This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 4501. |
Amongst the following statements, that which was not proposed by Dalton was : (1) all the atoms of a given element have identical properties including identical mass. Atoms of different elements differ in mass. (2) chemical reactions involve reorganisation of atoms. These are neither created nor destroyed in a chemical reaction. (3) when gases combine or reproduced in a chemical reaction they do so in a simple ratio by volume provided all gases are at the same T & P. (4) matter consists of indivisible atoms. |
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Answer» Answer is (3) At constant temperature and pressure V ∝ n ⇒ Avagadro's law not Dalton's law. Answer is (3) (3) when gases combine or reproduced in a chemical reaction they do so in a simple ratio by volume provided all gases are at the same T & P. Option(3) is according to Gaylussac's law of volume combination. |
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| 4502. |
_______ deals with how the social perceiver uses information to arrive at causal explanations for events. a) Attribution theory b) Social Perception Theory c) Selective Perception d) social Theory |
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Answer» a) Attribution theory |
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| 4503. |
Match the following coloumnPolymerMonomer(i) Buna-S(P) Styrene(ii) ethylene glycol(Q) terylene(iii) elastomer(R) chloropreneCorrect set of answer : (1) (i) – (P) (ii) – (Q) (iii) – (R) (2) (i) – (R) (ii) – (P) (iii) – (Q) (3) (i) – (Q) (ii) – (R) (iii) – (P) (4) (i) – (P) (ii) – (R) (iii) – (Q) |
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Answer» (1) (i) – (P) (ii) – (Q) (iii) – (R) |
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| 4504. |
Which of the following sets are correct regarding polymer ? (A) Copolymer : Buna–S (B) Condensation polymer : Nylon–6,6 (C) Fibre : Nylon–6,6 (D) Thermosetting polymer : Terylene (E) Homopolymer : Buna–N Choose the correct answer from given options below: (A) (A), (B) and (C) are correct (B) (B), (C) and (D) are correct (C) (A), (C) and (E) are correct (D) (A), (B) and (D) are correct |
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Answer» Correct options are: (A) (A), (B) and (C) are correct (B) (B), (C) and (D) are correct (C) (A), (C) and (E) are correct Bona - 5 is copolymer of butadiene + styrene Nylon 6.6 is condensation polymer of adipic Acid and hexanediamine. Nylon 6.6 is fiber Terylene is fiber not themosetting polymer Buna-N is copolymer nol Homopolymer. |
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| 4505. |
Amongst the following, the form of water with the lowest ionic conductance at 298 K is: (1) distilled water (2) water from a well (3) saline water used for intravenous injection (4) sea water |
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Answer» Answer is (1) Distilled water have lowest ionic conductance. Answer is (1) Distilled water The form of H2O with the lowest ionic conductance at 298 K is distilled water. |
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| 4506. |
Among the statements (a)-(d) the correct ones are: (a) Lithium has the highest hydration enthalpy among the alkali metals. (b) Lithium chloride is insoluble in pyridine. (c) Lithium cannot form ethynide upon its reaction with ethyne. (d) Both lithium and magnesium react slowly with H2O. (1) (a), (b) and (d) only (2) (b) and (c) only (3) (a), (c) and (d) only (4) (a) and (d) only |
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Answer» Answer is (3) Lithium has highest hydration enthalpy among alkali metals due to its small size. LiCl is soluble in pyridine because LiCl have more covalent character. Li does not form ethynide with ethyne. Both Li and Mg reacts slowly with H2O Answer is (3) |
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| 4507. |
Calcium is excreted by (A) Kidney (B) Kidney and intestine (C) Kidney and liver (D) Kidney and pancreas |
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Answer» (B) Kidney and intestine |
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| 4508. |
