SSC CGL 2017 · 2017-08-16 · Shift 3

The analogy pairs an animal with its biological class: a frog belongs to the class Amphibia. Applying the same relationship, a lizard — a cold-blooded vertebrate with scales that breathes through lungs and lays eggs on land — belongs to the class Reptilia. Rodents and mammals are warm-blooded; insects are invertebrates with six legs. Hence the answer is Reptile.

The pattern uses opposite letters of the alphabet — pairs whose positions sum to 27 (A↔Z, B↔Y, …). Check the first pair: D(4)↔W(23), J(10)↔Q(17), L(12)↔O(15), Q(17)↔J(10). Each sums to 27. Apply to DMSW: D(4) → W(23); M(13) → N(14); S(19) → H(8); W(23) → D(4). Therefore DMSW : WNHD.

In 7 : 56 7 × (7 + 1) = 56 Similarly, In 11 : ? 11 × (11 + 1) = 132 Hence, answer is 132.

Singer, Director and Actor are all persons who perform a role in the entertainment industry. Music, by contrast, is an art form — not a person or profession. Hence it is the odd one out.

Check the gaps between consecutive letter positions in each group: JGD: \(10\to7\to4\), differences \(-3,-3\). XUR: \(24\to21\to18\), differences \(-3,-3\). QNK: \(17\to14\to11\), differences \(-3,-3\). NLI: \(14\to12\to9\), differences \(-2,-3\). NLI breaks the \(-3,-3\) pattern, so NLI is the odd group.

71, 83 and 89 are all prime numbers (divisible only by 1 and themselves). 93 = \(3\times 31\), so it is composite. Hence 93 is the odd number.

Compare letter by letter. All start with C, so look at letter 2: 'a' (Carnation) < 'o' (Counter) < 'r' (Create, Creator, Crop). Among the Cr- words, compare letter 3: Create/Creator have 'e' vs Crop has 'o', so Create and Creator precede Crop. Between Create and Creator, the first five letters match; Create is shorter, so Create comes before Creator. Order: Carnation (4), Counter (1), Create (3), Creator (5), Crop (2) → 41352.

Positions: A(1), E(5), J(10), N(14), S(19), W(23). The gaps alternate \(+4,+5,+4,+5,+4\), so the next gap is \(+5\). \(23+5=28\). Wrapping around the 26-letter alphabet: \(28-26=2\), the 2nd letter. The missing term is B.

Each term follows \(a_{n+1}=2a_n+n\): \(3\times2+1=7\) \(7\times2+2=16\) \(16\times2+3=35\) \(35\times2+4=\mathbf{74}\).

Step 1 — Present age of N: N's age after 7 years is 32, so \(N=32-7=25\) years. Step 2 — Apply ratio: \(L:N=7:5\), so \(L=\dfrac{7}{5}\times 25=35\). Therefore L's present age is 35 years.

"The only child of my grandmother" must be Chetan's parent (father or mother). The girl is the daughter of that only child, i.e. the daughter of Chetan's parent — making her Chetan's sister. So Chetan is her Brother.

To determine which word cannot be formed, let's break down the available letters in the source word and compare them to the options. Source Word: N I G H T W A L K E R Letter Count N: 1 I: 1 G: 1 H: 1 T: 1 W: 1 A: 1 L: 1 K: 1 E: 1 R: 1 Evaluating the Options Option 1: TALKER Letters: T, A, L, K, E, R Status: Can be formed. (All letters are present in Nightwalker). Option 2: TAILER Letters: T, A, I, L, E, R Status: Can be formed. (All letters are present in Nightwalker). Option 3: WALLER Letters: W, A, L, L, E, R Status: Cannot be formed. The word "Nightwalker" only contains one 'L', but "Waller" requires two 'L's. Option 4: WINER Letters: W, I, N, E, R Status: Can be formed. (All letters are present in Nightwalker). Correct Answer: Option 3 (Waller)

The cipher is position-dependent, confirmed by two matches: in both SPICEY and PONDER, E at position 5 maps to A; and in PONDER, O at position 2 maps to K. HOUSED has O at position 2 (→ K) and E at position 5 (→ A). Only QKDZAO has K at position 2 and A at position 5.

Substitute the symbols: ×→+, –→×, ÷→−. The expression becomes \(14+12\times 16-18\). Apply BODMAS: \(12\times 16=192\), then \(14+192-18=\mathbf{188}\).

The hidden rule is \(a\times b-10\): \(18\times 12-10=216-10=206\) ✓ \(19\times 22-10=418-10=408\) ✓ Apply: \(23\times 36-10=828-10=\mathbf{818}\).

Read each column as (top × bottom) + middle²: Col 1: \(2\times 7+5^{2}=14+25=39\) ✓ Col 2: \(4\times 2+3^{2}=8+9=17\) ✓ Col 3: \(1\times 6+5^{2}=6+25=\mathbf{31}\).

