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.
| 301. |
Arrange the expansion of `(x^(1//2) + (1)/(2x^(1//4)))^n` in decreasing powers of x. Suppose the coefficient of the first three terms form an arithemetic progression. Then the number of terms in the expression having integer powers of x is -(A) 1 (B) 2 (C) 3 (D) more than 3A. 1B. 2C. 3D. more than 3 |
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Answer» Correct Answer - C `T_(r+1)=.^(n)C_(n)(x^(1//2))^(n-r)(1)/((2x^(1//4))^(r)) = (.^(n)C_(r))/(2^(r))x^((2n-3r)/(4))` `T_(1), T_(2), T_(3) rarr AP` ` (2.^(n)C_(1))/(2) = .^(n)C_(0) + (.^(n)C_(2))/(2^(2))` `n-1 = (n(n-1))/(8) rArr n = 8` `(16-3r)/(4) = "Integers" , r= 0,4,8` |
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| 302. |
For `0 lt theta lt (pi)/(2)`, four tangents are drawn at the four points `( pm 3 cos theta, pm 2 sin theta )` to the ellipse `(x^(2))/(9)+(y^(2))/(4)=1` . If A`(theta)` denote the area of the quadrilateral formed by these four tangents, the minimum value of `A(theta)` isA. 21B. 24C. 27D. 30 |
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Answer» Correct Answer - B `{:((x cos theta)/(3)+(y sin theta)/(2)=1),((x cos theta)/(3)-(y sin theta)/(2)=1):}}x= 3 sec theta,y=0` `(-x cos theta)/(3)+(y sin theta)/(2)=1` `(-x cos theta)/(3)-(y sin theta)/(2)=1` `x=0,y=2 cos theta` area `=4.(1)/(2) 3 sin theta. 2 cos theta` `=(12)/( sin theta cos theta)=(24)/( sin 2 theta)` `:. ` min. area =24 |
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| 303. |
Let S `={x in R: cos(x)+cos(sqrt(2)x)lt2}`. ThenA. `S= phi`B. S is a non-empty finite setC. S is an infinite proper subset of R{0}D. S=R{0} |
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Answer» Correct Answer - D `cos x + cos sqrt(2)x lt 2` ` cos x le 1 " and " cos sqrt(2)x le 15` `cos + cos sqrt(2)x le 2 at x=0 cos x + cos sqrt(2)x=2` `implies x in R-{0}` |
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| 304. |
The number of real solution x of the equation `cos^(2)(x sin (2x))+(1)/(1+x^(2))=cos^(2)x+sec^(2)x` is |
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Answer» Correct Answer - B `cos^(2)(x sin 2x)+(1)/(1+x^(2))=cos^(2)x+sec^(2)x` `LHS le2" "RHS ge2` LHS=RHS=2 `+. X=0` only solution |
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| 305. |
A table has a heavy circular top of radius `1m` and mass `20 kg`, placed on four light (considered massless) legs placed symmetrically on its circumference. The maximum mass that can be kept anywhere on the table without toppling it is close toA. `20 kg`B. `34 kg`C. `47 k`D. `59 kg` |
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Answer» Correct Answer - C |
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| 306. |
The intensity of sound during the festival season increased by 100 times. This could imply a decibel level rise from -A. 20 to 120 dBB. 70 to 72 dBC. 100 to 10000 dBD. 80 to 100 dB |
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Answer» Correct Answer - D |
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| 307. |
A planet of mass m is moving around a star of mass M and radius R in a circular orbit of radius r. The star abruplly shrinks to half its radius without any loss of mass. What change will be there in the orbit of the planet ? (A) The planet will escape from the star (B) The radius of the orbit will increase (C) The radius of the orbit will decrease (D) The radius of the orbit will not change |
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Answer» Correct Option :- (D) The radius of the orbit will not change Explanation :- If radius of star is decreasing without any change in mass of star then it will not affect the force exerted by star on planet which is the required centripetal force. So radius of the orbit of planet with remain unaffected. |
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| 308. |