Biochemical oxygen demand (BOD) is defined as ............ in ppm of O2. (1) Required to sustain life (2) The amount of oxygen required by bacteria to break down the organic matter present in a certain volume of a sample of water. (3) The amount of oxygen required by anaerobic bacteria to break down the inorganic matter present in a certain volume of a sample of water. (4) Required photochemical reaction to degrade waste |
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Answer» The answer is (2) The amount of oxygen required by bacteria to break down the organic matter present in a certain volume of a sample of water. The amount of oxygen required by bacteria to break down the organic matter present in a certain volume of a sample of water, is called Biochemical Oxygen Demand (BOD). |
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| 4509. |
Biochemical Oxygen Demand (BOD) is the amount of oxygen required (in ppm): (1) by anaerobic bacteria to breakdown inorganic waste present in a water body. (2) for the photochemical breakdown of waste present in 1 m3 volume of a water body. (3) by bacteria to break-down organic waste in a certain volume of a water sample. (4) for sustaining life in a water body. |
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Answer» Answer is (3) Biochemical oxygen demand (BOD) is amount of oxygen required by bacteria to break down organic waste in a certain volume of water sample. Answer is (3) can be right if inorganic waste is replaced by organic waste. |
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| 4510. |
Selenium is a constituent of the enzyme: |
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Answer» Selenium is a constituent of the enzyme glutathione peroxidase, which inactivates toxic hydrogen peroxide and hydroperoxides. |
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| 4511. |
Which one of the following alcohol will give Ethyl Methyl ketone on oxidation? |
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Answer» 2-butanol on oxidation gives ethyl methyl ketone. |
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| 4512. |
In the last 10 years much has been learned about the molecular structure of elemental sulfur. It is now known that many different types of rings are sufficiently metastable to exist at room temperature for several days. It is known that at high temperature, the equilibrium composition allows for a variety of rings and chains to exist in comparable concentration, and it is known that at the boiling point and above, the vapor as well as the liquid contains small species with three, four, and five atoms.The sulfur atom has the same number of valence electrons as oxygen. Thus, sulfur atoms S2 and S3 have physical and chemical properties analogous to those of oxygen and ozone. S2 has a ground state of 38 σ3s2 σ⋆3s2σ3pz2π3px2 = π3py2π*3px1 = π*3py1 . S3 , thiozone has a well-known uv spectrum, and has a bent structure, analogous to its isovalent molecules 03, SO2, and S20. The chemistry of the two elements, sulphur and oxygen, differs because sulfur has a pronounced tendency for catenation. The most frequently quoted explanation is based on the electron structure of the atom. Sulfur has low-lying unoccupied 3d orbitals, and it is widely believed that the 4s and 3d orbitals of sulfur participate in bonding in a manner similar to the participation of 2s and 2p orbitals in carbon.In the following questions, a statement of assertion followed by a statement of reason is given. Choose the correct answer out of the following choices on the basis of the above passage.A. Assertion and reason both are correct statements and reason is correct explanation for assertion.B. Assertion and reason both are correct statements but reason is not correct explanation for assertion.C. Assertion is correct statement but reason is wrong statement.D. Assertion is wrong statement but reason is correct statement.Q 1 Assertion: Sulphur belongs to same group in the periodic table as oxygen.Reason: S2 has properties analogous to O2.Q 2. Assertion: Thiozone has bent structure like ozone.Reason: Ozone has a lone pair which makes the molecule bent.Q 3. Assertion: S2 is paramagnetic in natureReason: The electrons in π*3px and π*3py orbitals in S2 are unpaired.Q 4.Assertion: Sulphur has a greater tendency for catenation than oxygen.Reason: 3d and 4s orbitals of Sulphur have same energy. |
