700, so k = 100. Male officers = 400.

CGI, EIK and AEG follow +4, +2 (e.g. A→E→G). FHJ follows +2, +2, so it is different.

The service sector – trade, transport, banking, education and so on – is the tertiary sector.

A + B = 1/20 and B + C = 1/30, so A − C = 1/60. With A = 2C, C = 1/60, and B = 1/30 − 1/60 = 1/60. B alone takes 60 days.

Water freezes at 0 °C = 273.15 K.

R.K. Narayan's first novel was 'Swami and Friends' (1935), set in the fictional town of Malgudi.

The first batch of 20 Smart Cities was announced in January 2016, led by Bhubaneswar.

245² = 60025, the largest square below 60065. 60065 − 60025 = 40 must be subtracted.

Article 80 sets the maximum strength of the Rajya Sabha at 250 (238 elected and 12 nominated).

ab = (100 − 68)/2 = 16. a³ + b³ = (a + b)³ − 3ab(a + b) = 1000 − 480 = 520.

sin⁶θ + cos⁶θ = 1 − 3sin²θcos²θ and sin⁴θ + cos⁴θ = 1 − 2sin²θcos²θ. So the expression = 2 − 6s²c² − 3 + 6s²c² = −1.

Nobel Prizes are given in six fields: Physics, Chemistry, Medicine, Literature, Peace and Economic Sciences.

Aryabhata, India's first satellite, was launched on 19 April 1975 from the Soviet Union.

Four Anglo-Mysore Wars were fought (1767–1799), ending with Tipu Sultan's death at Srirangapatna.

The first session of the Indian National Congress was held in Bombay on 28–31 December 1885, presided over by W.C. Bonnerjee.

The height difference = 40√3 × tan 30° = 40√3 × 1/√3 = 40 m. The first tower is 130 − 40 = 90 m high.

World Environment Day 2019, hosted by China, focused on air pollution ('Beat Air Pollution').

Each letter moves 5 places back: M→H, N→I, T→O, K→F. Applying −5 to RUNA gives MPIV.

Take x = 4, y = 9: 9x + 4y = 72 and 18x + 3y = 99. Ratio 72 : 99 = 8 : 11.

If B worked d days, A worked d + 10 days: d/60 + (d + 10)/40 = 1. Multiplying by 120: 2d + 3d + 30 = 120, so d = 18.

The Ghadar Party was founded in 1913 in the USA by Lala Har Dayal with Sohan Singh Bhakna and others.

For equal distances, average speed = 2 × 75 × 50/(75 + 50) = 7500/125 = 60 km/h.

Numerator = 25 + 24 − 4 = 45; denominator = 27 − 3 × 4 = 15. 45/15 = 3.

Squaring: 1225 × √(32/x) = 4900, so √(32/x) = 4 and 32/x = 16. x = 2.

Methane is CH₄ – one carbon atom bonded to four hydrogen atoms.

BC = √(6² + 8²) = 10 cm. The altitude to the hypotenuse = AB × AC/BC = 48/10 = 4.8 cm.

m = 8k + 5, so 7m = 56k + 35 = 8(7k + 4) + 3. The remainder is 3.

The Dowry Prohibition Act was enacted in 1961.

'4 of 3' = 12, so 84 ÷ 12 = 7, and 11 − 12 ÷ 3 = 7. The curly bracket is 7 − 7 = 0, the square bracket 135, and 245 − 135 = 110.

Annual compounding: P × 1.21. Half-yearly: P × 1.05⁴ = P × 1.21550625. The difference 0.00550625P = 1762, so P = Rs 3,20,000.

India's coastline including the island territories is about 7,517 km.

Census 2011: Kerala had the highest literacy rate among states, about 94%.

All D are A and no A is C, so no D is C – I follows. II contradicts I, so it does not follow.

The code is the sum of letter positions plus the number of letters: P = 16 + 1 = 17; TMR = 51 + 3 = 54. NARESH = 14 + 1 + 18 + 5 + 19 + 8 = 65, plus 6 = 71.

Reversed, the 24 letters read R A Y K R A T H C A F R A K R N A P H N S I D A. The 9th from the left is C; three places to its right is the 12th letter, R.

Each letter moves 3 places forward: COCK → FRFN. HANG +3 = KDQJ.

36 students: 24 boys and 12 girls. Reema is 19th with 13 boys before her, so 5 girls are before her. Girls after her = 12 − 5 − 1 = 6.

3 is common to both views. Going round face 3 in the same rotational sense, the first die shows 4 then 6 and the second 5 then 1, so the four faces round 3 are 4, 6, 5, 1 in order. Opposite faces are 4–5 and 6–1, so 4 is opposite 5.

From 12 Oct 1997 to 12 Oct 2008 is 11 years with 3 leap days (Feb 2000, 2004, 2008): 11 + 3 = 14 odd days ≡ 0. The day is again Saturday.

Clockwise round the circle the order is Praveen, Subhash, Pramod, Suresh, Alok, Umesh. After Alok and Subhash swap, Subhash sits in Alok's old seat, which is second to the right of Praveen.

34, 16 and 25 are composite; 29 is a prime number, so it is different.

132 = 11 × 12, a number times the next number. Similarly 72 = 8 × 9.

Cricket is a sport, so its circle lies inside Sports; a cockroach is unrelated, so it is a separate circle – option 3.

All phones are pens, so some pens are phones (IV). Some pens are pencils, so some pencils are pens (III). Nothing links phones and pencils, so I and II do not follow.

Entomology is the study of insects; etymology is the study of the origin of words.

As per the official RRB key, filling b, c, c, a, a, c gives abccab / bcaabc / abccab, in which the first and third blocks are the same.

Add the digit sums of the letter positions: LITTLE = 3 + 9 + 2 + 2 + 3 + 5 = 24, PARIS = 7 + 1 + 9 + 9 + 10 = 36, BOX = 2 + 6 + 6 = 14, PIN = 7 + 9 + 5 = 21. DONE = 4 + 6 + 5 + 5 = 20.

Each term is 3 × previous − 1: 2, 5, 14, 41, 122, 365, then 3 × 365 − 1 = 1094. So 1095 does not belong.