A planet of mass m is moving around a star of mass M and radius R in a circular orbit of radius r. The star abruplly shrinks to half its radius without any loss of mass. What change will be there in the orbit of the planet ?A. The planet will escape from the starB. The radius of the orbit will increaseC. The radius of the orbit will decreaseD. The radius of the orbit will not change |
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Answer» Correct Answer - D |
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| 309. |
Doping silicon with boron produces a – (A) n-type semiconductor (B) Metallic conductor (C) p-type semiconductor (D) Insulator |
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Answer» Correct :- (C) p-type semiconductor |
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| 310. |
The isoelectronic pair of ions is – (A) Sc2+ and V3+ (B) Mn2+ and Fe3+ (C) Mn3+ and Fe2+ (D) Ni3+ and Fe2+ |
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Answer» Correct :- (B) Mn2+ and Fe3+ Explanation :- Mn+2 = 23 e– Fe+3 = 23 e– |
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| 311. |
The volume of oxygen at STP required to burn 2.4 g of carbon completely is :A. 1.12 LB. 8.96 LC. 2.24 LD. 4.48 L |
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Answer» Correct Answer - D `C+O_(2)toCO_(2)` `2.4/12=0.2` mole of carbon `:. 0.2" mole of need 0.2 mole of " O_(2)` So vol. of 0.2 mole `O_(2)" at " STP=0.2xx22.4=4.48 L` |
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| 312. |
The isoelectronic pairs is :A. `CO,N_(2)`B. `O_(2),NO`C. `C_(2),HF`D. `F_(2),HCl` |
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Answer» Correct Answer - A `CO" and " N_(2)` are isoelectronic because both have 14 electrons. |
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| 313. |
If parents have free ear lobes and the offspring has attached ear lobes, then parents must beA. homosygousB. heterozygousC. co-dominantD. nullizygous |
| Answer» Correct Answer - B | |
| 314. |
The length of one complete turn of a DNA double helix is -A. `34 Å`B. `34 nm`C. `3.4 Å`D. `3.4 mum` |
| Answer» Correct Answer - A | |
| 315. |
The length of one complete turn of a DNA double helix is- (A) 34 Å (B) 34 nm (C) 3.4 Å (D) 3.4 µm |
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Answer» Correct Option :- (A) 34 Å |
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| 316. |
As isolated box, equally partitioned contains two ideal gases A and B as shown What the partition is removed, the gases mix. The changes in enthalpy `( Delta H)` and entropy `( Delta S)` in the process, respectively, areA. zero, positiveB. zero, negativeC. positive, zeroD. negative, zero |
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Answer» Correct Answer - A According to KTG Force of attraction and repulsion amongst molecules of ideal gas are negligible So, ` Delta H=0` and randomness increases due to increase in volume so `Delta S = + ve`. |
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| 317. |
As isolated box, equally partitioned contains two ideal gases A and B as shown When the partition is removed, the gases mix. The changes in enthalpy (∆H) and entropy (∆S) in the process, respectively, are (A) zero, positive (B) zero, negative (C) positive, zero (D) negative, zero |
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Answer» Correct option (A) zero, positive Explanation: According to KTG Force of attraction and repulsion amongst molecules of ideal gas are negligible So, ∆H = 0 and randomness increases due to increase in volume so ∆S = +ve. |
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| 318. |
Assuming ideal behaviour, the enthalpy and volume of mixing of two liquids, respectively, are(A) zero and zero (B) + ve and zero (C) –ve and zero (D) – ve and – ve |
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Answer» Correct Option :- (A) zero and zero Explanation : For Ideal Solution ∆H Mix =0 ∆V Mix = 0 |