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Answer» 1 (B) Assertion and reason both are correct statements but reason is not correct explanation for assertion. 2 (B) Assertion and reason both are correct statements but reason is not correct explanation for assertion. 3 (A) Assertion and reason both are correct statements and reason is correct explanation for assertion. 4 (C) Assertion is correct statement but reason is wrong statement. |
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| 4513. |
What is the catalyst used for oxidation of `SO_(2)` to `SO_(3)` in lead chamber process for manufacture of sulphuric acid?A. Nitric acidB. Nitrous oxideC. Potassium iodideD. Dilute HCl |
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Answer» Correct Answer - A Nitric oxide. |
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| 4514. |
Which of the following compounds reacts immediately with Lucas reagent ?A. `CH_(3)CH_(2)OH`B. `CH_(3)CH_(2)CH_(2)OH`C. `CH_(3) -underset(OH)underset(|)(CH)-CH_(3)`D. `CH_(3) -overset(CH_(3))overset(|)underset(OH)underset(|)C-CH_(3)` |
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Answer» Correct Answer - D `CH_(3)-underset(OH)underset(|)overset(CH_(3))overset(|)C-CH_(3)` `3^(@)` alcohol reacts with lucas reagent (HCl + anhydrous `ZnCl_(2)`) immediately and gives two separate layers. |
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| 4515. |
Biopolymers are polymers that are generated from renewable natural sources, are often biodegradable and nontoxic. They can be produced by biological systems (i.e. microorganisms, plants and animals), or chemically synthesized from biological materials (e.g., sugars, starch, natural fats or oils, etc.). Two strategies are applied in converting these raw materials into biodegradable polymers: extraction of the native polymer from a plant or animal tissue, and a chemical or biotechnological route of monomer polymerization. Biodegradable biopolymers (BDP) are an alternative to petroleum-based polymers (traditional plastics). Some BDP degrade in only a few weeks, while the degradation of others takes several months. In principle the properties relevant for application as well as biodegradability are determined by the molecular structure. According to the American Society for Testing and Materials, biopolymers are degradable polymers in which degradation results from the action of naturally occurring microorganisms such as bacteria, fungi and algae.Polylactic acid (PLA) is an example of biopolymer. It is a thermoplastic polyester. Generally, there are two major routes to produce polylactic acid from the lactic acid (CH3CH(OH)- COOH)monomer. The first route involves condensation–water removal by the use of solvent under high vacuum and temperature. This approach produces a low to intermediate molar mass polymer. An alternative method is to remove water under milder conditions, without solvent, to produce a cyclic intermediate dimer, referred to as lactide. This intermediate is readily purified by vacuum distillation. Ring opening polymerization of the dimer is accomplished under heat, again without the need for solvent. By controlling the purity of the dimer it is possible to produce a wide range of molar masses .PLA is a good material for production of clothing, carpet tiles, interior and outdoor furnishing, geotextiles, bags, filtration systems, etc.The primary biodegradability of PLA was tested using hydrolysis tests at various composting temperatures and pH. It was demonstrated that composting is a useful method for PLA biodegradation. The degradation rate is very slow in ambient temperatures. A 2017 study found that at 25 °C in sea water, PLA showed no degradation over a year. As a result, it is poorly degraded in landfills and household composts, but is effectively digested in hotter industrial composts.In