Triangles in the figure: ABE, AEG, AGD, ABG, AED, ABD, BCD, BCFand DCF. Hence, total of 9 triangles are there in the given figure.

I. Some cups are not spoon — Some cups are plates (I); no plates are spoons (III); so those cups (which are plates) are not spoons. Follows. II. Some plates are not blue — no link forces plates to be non-blue; all plates could be blue. Does not follow. III. Some cups are not blue — no link between cups and blue is forced. Does not follow. IV. Some blue are not plates — all spoons are blue (II) and no spoons are plates (III), so those spoons (which are blue) are not plates. Follows. Hence only I and IV follow.

On observing the given first two dices, we say that "β" will come opposite to "ψ". So, it's confirmed that neither 1 or 2 will be "β". Therefore, options 2 and 3 will not correct. On observing the given last two dices, we say that "α" will come opposite to "δ". So, they are not on the adjacent sides. Therefore, options 1 is also false. Hence, the answer is θ and α.

Number of huts that are covered and muddy = 19 (The no. present in the three shapes i.e. square (huts), square (covered) and circle (muddy). Hence, answer is option 19.

Figure 4 will complete the incomplete figure as shown in the diagram.

Clearly, the given question figure is hidden in option 2. Hence, answer is option 2.

Hence, the answer is option 3.

Hence, answer is figure 3.

Read each code as row, column. For TAKE we need T, A, K, E in order. Option 2 — 41, 00, 89, 75: 41 → Matrix I (4,1) = T; 00 → Matrix I (0,0) = A; 89 → Matrix II (8,9) = K; 75 → Matrix II (7,5) = E. All four letters match, so the code for TAKE is 41, 00, 89, 75.

Under perfect competition, a large number of firms sell identical products with free entry and exit, so each firm is a price taker — the market price is set by aggregate demand and supply and no single firm can influence it. A monopolist is a price maker; oligopolists have partial control through strategic interaction; "mixed competition" is not a standard structure.

The Lorenz Curve, developed by Max Lorenz (1905), graphically represents the distribution of income or wealth in a population. The horizontal axis plots the cumulative percentage of recipients (poorest first); the vertical axis plots the cumulative percentage of income they hold. The straight 45° line from (0,0) to (100,100) denotes perfect equality. The greater the curve bows away from this line, the higher the income inequality. The Gini coefficient is derived from this curve. Hence the Lorenz Curve represents Income Distribution.

Fundamental Duties are listed under Article 51A in Part IVA of the Constitution, added by the 42nd Amendment (1976) on the recommendation of the Swaran Singh Committee. Abiding by the Constitution and respecting the National Flag [51A(a)], promoting harmony and brotherhood [51A(e)], and upholding the sovereignty, unity and integrity of India [51A(c)] are all Fundamental Duties. However, abolition of titles except military and academic is contained in Article 18 under Part III — it is a Fundamental Right (Right to Equality), not a duty. Hence it is the odd one out.

Emergency provisions are in Part XVIII of the Constitution. Article 360 empowers the President to proclaim a Financial Emergency if the financial stability or credit of India (or any part of it) is threatened. The other articles deal with different matters: Article 32 — Right to Constitutional Remedies; Article 349 — special procedure for legislation on language; Article 365 — consequences of a State failing to comply with Union directions (a ground for President's Rule under Article 356). A Financial Emergency under Article 360 has never been declared in India.

The Poona Pact was signed on 24 September 1932 at Yerawada Central Jail, Pune, between Mahatma Gandhi and Dr. B. R. Ambedkar. It was concluded in response to the Communal Award (1932) of British PM Ramsay MacDonald, which had granted separate electorates to the Depressed Classes. Gandhi opposed this through a fast unto death. The pact replaced separate electorates with joint electorates, increasing reserved seats for the Depressed Classes from 71 to 147 in provincial legislatures and 18% in the Central Legislature.

The Sati System was abolished by Lord William Bentinck, Governor-General of Bengal (1828–1835), through Regulation XVII of 1829, which declared sati a punishable offence (culpable homicide). The reform was strongly supported by Raja Ram Mohan Roy. The other options served much later and are linked to different events: Lord Dalhousie (Doctrine of Lapse), Lord Canning (1857 Revolt, first Viceroy), and Lord Ripon (local self-government, Ilbert Bill).

The primary greenhouse gases in Earth's atmosphere are water vapour (H2O), carbon dioxide (CO2), methane (CH4), nitrous oxide (N2O) and ozone (O3). These molecules absorb and re-emit infrared radiation, trapping heat. Hydrogen (H2) is a symmetric diatomic molecule with no dipole moment and does not absorb infrared radiation significantly, so it is not a primary greenhouse gas. Methane, ozone and nitrous oxide are all recognised primary GHGs.