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| 319. |
Let r be a root of the equation `x^(2)+2x+6=0.` The value of `(r+2)(r+3)(r+4)(r+5)` is equal to-A. 51B. -51C. -126D. 126 |
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Answer» Correct Answer - C r is root, therefore `r^(2)+2r+6=0` `(r+2)(r+3)(r+4)(r+5)=(r^(2)+2r+6+3r)(r^(2)+4r+5r+20)` `=(3r)(7r+14)` `21(r^(2)+2r)=21(-6)=-126` |
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| 320. |
Let x and y be two 2-digit numbers such that y is obtained by recersing the digits of x. Suppose they also satisfy `x^(2)-y^(2)=m^(2)` for same positive integer m. The value of x + y + m is-A. 88B. 112C. 144D. 154 |
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Answer» Correct Answer - D `x=ab=10a+b` `y=ba=10b+a" "1lea, ble9` `x^(2)-y^(2)=m^(2)` `100a^(2)+b^(2)+20ab-(100b^(2)+a^(2)+20sb)=m^(2)` `99(a^(2)-b^(2))=m^(2)` `9xx11xx(a-b)(a+b)=m^(2)` m is interger so`" "a=6" "{Note :"a-bne9"(think why ?)"}` `b=5` `m^(2)=9xx11xx1xx11rArrm=3xx11` `x+y+m=10a+b+10b+a+33` `=11(a+b)+33=11(11)+33=121+33=154` |
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| 321. |
Upon mixing equal volumes of aqueous solutions of 0.1 M HCl and 0.2 M `H_(2)SO_(4)`, the concentration of `H^(+)` in the resulting solution is-A. `0.30mol//L`B. `0.25mol//L`C. `0.15mol//L`D. `0.10mol//L` |
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Answer» Correct Answer - A::B::C::D `H^(+)` moles `=0.2xx2xxV=0.4V` Total moles of `H^(+)=0.4+0.1V=0.5V` `[H^(+)]=("Moles")/(Vol.)=(0.5V)/(2V)=0.25M//L` |
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| 322. |
The final major product obtained in the following sequence of reactons is - A. B. C. D. |
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Answer» Correct Answer - B `PhC-=CHoverset(NaNH_(2)//NH_(3))rarrPhC-=C^(-)overset(CH_(3)I)rarrPhC-=C-CH_(3)overset(H_(2),Pd//C)rarrPhCH=CH-CH_(3)` |
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| 323. |
The equilibrium constant for the following reactions are `K_(1)` and `K_(2)`, respectively , `2P(g)+3Cl_(2)(g)hArr2PCl_(3)(g)` `PCl_(3)(g)+Cl_(2)(g)hArrPCl_(5)(g)` Then the equilibrium constant for the reaction `2P(g)+5Cl_(2)(g)hArr2PCl_(5)(g)` is -A. `K_(1)K_(2)`B. `K_(1)K_(2)^(2)`C. `K_(1)K_(2)^(2)`D. `K_(1)^(2)K_(2)` |
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Answer» Correct Answer - B `2P(g)+3Cl_(2)(g)hArr2PCl_(3)(g)" "K_(1)` `2PCl_(3)(g)+2Cl_(2)(g)hArr2PCl_(5)(g)" "K_(2)^(2)` Net reaction : `2(P)(g)+5Cl_(2)(g)hArr2PCl_(5)(g)" "K=K_(1)K_(2)^(2)` |
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| 324. |
A solution containing `8.0 g` of nicotine in `92 g` of water-frezes `0.925` degrees below the normal freezing point of water. If the freezing point depression constant `K_(f) = -1.85^(@)C mol^(-1)` then the molar mass of nicotine is -A. 16B. 80C. 320D. 160 |
| Answer» Correct Answer - D | |
| 325. |
Nitroglycerine (MW =227.1) detonates according to the following equation : `2C_(3)H_(5)(NO_(3))_(3)I to 3N_(2)(g)+1//2O_(2)(g)+6CO_(2)(g)+5H_(2)O(g)` The standard molar enthalpies of formation, `DeltaH_(f)^(@)` for the compounds are given bellow: `DeltaH_(f)^(@)[C_(3)H_(5)(NO_(3))_(3)]= -364 kJ//mol` `DeltaH_(f)^(@)[CO_(2)(g)]= -395.5 kJ//mol` `DeltaH_(f)^(@)[H_(2)O(g)]= -241.8 kJ//mol` `DeltaH_(f)^(@)[N_(2)(g)]= 0 kJ//mol` `DeltaH_(f)^(@)[O_(2)(g)]= 0 kJ//mol` The enthalpy change when 10g of nitroglycerine is detonated isA. `-100.5 kJ`B. `-62.5 kJ`C. `-80.3 kJ`D. `-74.9 kJ` |
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Answer» Correct Answer - B `{:(2C_(3)H_(5)(NO_(3))_(3)(l) ,+ 3N_(2)(g),+1//2O_(2)(g),+6CO_(2)(g),+5H_(2)O(g)),(," " darr," " darr," " darr," " darr ),(,DeltaH_(f)^(@)=O,DeltaH_(f)^(@)=O,DeltaH_(f)^(@)=O,DeltaH_(f)^(@)=O):}` `DeltaH_("reaction")^(@)=3xx0+(1)/(2)xx0+6xx-393.5+5xx-241.8-2xx-364` = -2842kJ ` to` for 2 mole of nitroglycerine for 1 mole or for 227.1g ` = -(2842)/(2)` For 1 g `= -(2842)/(2xx227.1)xx10= - 62.5 kJ` |