the following questions, a statement of assertion followed by a statement of reason is given. Choose the correct answer out of the following choices on the basis of the above passage.A. Assertion and reason both are correct statements and reason is correct explanation for assertion.B. Assertion and reason both are correct statements but reason is not correct explanation for assertionC. Assertion is correct statement but reason is wrong statement.D. Assertion is wrong statement but reason is correct statement.Q 1.Assertion: Biodegradable polymers degrade in few weeks.Reason: Microorganisms bring about degradation of biopolymers.Q 2. Assertion: Lactic acid on polymerisation formsReason: PLA is used in producing geotextiles.Q 3. Assertion: Lactic acid undergoes condensation polymerisationReason: Lactic acid is a bifunctional monomeric unit.Q 4. Assertion: The degradation of PLA is very slow in ambient temperature.Reason: PLA is a thermoplastic.Q 5.Assertion: PLA is poorly degraded in landfills. Reason: The degradation rate of PLA is very slow in ambient temperatures. |
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Answer» 1 (D) Assertion is wrong statement but reason is correct statement. 2 (B) Assertion and reason both are correct statements but reason is not correct explanation for assertion. 3 (A) Assertion and reason both are correct statements and reason is correct explanation for assertion. 4 (B) Assertion and reason both are correct statements but reason is not correct explanation for assertion. 5 (A) Assertion and reason both are correct statements and reason is correct explanation for assertion. |
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| 4516. |
Which among the following oxoacids of phosphorus shows a tendency of disproportionation?A. Phosphinic acid `(H_(3)PO_(2))`B. Orthophosphoric acid `(H_(3)PO_(4))`C. Phosphonic acid `(H_(3)PO_(3))`D. Pyrophosphoric acid `(H_(4)P_(2)O_(7))` |
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Answer» Correct Answer - C `4H_(3)PO_(3) to 3H_(3)PO_(4) + PH_(3)` phosphonic acid |
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| 4517. |
She is a doctor and ALSO a student. A) else B) too C) either D) neither E) so |
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Answer» Correct option is B) too |
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| 4518. |
Alice is ________ as the boys. A) too strong B) so strong C) as strong D) also strong |
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Answer» Correct option is C) as strong |
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| 4519. |
There must be some other reason for her failure ________ this. A) as well B) too C) also D) besides |
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Answer» Correct option is D) besides |
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| 4520. |
______ being useful, glass is also ornamental. A) Besides B) Aside C) Though D)Because |
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Answer» Correct option is A) Besides |
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| 4521. |
Enlist four diseases of ornamental crops. |
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Answer» Leaf spot, dieback, wilt, damping off of seedlings, botrytis rot. |
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| 4522. |
The branch of agriculture which deals with fruit crops, vegetable crops, ornamental crops, medicinal & aromatic crops, spices & plantation crops and post-harvest management and processing, is known as a) Apiculture b) Horticulture c) Floriculture d) Olericulture |
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Answer» Correct option: b) Horticulture |
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| 4523. |
Write the protected cultivation of carnation on the following heads: (a) Propagation (b) Planting time (c) Nutrition (d) Pinching |