Tropical Deciduous Forests, also called monsoon forests, are the most widespread forest type in India. They thrive in regions receiving annual rainfall between 70 cm and 200 cm — conditions that cover most of central India, the Deccan plateau, eastern plains and Western Ghats foothills. They are divided into moist deciduous (100–200 cm) and dry deciduous (70–100 cm), supporting commercially valuable trees like teak, sal, sandalwood and bamboo. Trees shed leaves for 6–8 weeks in the dry season. Evergreen, montane and mangrove forests are restricted to much narrower climatic zones.

A universal donor's red blood cells must carry no antigens that the recipient's plasma antibodies can attack. O– blood lacks A antigens, B antigens and the Rh(D) antigen. With none of these antigens present, O– red cells can be safely transfused to recipients of any ABO/Rh group, making it the universal red cell donor. O+ still carries the Rh antigen and is unsafe for Rh-negative recipients. AB– and AB+ carry A and B antigens, restricting them to AB recipients only. (AB+ is the universal recipient, not donor.)

Anatomically, the human brain is divided into three main parts: Forebrain — cerebrum, thalamus, hypothalamus; responsible for thinking, memory, voluntary action and sensory processing. Midbrain — part of the brainstem; controls visual and auditory reflexes and relays signals between forebrain and hindbrain. Hindbrain — cerebellum, pons and medulla oblongata; controls balance, posture and vital functions like breathing and heart rate.

Adrenaline (epinephrine) is secreted by the adrenal medulla directly into the bloodstream, where it travels to target organs such as the heart, lungs, blood vessels and liver to trigger the "fight-or-flight" response (raised heart rate, blood pressure and glucose release). Acting as a chemical messenger from an endocrine gland makes it a hormone (a catecholamine derived from tyrosine). It is not an enzyme (no catalytic role), not a protein (it is a small amino-acid derivative), and not a fat.

Supercooling is the process of cooling a liquid below its freezing point without it solidifying. The liquid remains in a metastable state because crystal nucleation has not started — usually due to high purity or absence of nucleation sites. For example, very pure water can stay liquid well below \(0^\circ\text{C}\). Any disturbance or seed crystal then triggers rapid freezing. Cooling "at" or "above" the melting point does not describe this phenomenon.

When light passes from one transparent medium to another, its speed changes (because the refractive indices differ). This change in speed at the boundary causes the ray to bend — a phenomenon called refraction, governed by Snell's law. Diffraction is the bending of waves around obstacles or through narrow slits, not at a media boundary. Propagation simply means the transmission of light through a medium and does not involve a directional change. Hence the correct answer is Refraction.

An input device feeds data into the computer; an output device delivers processed data out. A Plotter takes computer instructions and draws graphics or large-format prints (CAD drawings, blueprints) on paper — it is an output device. MICR (reads magnetic ink characters on cheques), OMR (reads marked answer sheets/forms) and Barcode Readers (read printed barcodes) all convert physical information into digital data sent to the computer, so they are input devices.

Phenol (C6H5OH) is the aromatic compound historically known as Carbolic Acid. It was first isolated from coal tar and famously used by Joseph Lister (1860s) as an antiseptic in surgery. Its acidic nature comes from the –OH group attached to the benzene ring. Hydroxide (OH–) is merely an ion, sulphuric acid (H2SO4) is an inorganic mineral acid, and ethanol (C2H5OH) is an aliphatic alcohol — none of these is Carbolic Acid.

The electron was discovered by Sir J. J. Thomson in 1897 through his cathode-ray tube experiments. He showed cathode rays were deflected by electric and magnetic fields, proving they were negatively charged particles, and measured their charge-to-mass ratio \(e/m\), which was independent of the cathode material. E. Goldstein discovered canal (anode) rays leading to the proton concept; Ernest Rutherford discovered the atomic nucleus and proton; James Chadwick discovered the neutron (1932).

Medha Patkar is the principal founder and leader of the Narmada Bachao Andolan, launched in 1985 against the Sardar Sarovar and other dams on the Narmada river. She organised tribal communities, farmers and environmentalists, led padyatras and indefinite fasts, and took the displacement and rehabilitation issue to the Supreme Court. Anna Hazare led the anti-corruption Jan Lokpal movement; Shantha Sinha is known for anti-child-labour work (MV Foundation); Manasi Pradhan campaigns against violence on women. None of them is linked to the NBA.

Under the UDAN (Ude Desh ka Aam Naagrik) regional connectivity scheme launched in October 2016 by the Ministry of Civil Aviation, airfares on RCS routes connecting tier-2 and tier-3 cities are capped at Rs 2,500 per hour of flight (about 500-600 km) for a fixed quota of seats. The shortfall against operational cost is met through Viability Gap Funding (VGF) financed by a regional connectivity levy on other domestic routes.

Among the given options, Heinrich Hertz is the one credited in this answer key. The German physicist proved the existence of electromagnetic waves in 1887 and showed that they could be reflected by metallic objects — the very principle on which radar (RAdio Detection And Ranging) operates. Practical radar systems were later built by Christian Hulsmeyer (1904) and Robert Watson-Watt (1935), but Hertz laid the scientific foundation. Roentgen discovered X-rays; Fred Morrison invented the Frisbee; Van Tassel is unrelated to radar.