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| 326. |
The reaction that gives the following molecule as the major product is - A. B. C. D. |
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Answer» Correct Answer - B `{:(" "H_(3)C" "CH_(3)),(" | |"),(H_(3)C-C-ONaoverset(CH_(3)Br)rarrH_(3)C-C-OCH_(3)),(" | |"),(" "CH_(3)" "CH_(3)):}` |
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| 327. |
Plots showing the variation of the rate constant `(k)` with temperature `(T)` are given below. The plot that follows the Arrhenius equation isA. B. C. D. |
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Answer» Correct Answer - D `K=Ae^(-)(E_(0))/(RT)` `ln K =ln A-(E_(0))/(RT)` |
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| 328. |
Given below are the four schematics that describe the dependence of the rate of an enzymatic reaction on temperature. Which of the following combinations is true for thermophilic and psychrophilic organisms?(A) P and P (B) P and S (C) P and R (D) R and R |
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Answer» Correct Option :- (D) R and R Explanation :- Being mostly proteinaceous enzymes are liable to temperature. Thermophiles are living at very high temperature while psychrophiles live in the range of –20°C to +10°C. In either case rising temperature will first raise the rate of reaction but if temperature is still raised continuously enzyme get denatured hence reaction rate decreases. |
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| 329. |
Match the different types of heart given in Column A with organisms given in the column B. Choose the corrent combination. `{:("Column A","Column B",),("P. Neurogenic Heart","i. Human",),("Q.Bronchial heart","ii. King crab",),("R. pulmonary heart","iii. Shark",):}`A. P-ii,Q-iii,R-iB. P-iii,Q-ii,R-iC. P-I,Q-iii,R-iiD. P-ii,Q-I,R-iii |
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Answer» Correct Answer - a `- "Neurogenic Heart"to "King carb [Arthropod]"` `-"Bronchial Heart"to"Shark [Single cirulation]"` `- "Pulmonary Heart" to "Human"` |
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| 330. |
Given below are the four schematic that descirbe the dependence of the rate of an enzymatic reaction on temperature.which of the following combinations is true for themophilic and psychrophilic organisms ? A. P and PB. P and SC. P and RD. R and R |
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Answer» Correct Answer - d Being mostly proteinaceous enzymes are liable to temperature. Themosphiles are living at very high temperature while psyrophiles live in the range of `-20^(@)C "to" + 10^(@)C` . In either case rising temperature will first raise the rate of reaction but if temperature is still raised continuosly enzyme get denatured hence reaction rate decreases. |
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| 331. |
An organic compound having molecular formula `C_(2)H_(6)O` undergoes oxidation with `K_(2)Cr_(2)O_(7)//H_(2)SO_(4)` to produce X which contains `40%` carbon, `6.7%` hydrogen and `53.3%` oxygen. The molecular formula of the compound X isA. `CH_(2)O`B. `C_(2)H_(4)O_(2)`C. `C_(2)H_(4)O`D. `C_(2)H_(6)O_(2)` |
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Answer» Correct Answer - B `underset(underset(underset((C_(n)H_(2n+2)O))("Alcohol"))((C_(2)H_(60))))(CH_(3)-CH_(2)-OH)overset(K_(2)Cr_(2)O_(7)//H_(2)SO_(4))to underset(underset(underset(underset(underset(H=4(6.7%))(O=32(53.3%)))(C=24(40%" carbon")))("Total wt = 60"))("Carboxylic acid"))underset(O" ")underset(||" ")(CH_(3)-C-O-H)` |
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| 332. |
`MnO_(2)` when fused with KOH and oxidized in air gives a dark green compound X. In acidic solution, X undergoes disproportionation to give an intense purple compound Y and `MnO_(2)`. compounds X and Y, respectively, areA. `K_(2)MnO_(4) and KMnO_(4)`B. `Mn_(2)O_(7) and KMnO_(4)`C. `K_(2)MnO_(4) and Mn_(2)O_(7)`D. `KMnO_(4) and K_(2)MnO_(4)` |