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Answer» (a) Propagation: Carnation (D.caryophyllus) for cut flower is multiplied through cuttings. There are annual carnations that are multiplied by seeds. These annual carnations are suitable as potted ornamental plants. D.chinensis and D. barbatus are multiplied through seeds. (b) Planting time: Planting can be done in different spacing. Normally, 30-45 plants per m2 are considered to be ideal. The different spacing followed based on branching habit of the plant is 15 x 8cm, 15 x 10cm, 15 x 15cm and 15 x 20cm. In case information is lacking about the plant habit 15 x 20cm spacing can be conveniently followed. Alternate planting in adjacent rows is beneficial in terms of reduced incidence of disease. (c) Nutrition: For the first three weeks after planting, plant does not require any fertilizer. Nitrogen, Phosphorous and Potash is 30:20:30 gm per m2 per year. A basal dose of 20:20:10gm/ m2 is given at the time of planting. Remaining fertilizer is applied in equally distributed dosage over. (d) Pinching: When the plant attains six nodes, the first pinch is given. This is referred as ‘single pinch’. This would give rise to six laterals In a ‘one and half pinch’; 2-3 of these lateral shoots are pinched again. For the ‘double pinch’, all the lateral shoots are pinched off. Ideal time for pinching is morning. |
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| 4524. |
At STP, a container has 1 mole of Ar, 2 mole of `CO_(2)`, 3 moles of `O_(2)` and 4 moles of `N_(2)`. Without changing the total pressure if one mole of `O_(2)` is removed, the partial pressure of `O_(2)`A. is changed by about 26 %B. is halvedC. is unchangedD. changes by 33 % |
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Answer» Correct Answer - 1 In the first case, `n_(Ar)=1,n_(CO_(2))=2, n_(O_2)=3 n_(N_(2))=4` `therefore "Total no. of moles"=1+2+3+4=10` If P in the total pressure, `P_(o_(2))=(3P)/(10)` In the second case, `n_(o_(2))=2,n_("total")=9` As P remains the same, `P_(o_(2))=(2P)/(9)` `therefore "Decreasc in Partial pressure of" CO_(2)` `=(3P)/(10)-(2P)/(9)=(7P)/(90)` `therefore "decrease in partial pressure of" CO_(2)` `=(7P//90)/(3P//10)xx100=(700)/(27)=26%` |
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| 4525. |
Purpose of Static offset MHO relay: Type- YTGM. |
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Answer» This relay is a static single phase, single step, and distance protection with MHO offset MHO characteristic. With suitable current/voltage input selection, the relay can be made to have the required character in the R-X plane for various applications such as Generator Field failure protection, Generator backup impedance protection and as offset MHO relay for use in conjunction with generator pole slipping protection. |
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| 4526. |
What is the purpose of OSLG? |
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Answer» This gear mainly used to control the steam flow so as to limit the machine from over speeding. On following occasions, the over speed limiting gear acts. a) When the flow of steam corresponds to load is 2/3 and b) Electrical power on generator falls 1/3 of full load. |
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| 4527. |
What is the purpose of LLG? |
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Answer» To ensure that the turbine load never exceed the reactor output, to incorporate turbine follow reactor feature governing system. |
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| 4528. |
Why double squirrel cage motor used in barring gear? Why? |
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Answer» To have high starting torque. In AC motors torque is directly proportional to φ (flux), I2 and cosφ2. i.e T ;φ (flux* I2 * cos φ2. ∴ T = k * φ (flux)* I2 * cos φ2. Rotor at standstill E2;φ (flux) ∴ T = k * E2 * I2 * cos φ2. In double squirrel cage motor inner cage is low resistive and high inductive. The outer cage is high resistive and low inductive. In case of inner cage Z (impedance) is less (XL = 2π f L). If the rotor is having high inductance at starting I2 will lag E2 by large and cos φ2 (Rotor PF = R2 / Z2) is very less. So torque is less. At staring rotor torque is proportional to the rotor resistance. At starting inductance is high and the Z is |