David Warner is a left-handed opening batter who represents the Australian national cricket team across Tests, ODIs and T20Is. He made his international debut for Australia in January 2009 and has been a mainstay of their top order, winning multiple ICC trophies including the 2015 ODI World Cup and the 2021 T20 World Cup with Australia.

Ikebana is the traditional Japanese art of flower arrangement, in which flowers, branches, leaves and the container are composed with attention to line, space and asymmetry. It originated from ritual floral offerings in Buddhist temples and developed into formal schools such as Ikenobo, Ohara and Sogetsu. Paper folding is Origami, miniature tree cultivation is Bonsai, and sand art is unrelated to Ikebana.

Vishwa Mohan Bhatt, the Grammy-winning classical musician and inventor of the Mohan Veena (a modified Hawaiian slide guitar), was conferred the Padma Bhushan in 2017 in the Art-Music category for his contribution to Hindustani classical music. K. J. Yesudas received the Padma Vibhushan in 2017 (not Padma Bhushan); Anuradha Paudwal got the Padma Shri (2017); Devi Prasad Dwivedi received the Padma Bhushan for Literature & Education, not music.

'An Unsuitable Boy' (2017) is the autobiography of filmmaker Karan Johar, co-written with journalist Poonam Saxena. The title is a deliberate play on Vikram Seth's novel A Suitable Boy, and the book covers Johar's childhood, his entry into Bollywood through Kuch Kuch Hota Hai, his friendships and personal struggles. Rishi Kapoor's autobiography is Khullam Khulla; MS Dhoni has not written an autobiography; Vikram Seth authored the novel A Suitable Boy, not this autobiography.

The Indian Ocean Rim Association (IORA), founded in 1997 with its secretariat in Ebene, Mauritius, comprises 23 littoral states of the Indian Ocean. Sri Lanka, Mauritius and Seychelles are all founding/full Member States. China is not a littoral state of the Indian Ocean and is included only as a Dialogue Partner, not a Member State. Hence, China is the country in the list that is not a member of IORA.

In January 2017, China launched the Shanghai-Kunming High-Speed Railway, spanning approximately 2,252 km through Zhejiang, Jiangxi, Hunan, Guizhou and Yunnan provinces. It became the world's longest single bullet-train line at that time, with trains running at up to 330 km/h and cutting the Shanghai-Kunming journey from over 34 hours to about 11 hours. Japan operates the Shinkansen network but did not launch a 2,252 km line in January 2017; Afghanistan and Myanmar do not have high-speed rail.

Step 1 — List primes between 60 and 80: Checking divisibility by 2, 3, 5, 7 for each number in (60, 80), the primes are \(61,\ 67,\ 71,\ 73,\ 79\). Step 2 — Add them: \[61+67+71+73+79 = 351\] Therefore the required sum is 351.

Step 1 — Individual rates: \(A=\dfrac{36}{9}=4\) pages/hr; \(B=\dfrac{40}{5}=8\) pages/hr. Step 2 — First 60 pages (A alone): \[\dfrac{60}{4}=15\text{ hours}\] Step 3 — Last 60 pages (A + B together): Combined rate \(=4+8=12\) pages/hr, so time \(=\dfrac{60}{12}=5\) hours. Step 4 — Total time: \(15+5=\mathbf{20}\) hours.

Step 1 — Hypotenuse: \(AC=\sqrt{5^{2}+12^{2}}=\sqrt{169}=13\) cm. Step 2 — Radius of common base (altitude from B to AC): Using area in two ways, \(\tfrac{1}{2}\cdot 5\cdot 12=\tfrac{1}{2}\cdot 13\cdot r\), giving \(r=\dfrac{60}{13}\) cm. Step 3 — Volume of double cone: The two cones share radius \(r\) and their heights add up to the hypotenuse, so \[V=\tfrac{1}{3}\pi r^{2}\cdot AC=\tfrac{1}{3}\pi\left(\tfrac{60}{13}\right)^{2}\!\cdot 13=\dfrac{1200\pi}{13}\] \(\approx 289.5\) cm3, closest to 290 cm3.

Step 1 — Selling price after 15% discount: \[SP=1360\times\tfrac{85}{100}=1156\] Step 2 — Cost price from 15.6% profit: \[CP=\dfrac{SP}{1+\tfrac{15.6}{100}}=\dfrac{1156}{1.156}=1000\] Therefore the cost price is Rs 1000.

Let the weights of the three pieces be \(3k,5k,7k\); total original weight \(=15k\). Since price \(\propto\) (weight)2, take price \(=Cw^{2}\). Step 1 — Original vs broken value (in units of \(Ck^{2}\)): Original \(=(15)^{2}=225\); broken \(=3^{2}+5^{2}+7^{2}=9+25+49=83\). Step 2 — Loss equation: \[(225-83)\,Ck^{2}=142\,Ck^{2}=42600\;\Rightarrow\;Ck^{2}=300\] Step 3 — Original price: \(225\times 300=\mathbf{67500}\). Hence the diamond originally cost Rs 67,500.