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Answer» Correct Answer - A `{:(MnO_(2)+KO_(2)overset("Oxidized")underset("In Air")(to)dark green compound (X)+MnO_(4)^(-2) & K_(2)MnO+_(4)),(" ""Disproportionation"darr),(" ""Purple colour"(Y)+Mnoverset(+4)(O_(2))),(" "overset(" "+7)(KMn)O_(4)):}` `" "(X)toK_(2)MnO_(4)` `" "(Y)toKMnO_(4)` |
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| 333. |
A man wants to reach a centain destination. One-sixth of the total distance is muddy while half the distance is tar road. For the remaining distance he takes a boat. His speed of traveling in mud, in water, on tar road is in the ratio ` 3 : 4 : 5`. The ratio ratio of the durations he requires to cross the patch of mud, stream and tar road isA. `1/2:4/3:5/2`B. `3 : 8 : 15`C. `10 : 15 : 18`D. `1: 2 : 3` |
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Answer» Correct Answer - C Let distance is 6 x `{:(,,"mud",:,"tar",:,"stream"),("distance",,"x",:,"3x",:,"2x"),("speed",,"3v",:,"5v",:,"4v"),("time",,(x)/(3v),:,(3x)/(5v),:,(2x)/(4v)),(,,10,:,18,:,15):}` |
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| 334. |
The fluid part of blood flows in and out of capillaries in tissue to exchange nutrients and waste materials. Under which of the following conditions will fluid flow out from the capillaries into the surrounding tissue ?A. When arterial blood pressure exceeds blood osomotic pressureB. When arterial blood pressure is less than blood osomotic pressureC. When arterial blood pressure is equal to blood osmotic pressureD. Arterial blood pressure and blood osmotic pressure have nothing to do with the outflow of fluid from capillaries |
| Answer» Correct Answer - A | |
| 335. |
Estimate the order of the speed of propagation of an action potential or nerve impulse - (A) nm/s (B) micron/s (C) cm/s (D) m/s |
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Answer» Correct Option :- (D) m/s |
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| 336. |
In a diploid organism, there are three different alleles for a particular gene. Of these alleles one is recessive and the other two alleles exhibit co-dominance. How many phenotypes are possible with this set of alleles ?A. 3B. 6C. 4D. 2 |
| Answer» Correct Answer - C | |
| 337. |
Which ONE of the following statement is INCORRECT ?A. Alleles are different form of the same gene.B. Alleles are present at the same locus.C. Alleles code for different isoforms of a protein.D. Alleles are non-heritable. |
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Answer» Correct Answer - D Alleles are alternate form of gives of one charcter present on same locus. |
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| 338. |
In a chemical reaction, enzymes catalyze the reaction byA. lowering the activation energyB. increasing the activation energy.C. decreasing the free energy change between reactants and products.D. increasing the free energy chain between reactants and product. |
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Answer» Correct Answer - A Enzyme decrease activation energy in reaction. |
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| 339. |
Cyclic electron flow during photosynthesis generatesA. NADPH alone.B. ATP and NADPH.C. ATP alone.D. ATP,NADPH and `O_(2)` |
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Answer» Correct Answer - C In Cyclic photophosphorylation only ATP is formed. |
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| 340. |
Match the type of cells given in Column I with organism given in Column II. Choose the appropriate combination from the options below . A. P-iii,Q-i,R-iiB. P-iii,Q-ii,R-iC. P-i,Q-ii,R-iiiD. P-i,Q-iii,R-ii |