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| 4529. |
What are the purposes of barring gear? |
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Answer» Start rotor from rest. Eliminates sag in rotor - straighten and avoid rubbing at glands. Avoid direct contact journals and bearings. Avoid differential temp between top and bottom of cylinder due to convection of Steam or hot air inside turbine cylinders. |
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| 4530. |
If \( 0_{1}+0_{2}=\frac{\pi}{2} \) and \( 0_{1}=20_{2} \), then value of \( \sin ^{2} \theta_{1}+\cos ^{2} \theta_{2} \) is(1) \( \frac{1}{2} \)(2) 1(3) \( \frac{3}{2} \)(4) 2 |
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Answer» what is value of theta 1 |
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| 4531. |
What is requirement of speeder gear assembly? |
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Answer» To bring the turbine to synchronous speed and get tight lock with grid by grid frequency. BPC signal is given in Auto mode to the speeder gear motor. |
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| 4532. |
State turbine governor setting. |
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Answer» On 2560 rpm turbine governor becomes effective and on 2760 rpm is turbine governor take over speed. |
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| 4533. |
What is the type turbine installed in KGS? |
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Answer» Tandem compounded to expansion of steam, impulse reaction type. |
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| 4534. |
Explain resistance and resistivity of conduct with mathematical expansion |
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Answer» Resistance of a conductor is given by R=ρ A/L L is length of conductor A is area of cross section. And ρ is resistivity of material of conductor and it is the measure of opposition offered to current flow by that conductor material. Resistance of a conductor is given by R=ρ A/LL is length of conductor A is area of cross section. And ρ is resistivity of material of conductor and it is the measure of opposition offered to current flow by that conductor material. |
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| 4535. |
Angle made by vector `sqrt(3)hat(i)+sqrt(2)hat(j)-2hat(k)` with `-ve y-` axis is `:`A. `cos^(-1)((sqrt(2))/(3))`B. `cos^(-1)(-(sqrt(2))/(3))`C. `pi-cos^(-1)((sqrt(2))/(3))`D. `pi-cos^(-1)(-(sqrt(2))/(3))` |
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Answer» Correct Answer - B::C `cos theta=((sqrt(3)hat(i)+sqrt(2)hat(j)-2hat(k))(-hat(j)))/(sqrt(3+2+4(1)))=(-sqrt(2))/(3)` `theta=cos^(-1)((-sqrt(2))/(3))or pi-cos^(-1)((sqrt(2))/(3))` |
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| 4536. |
Define the electromagnetic spectrum? write the various types of electromagnetic induction. |
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Answer» The electromagnetic (EM) spectrum is the range of all types of EM radiation. Radiation is energy that travels and spreads out as it goes – the visible light that comes from a lamp in your house and the radio waves that come from a radio station are two types of electromagnetic radiation. The other types of EM radiation that make up the electromagnetic spectrum are microwaves, infrared light, ultraviolet light, X-rays and gamma-rays. Radio: Your radio captures radio waves emitted by radio stations, bringing your favorite tunes. Radio waves are also emitted by stars and gases in space. Microwave: Microwave radiation will cook your popcorn in just a few minutes, but is also used by astronomers to learn about the structure of nearby galaxies. Infrared: Night vision goggles pick up the infrared light emitted by our skin and objects with heat. In space, infrared light helps us map the dust between stars. Visible: Our eyes detect visible light. Fireflies, light bulbs, and stars all emit visible light. Ultraviolet: Ultraviolet radiation is emitted by the Sun and are the reason skin tans and burns. "Hot" objects in space emit UV radiation as well. X-ray: A dentist uses X-rays to image your teeth, and airport security uses them to see through your bag. Hot gases in the Universe also emit X-rays. Gamma ray: Doctors use gamma-ray imaging to see inside your body. The biggest gamma-ray generator of all is the Universe. |