Step 1 — Total weights: All 100 students: \(100\times 32=3200\) kg. First 49: \(49\times 30=1470\) kg. Last 50 (students 51-100): \(50\times 34=1700\) kg. Step 2 — Isolate the 50th student: The 50th student is the only one not counted in either subgroup, so \[W_{50}=3200-(1470+1700)=3200-3170=30\text{ kg}\] Therefore the 50th student weighs 30 kg.

Step 1 — Find CP from the 20% loss: \[CP=\frac{SP}{1-\tfrac{L}{100}}=\frac{80}{0.80}=\text{Rs }100\] Step 2 — Apply 20% profit on CP: \[SP'=CP\times\left(1+\tfrac{20}{100}\right)=100\times1.20=\text{Rs }120\] Hence the required selling price of 90 pens is Rs 120.

Step 1 — Assume income = 100: Expenditure = 80, Savings = 100 − 80 = 20. Step 2 — Apply the changes: \[\text{New Income}=100\times1.25=125,\quad \text{New Expenditure}=80\times1.10=88\] Step 3 — New savings and percentage rise: \[\text{New Savings}=125-88=37\] \[\% \text{ increase}=\frac{37-20}{20}\times100=\frac{17}{20}\times100=85\%\] Hence savings rise by 85%.

For equal distances the average speed is the harmonic mean of the four speeds. Speeds halve each trip: 60, 30, 15, 7.5 km/hr. \[\text{Avg}=\frac{4}{\tfrac{1}{60}+\tfrac{1}{30}+\tfrac{1}{15}+\tfrac{1}{7.5}}=\frac{4}{\tfrac{1+2+4+8}{60}}=\frac{4}{\tfrac{15}{60}}=\frac{4\times60}{15}\] \[\text{Avg}=16\text{ km/hr}\] Hence the average speed is 16 km/hr.

Total simple interest equals the sum of \(\tfrac{PRT}{100}\) for each period. \(SI=\frac{P(3\cdot3+4\cdot5+6\cdot7)}{100}=\frac{P(9+20+42)}{100}=\frac{71P}{100}\) Set equal to 2059 and solve: \(\frac{71P}{100}=2059 \;\Rightarrow\; P=\frac{2059\times100}{71}=2900\) Hence the sum borrowed is Rs 2900.

Use the identity \((x-y)^2=(x+y)^2-4xy\), so we need \(xy\). Step 1 — Find xy: From \(x^3+y^3=(x+y)^3-3xy(x+y)\): \[35=125-3xy(5)\;\Rightarrow\;15xy=90\;\Rightarrow\;xy=6\] Step 2 — Compute the difference: \[(x-y)^2=5^2-4(6)=25-24=1\;\Rightarrow\;|x-y|=1\] Hence the positive difference is 1.

Step 1 — Rationalise: Multiply numerator and denominator inside the root by \((2+\sqrt3)\): \[x=\sqrt{\frac{(2+\sqrt3)^2}{(2)^2-(\sqrt3)^2}}=\sqrt{(2+\sqrt3)^2}=2+\sqrt3\] Step 2 — Evaluate: \(x^2=(2+\sqrt3)^2=7+4\sqrt3\). \[x^2+x-9=(7+4\sqrt3)+(2+\sqrt3)-9=0+5\sqrt3=5\sqrt3\] Hence the value is \(5\sqrt3\).

Reading the expression as \(\dfrac{x^3}{3z}+\dfrac{y^3}{3xz}+\dfrac{z^3}{3x}\) (a standard typo for the y-term), take common denominator \(3xz\): \[\frac{x^3+y^3+z^3}{3xz}\] Since \(x+y+z=0\), the identity \(x^3+y^3+z^3=3xyz\) applies: \[\frac{3xyz}{3xz}=y\] Hence the value is y.

Step 1 — Simplify the bracket: \[\frac{1}{x-1}-\frac{1}{x+1}=\frac{2}{x^2-1},\quad \frac{1}{x^2+1}-\frac{1}{x^2-1}=\frac{-2}{x^4-1}\] Combining and factoring: \[\frac{1}{x}\cdot\frac{2}{x^2-1}\left(1-\frac{1}{x^2+1}\right)=\frac{2x}{(x^2-1)(x^2+1)}\] Step 2 — Use the condition: \(x-\tfrac1x=1\Rightarrow x^2-1=x\), so \(x^2=x+1\). Substituting: \[\frac{2x}{x(x^2+1)}=\frac{2}{x+2}\] Step 3 — Solve \(x^2-x-1=0\): \(x=\tfrac{1\pm\sqrt5}{2}\), giving \(x+2=\tfrac{5\pm\sqrt5}{2}\), so the value is \(\tfrac{4}{5\pm\sqrt5}\). Hence the answer is \(\dfrac{4}{5\pm\sqrt5}\).

Since RS ∥ PQ, arcs PR and QS are equal, so \(\angle POR=\angle QOS\). On the diameter: \[2\angle POR+40^\circ=180^\circ\;\Rightarrow\;\angle POR=\angle QOS=70^\circ\] Angle \(\angle ROQ=\angle ROS+\angle SOQ=40^\circ+70^\circ=110^\circ\); similarly \(\angle POS=110^\circ\). By the inscribed-angle theorem: \[\angle RPQ=\tfrac12(110^\circ)=55^\circ,\quad \angle SQP=\tfrac12(110^\circ)=55^\circ\] In \(\triangle PTQ\): \[\angle PTQ=180^\circ-55^\circ-55^\circ=70^\circ\] Hence \(\angle PTQ=\mathbf{70^\circ}\).

Given: ∠AMB = 130° Calculation: According to the alternate segment theorem, in a circle, the angle between a chord and a tangent at the intersection is equal to the angle in the alternate section Hence, in the given figure, ∠ABP = ∠AMB = 130° ∴ ∠ABQ = 180° – ∠ABP = 180° – 130° = 50° So, the value of ∠ABQ is 50 °

Given: AP = 3 cm, AR = 6 cm, RS = 9 cm Concept used: AR × AS = AP × AQ Calculation: AR × AS = AP × AQ ⇒ 6 × (6 + 9) = 3 × (3 + PQ) ⇒ PQ + 3 = 30 ⇒ PQ = 27 cm ∴ PQ = 27 cm So, the value of PQ = 27 cm.

A quadrilateral whose all four sides touch a circle, is known as cyclic quadrilateral Also, when two tangents are drawn from an external point to a circle, the lengths of the tangents is equal Hence, in the given figure, ⇒ AP = AS ⇒ BP = BQ ⇒ CR = CQ ⇒ DR = DS Adding all four equations, we get, ⇒ AP + BP + CR + DR = AS + DS + BQ + CQ ⇒ AB + CD = AD + BC Substituting values, ⇒ 2x + 3 + x + 6 = 3x – 1 + x + 4 ⇒ 3x + 9 = 4x + 3 ⇒ 4x – 3x = 9 – 3 ⇒ x = 6

Given \(\csc^2\theta=\tfrac{625}{576}\), so \(\sin^2\theta=\tfrac{576}{625}\Rightarrow \sin\theta=\tfrac{24}{25},\;\cos\theta=\tfrac{7}{25}\) (right-triangle 7-24-25). Divide numerator and denominator of the target by \(\cos\theta\): \[\frac{\sin\theta-\cos\theta}{\sin\theta+\cos\theta}=\frac{\tan\theta-1}{\tan\theta+1}=\frac{\tfrac{24}{7}-1}{\tfrac{24}{7}+1}=\frac{17}{31}\] Hence the value is \(\tfrac{17}{31}\).

Since \(51^\circ=90^\circ-39^\circ\), we have \(\sin 51^\circ=\cos 39^\circ\), so the first term reduces: \[\frac{3}{2}\cdot\frac{\cos 39^\circ}{\sin 51^\circ}=\frac{3}{2}\cdot 1=\frac{3}{2}\] Under the root, \(\sin^2 39^\circ+\sin^2 51^\circ=\sin^2 39^\circ+\cos^2 39^\circ=1\), so \(\sqrt{1}=\pm1\). The expression becomes \(\tfrac{3}{2}\mp1\), giving \(\tfrac{1}{2}\) or \(\tfrac{5}{2}\). Hence the answer is either 1/2 or 5/2.

Use half-angle identities: \(\sin B=2\sin\tfrac{B}{2}\cos\tfrac{B}{2}\) and \(1-\cos B=2\sin^2\tfrac{B}{2}\). \[\cot A=\frac{2\sin\tfrac{B}{2}\cos\tfrac{B}{2}}{2\sin^2\tfrac{B}{2}}=\frac{\cos(B/2)}{\sin(B/2)}=\cot\tfrac{B}{2}\] So \(A=\tfrac{B}{2}\), giving \(2A=B\). Hence \(\cot 2A=\mathbf{\cot B}\).