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| 4537. |
In a house 15 Bulbs of 45 W, 15 bulbs of 100 W, 15 bulbs of 10 W and Two heaters of 1 KW each is connected to 220 V Mains supply then find minimum fuse current(1) 5 A (2) 20 A (3) 25 A (4) 15 A |
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Answer» Answer is (2) 20 A Total power is (15 × 45) + (15 × 100) + (15 × 10) + (2 × 1000) = 4325 W So current is = 4325/220 19.66 A |
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| 4538. |
For the given P-V graph for an ideal gas, chose the correct V- T graph. Process BC is adiabatic. |
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Answer» Answer is (1) For process A – B; Volume is constant ; PV = nRT ; as P increases; T increases For process B – C; PVγ = Constant ; ⇒ TVγ–1 = Constant For process C – A ; pressure is constant V = kT |
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| 4539. |
Statement-1: Electric field changes the speed of change particle but magnetic field does not change the speed.Statement-2: Charge particle travels perpendicular to electric field and parallel to magnetic field(a) Statement-1 is false, statement-2 is true(b) Both statement is true & statement 2 is not the correct explanation of statement-1.(c) Statement-1 is true, statement-2 is false.(d) Statement-1 is true, statement-2 is true and statement-2 is the correct explanation of statement-1. |
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Answer» (c) Statement-1 is true, statement-2 is false. |
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| 4540. |
Statement-1: An object is moving from pole to equator on earth surface. Gravitational force on it remains constant.Statement-2: Direction of gravitational force on object at equator is towards centre of the earth.(1) Statement-1 is true, Statement-2 is true(2) Statement-1 is false, Statement-2 is false(3) Statement-1 is false, Statement-2 is true(4) Statement-1 is true, Statement-2 is false |
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Answer» (3) Statement-1 is false, Statement-2 is true |
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| 4541. |
Statement-1: In uniform magnetic field speed and energy of a charge particle remains constant.Statement-2: Magnetic force is perpendicular to velocity (1) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (2) Statement-1 is True, Statement-2 is True: Statement-2 is NOT a correct explanation for Statement-1 (3) Statement-1 is True, Statement-2 False(4) Statement-1 is False Statement-2 is True. |
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Answer» Correct option is (1) Statement-1 is True, Statement 2 is True; Statement-2 is a correct explanation for Statement-1 |
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| 4542. |
A varable force, given by the 2- dimensional vector`overlineF=(3xx^(2)hati+4 hatj),` acts on a particle. The force is in newton and x is in metre. What is the change in the kinetic energy of the particle as it moves from the point with coordinates (2,3) to (3,0) (The coornates are in metres)A. `-7J`B. zeroC. `+7J`D. `+19J` |
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Answer» [3] `W=int_(2)^(3) 3x^(2)dx+int_(3)^(0) 4dy` |
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| 4543. |
A constant power P is applied to a car starting from rest. If v is the velocity of the car at time t, then:A. `vprop t`B. `v prop (1)/(t)`C. `v prop sqrt(t)`D. `v prop (1)/sqrt(t)` |
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Answer» [3] Power, `P=mxxaxxv` `P=mxx(v^(2))/(t)` If p is constant, then for a given body `v^(2)propt` or `vprop sqrt(t)` |
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| 4544. |
Two identical samples (same material and same amout) `P and Q` of a radioactive substance having mean life `T` are observed to have activities `A_P` and `A_Q` respectively at the time of observation. If `P` is older than `Q`, then the difference in their age isA. `T "ln"((A_(P))/(A_(Q)))`B. `T "ln"((A_(Q))/(A_(P)))`C. `T ((A_(P))/(A_(Q)))`D. `T ((A_(Q))/(A_(P)))` |