For company 1 total production from year 2011 to 2016 can be given as ⇒ total production = sale per year × (sum of ratios of all year), because sale is same in all years ⇒ total production for company 1 = 20000 × (0.6 + 0.9 + 0.7 + 0.9 + 1.3 + 1.3) ⇒ total production = 114000 ⇒ Average = 114000/6 = 19000 For company 2 total production from year 2011 to 2016 can be given as ⇒ total production = sale per year × (sum of ratios of all year), because sale is same in all years ⇒ total production for company 2 = 10000 × (0.8 + 0.75 + 0.4 + 1.45 + 1.3 + 1.1) ⇒ total production = 58000 ⇒ Average = 58000/6 = 9666.66 ⇒ Difference is 19000 – 9666.66 ∴ The difference is 9333.34

From the graph the ratio of production and sale for company 1 in 2014 is 0.9 and for company 2 in 2012 is 0.75 For company 1 in year 2014, 0.9 = production/sale ⇒ sale = 18000/0.9 = 20000 Difference between sales and production can be given as ⇒ 20000 – 18000 = 2000 Given that for company 2, the sale in 2012 is equal 15000 For year 2012, 0.75 = production/sale ⇒ production = 0.75 × 15000 = 11250 Difference between sales and production can be given as ⇒ 15000 – 11250 = 3750 Ratio can be given as 2000/3750 ∴ The required ratio is 8 : 15

From the graph the ratio of production and sale for company 2in 2012 is 0.75 and that in 2013 is 0.4 ⇒ For year 2012, 0.75 = production/sale ⇒ sale = 30000/0.75 = 40000 Given that sale in 2012 is equal to sale in 2013 ⇒ For year 2013, 0.4 = production/sale ⇒ production = 0.4 × 40000 = 16000 ∴ The production in 2013 is 16000

From the graph ratio of production to sales in year 2015 is 1.3 ⇒ 1.3 = production/sales ⇒ production = 1.3 × 50000 = 65000 ∴ The production of Company 1 in year 2015 is 65000 units

For general modes of transport, the preposition by takes the noun directly without an article: by car, by bus, by train. The phrase "by the car" in segment (3) is wrong; it should read "by car". Segments (1) and (2) are grammatically sound ("did not go", "on foot" are idiomatic). Hence the error lies in segment (3).

The verb ascend, when used for taking power, is transitive and takes the object directly — "ascended the throne", not "ascended to the throne". The preposition "to" in segment (2) is redundant. Segments (1) and (3) are correct ("at the early age of" is standard). Hence the error lies in segment (2).

The blank needs a phrasal verb meaning "to pass / succeed in". Get through precisely carries this sense ("get through an exam" = pass it). Her mother's annoyance follows from Neha failing to pass. The other options don't fit: get off = leave/escape, get on = make progress / board, get upon is not standard idiomatic English. Hence the answer is Get through.

The sentence sets up a conditional: an apology will be followed by a positive response from the speaker. The verb that logically pairs with receiving an apology is forgive — to stop feeling angry or resentful for an offence. "Sorry" is an adjective, not a verb that follows "shall". "Punish" and "scold" are negative reactions and contradict the idea of accepting an apology. Hence the completed sentence reads: "I shall forgive her if she apologises to me for her misbehaviour."

Ebullient means cheerful and full of energy — lively, exuberant, bubbling with positive excitement. The closest match among the options is Enthusiastic, which shares the sense of eager, energetic positivity. "Deceitful" (dishonest) and "Insincerity" (lack of genuineness) are unrelated to high spirits, and "Prejudice" (biased opinion) carries no connotation of energy or cheer.

Truculent means aggressively defiant, hostile, fierce, or eager to fight. The option that captures this savage, aggressive quality is Ferocious, which means savagely fierce, cruel, or violent. "Luxurious", "Luscious", and "Delicious" all relate to pleasure, taste, or comfort and bear no link to hostility or aggression.

Niggardly means stingy — reluctant to give or spend. Its direct antonym is Generous, which describes a readiness to give freely. "Mingy" is a synonym, not an antonym. "Inefficient" (unproductive) and "Sinful" (immoral) are unrelated to giving habits.

A dissident opposes official policy or established beliefs. Its opposite must describe someone who conforms to accepted views — that is Orthodox, meaning one who follows traditional or established doctrines. "Iconoclast" is a near-synonym (someone who attacks cherished beliefs). "Alienated" describes a feeling of estrangement, and "Divisive" describes an effect — neither is the opposite of dissident.

The idiom "Bear the palm" originates from the ancient practice of awarding a palm branch to the victor of a contest. It therefore means to win or be victorious. "Face the consequences", "meet death", and "predict the future" have no link to the symbolism of triumph that the palm branch represents.

The idiom "To give the devil his due" means to acknowledge the merits or good qualities of someone who is otherwise disliked or considered bad. It reflects fairness in judgment — giving credit where it is deserved, even to a notorious person. Hence the best match is "To give credit to even a notorious person". The other options relate to punishment, opposition, or letting an enemy learn — none captures the idea of fair acknowledgment.

When a sentence begins with the negative adverb "No sooner", inversion is required: No sooner + auxiliary (did/had) + subject + main verb. The correlative conjunction is than (not "when"). The original lacks inversion. Option 2 — "No sooner did the advertisement regarding the launch of new smart phone appear" — correctly places the auxiliary "did" before the subject, with the main verb in its base form. Options 1 and 3 are grammatically faulty, and Option 4 ("No improvement") ignores the missing inversion.

The verb "adapt" takes different prepositions depending on meaning: adapted to = adjusted to an environment/condition; adapted for = modified for a specific purpose or use; adapted from = derived from a source. Here the equipment is made suitable for use in cotton industries — a purpose, not an environment. The correct preposition is therefore "Adapted for".

A Stevedore (also called a docker or longshoreman) is a person employed at a port to load and unload cargo from ships. This exactly matches the given phrase. A "Transgressor" is a lawbreaker, a "Lapidist" cuts and polishes gemstones, and "Reticent" is an adjective meaning reserved — none refers to port cargo work.

Heresy means a belief or opinion that strongly contradicts orthodox or generally accepted doctrine — originally religious, but extended to any prevailing view. This is exactly what the phrase describes. "Invocation" (a calling upon a deity), "Incognito" (with concealed identity), and "Mercenary" (a hired soldier) bear no relation to dissenting beliefs.

The misspelt word is Occurence. The correct spelling is Occurrence — with a double "r" and double "c". The suffix "-ence" is added to "occurr-", and consonant doubling applies because the stress falls on the final syllable of "occur". "Tomorrow", "Temperature", and "Preferable" are all spelt correctly.

The misspelt word is Receeding. The correct spelling is Receding — with a single "e" after the "c". It comes from "recede" (to move back), and dropping the silent "e" before adding "-ing" gives "receding". "Cemetery", "Parallelogram", and "Rehearsal" are all spelt correctly.

S opens the paragraph — the phrase "Having discussed the problems and requirements of rural life" is an introductory participial clause that sets the context. Q follows naturally with "Let us consider the village artisans", narrowing focus to a specific group. P then explains the outcome — if village requirements are met, peasants will utilise their spare time. R concludes with an additional benefit signalled by "This will also provide employment". Hence the order is SQPR.

R introduces the topic — making agriculture compulsory in higher secondary schools and an alternative for urban students. P elaborates on what such agricultural education involves: practical farming, including fruit and vegetable farming. Q addresses the resource concern — "These schools" (referring back to R) need no farms of their own because the village offers field facilities. S concludes with "Therefore... theoretical education... would suffice" for village students at this stage. The coherent order is RPQS.

For a perception verb (see/hear/watch) followed by object + present participle in the active, the passive keeps the participle: Object + was/were + seen + present participle + by + agent. Active: "I saw him leaving the movie theatre." Object "him" becomes subject "He"; "saw" becomes "was seen"; "leaving the movie theatre" stays unchanged; agent "by me" closes the sentence. Hence the correct passive is "He was seen leaving the movie theatre by me." Option 2 misplaces the participle phrase; option 3 wrongly inserts "to be"; option 4 shifts tense to past perfect.

Imperative direct speech converts to indirect using a suitable reporting verb (ordered / told / urged / requested) + object + to + base verb. The inverted commas and vocative are dropped. "Be quiet, girls" is a positive imperative addressed to the girls. The structure becomes: The principal + reporting verb + the girls + to be quiet. Among the options, "The principal urged the girls to be quiet" follows this exact structure. Option 2 uses an ungrammatical "that they be quiet" clause; option 4 reduces a command to a mere statement with "said that"; option 1 adds an unstated action ("called the girls").

The passage paints modern man as imprisoned by routine, so the blank in "His life is all care and _____" needs a negative noun that pairs idiomatically with care. "Care and worry" is the standard collocation describing a life burdened by responsibilities and anxieties, matching the passage's tone. "Wisdom" and "success" are positive and break the tone; "anxiety" is close in meaning but is not the conventional pairing with "care". Hence worry fits best.

The passage opens by saying modern man is "imprisoned by his time-table and his routine" — clearly a complaint about lack of time. The blank fits that exact idea: "He does not have time for anything but his duties and occupation." "Resources", "material" and "money" do not connect to the time-table/routine framing; only time is the scarce thing a rigid schedule eats up.

The phrase "occupation for _____ money" needs a verb that describes earning money through one's work. "Making money" is the standard idiom for earning income from an occupation. "Minting" literally means producing coins; "collecting" suggests gathering dues; "spending" is the opposite of earning. Hence making fits the sentence.

The sentence contrasts how Indians and Westerners have suffered the "disease" of routine-bound life over time, so the blank needs a noun denoting historical periods. "Men, in all ages" idiomatically means men throughout history — exactly the universal-across-time sense the sentence requires. "Spheres" and "areas" suggest domains of activity; "streams" suggests flows/categories — none capture the temporal sweep the passage needs.

The passage calls routine-bound life a "disease". The blank needs a verb meaning suffered from / harmed by, used with the preposition by. "Inflicted" means caused to suffer something harmful and pairs naturally with "by" in this context. "Infected" is used for literal pathogens, not metaphorical lifestyle diseases; "accompanied" and "associate" do not convey suffering. Hence inflicted fits best. Note: "afflicted by" is the strictly correct usage; "inflicted by" is widely accepted in Indian-English question banks and is the intended answer here.