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Answer» Correct Answer - B `A_(Q) overset(t=?)rarrA_(p)` (T=mean life) `A = A_(0)e^(-lambdat) , A_(p) = A_(Q)e^(-lambdat)` `rArr e^(lambdat) = (AQ)/(AP)` `lambdat = "ln"((A_(Q))/(A_(P)))t = T "ln" ((A_(Q))/(A_(P)))` `lambda = (1)/(T)` |
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| 4545. |
An object moving along the x axis is acted upon by a forse `F_(x)` that varies with position as shown . How much work is done by this force as the moves from `x=2m` to `x = 8 am`? A. `-10 J`B. `+10 J`C. `+30 J`D. `-30 J` |
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Answer» [3] W`=(1)/(2)xx20xx4-(1)/(2)xx10xx2` `=30J` |
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| 4546. |
Two capacitors `C_(1)` and `C_(2)` are connected in a circuit as shown in figure. The potential difference `(V_(A) - V_(B))` is A. `8V`B. `-8V`C. `12V`D. `-12V` |
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Answer» Correct Answer - B By using KVL A to A `12 + q/4 - 24 + q/2 = 0` `q/2 + q/4 = 12` `q = (12 xx 4)/(3) = 16 muC` `V_(A) - V_(B) = (-q)/(2muC) = - 8V` |
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| 4547. |
Evaluate ∫dx/(x-√(x2+2x-4)) |
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Answer» d\dxSIN(2X + 1) cosX (2X) 2cos ^2X) |
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| 4548. |
A charged sphere of diameter `4` cm has a charge density of `10^(-4) "coulmb"//cm^(2)`. The work done in joule when a charge of 40 nano-columbs is moved from infinity to a point which is at a distance of 2 cm from the surface of the sphere is-A. `14.4 pi`B. `28.8 pi`C. `144 pi`D. `288 pi` |
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Answer» Correct Answer - A `w= qDeltaV` `sqrt(AB) = sqrt(2) = 1.4` and error in `sqrt(AB)` Let `Z = sqrt(AB)` `(DeltaZ)/(Z) = (1)/(2) (DeltaA)/(A) + 1/2 (DeltaB)/(B)` `(DeltaZ)/(1.4) = 1/2 ((0.2)/(1)) + 1/2 ((0.2)/(2))` `(DeltaZ)/(1.4) = 0.1+ 0.05` `Delta Z = (0.15)(1.4) = 0.21` `Z = (1.4+0.2) m` |
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| 4549. |
Solve \( x \frac{d y}{d x}+\frac{2 y}{x}=\frac{1}{x^{3}} \) |
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Answer» x\(\frac{dy}{dx}+\frac{2y}x=\frac1{x^3}\) ⇒ \(\frac{dy}{dx}+\frac{2}{x^2}y=\frac1{x^4}\) which is linear differential equation. ∴ I.F. = \(e^{\int\frac2{x^2}dx} = e^{\frac{-2}x}\) y x I.F. = \(\int\frac1{x^4}(I.F)dx\) ⇒ y. e\(\frac{-2}x\) = \(\frac{e^{\frac2x}}{x^4}dx\) Let \(\frac{-2}x=t\) ⇒ \(\frac2{x^2}dx=dt\) ∴ ye\(\frac{-2}x\) = \(\frac12\int\frac{t^2}4e^tdt\) = \(\frac18\)(t2et - 2tet + et) + c = \(\frac18\)(t2 - 2t + 1)et + c left part y.e-2/x = \(\frac18\)(t - 1)2et + c ⇒ ye-2/x = \(\frac18\) (-2/x - 1)2e-2/x + c ( ∵ t = -2/x) ⇒ y = \(\frac18\)(2/x + 1)2 + ce2/x which is general solution of given differential equation. |
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| 4550. |
\[f(x)=\left\{\begin{array}{ll}\frac{1-\cos k x}{x \sin x} & \text { if } x \neq 0 \\1 / 2 & \text { if } x=0\end{array}\right.\]find \( K \) if \( x \) is continvous at \( x=0 \) |
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Answer» ∵ f is continuous at x = 0. Then f(0) = \(\underset{x\rightarrow0}{lim}\) f(x) ⇒ \(\underset{x\rightarrow0}{lim}\) \(\frac{1-cos\,kx}{x\,sin\,x}\) = 1/2 ⇒ \(\underset{x\rightarrow0}{lim}\) \(\frac{k\,sin\,kx}{x\,cos\,x+sin\,x}\) = 1/2 (By D.L.H. Rule) ⇒ \(\underset{x\rightarrow0}{lim}\) \(\cfrac{k^2x\,\frac{sin\,kx}{kx}}{x(cos\,x+\frac{sin\,x}x)}\) = 1/2 ⇒ \(\underset{x\rightarrow0}{lim}\) \(\cfrac{k^2\times\frac xx\times\frac{sin\,kx}{kx}}{cos\,x+\frac{sin\,x}x}\) = 1/2 ⇒ k2 \(\cfrac{\underset{kx\rightarrow0}{lim}\frac{sin\,kx}{kx}}{\underset{x\rightarrow0}{lim}\,cos\,x+\underset{x\rightarrow0}{lim}\,\frac{sin\,x}x}\) = 1/2 ⇒ \(\frac{k^2\times1}{cos\,0+1}\) = 1/2 (∵ \(\underset{x\rightarrow0}{lim}\) sinx/x = 1) ⇒ k2/2 = 1/2 ⇒ k2 = 1 ⇒ k = ±1 for k = 1 or k = -1, the given function f(x) is continuous. |
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