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Answer» Correct Answer - A Flame cells are for secretion and osmoregulation in flatworms. Collar cells line spongocoel and cavars in sponges and creat water amount. Cnidocyts are stringing cells and help in defense, affiance and capture of prey these cells also help in attachment with substrate. |
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| 341. |
Which ONE of the following option is TRUE with respect to Emigration ?A. It is the difference between the births and deaths in a population.B. It is the difference between individuals who have come to a habitat and who have left the habitatC. It involved individuals of different species coming to a habitat from elsewhere during the period under considerationD. It involves individuals of a population leaving a habitat during the time period under consideration. |
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Answer» Correct Answer - D Emigration going out from one population |
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| 342. |
Molecular weight of E. Coli DNA is `3.1xx10^(9)` g/mol. Average molecular weight of nucleotide pair is 660 g/mol and each nucleotide pair contirbutes ot 0.34 nm to the length of DNA. The length of E. coli DNA molecule will be approximatelyA. 0.8 nmB. 1.6 nmC. `1.6 mum`D. `1.6 mm` |
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Answer» Correct Answer - C `(3.1xx10^(9))/(660)xx0.34` |
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| 343. |
How many different protein consisting of 100 amino acids can be formed from 20 different amino acids ?A. `20^(100)`B. `100^(20)`C. `2^(20)`D. `20xx100` |
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Answer» Correct Answer - A `20^(100)` |
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| 344. |
Blood clotting involves the conversion of (A) prothrombin to thromboplastin (B) thromboplastin to prothrombin (C) fibrinogen to fibrin (D) fibrin to fibrinogen |
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Answer» Blood clotting involves the conversion of fibrinogen to fibrin. |
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| 345. |
A buffer solution can be prepared by mixing equal volumes ofA. 0.2 M `NH_(4)OH` and 0.1 M HClB. 0.2 M `NH_(2)OH` and 0.2 M HClC. 0.2 M NaOH and 0.1 M `CH_(3)COOH`D. 0.1 M `NH_(4)OH` and 0.2 M HCl |
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Answer» Correct Answer - A Mixing equal volume of `NH_(4)OH`(0.2M) and HCl (0.1M) result in formation of `NH_(4)OH+NH_(4)Cl` basic buffer mixture. |
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| 346. |
The average energy of each hydrogen bond in A-T pair is x kcal mol–1 and that in G-C pair is y kcal mol–1. Assuming that no other interaction exists between the nucleotides, the approximate energy required in kcal mol–1 to split the following double stranded DNA into two single strands is [Each dashed line many represent more than one hydrogen bond between the base pairs] (A) 10x + 9y (B) 5x + 3y (C) 15x + 6y (D) 5x + 4.5y |
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Answer» Correct option (A) 10x + 9y Explanation: no. of hydrogen bond between A – T = 2 no. of hydrogen bond between a – c = 3 so total energy required = 10 x + 9y |
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| 347. |
For a process to occur spontaneously (A) only the entropy of the system must increase (B) only the entropy of the suroundings must increase (C) either the entropy of the system or that of the surroundings must increase (D) the total entropy of the system and the surroundings must increase |
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Answer» Correct Option :- (D) the total entropy of the system and the surroundings must increase Explanation :- (∆S)system + (∆S)surrounding > 0 (irreversible process) |
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| 348. |
The rate of gas phase chemical reactions generally increases rapidly with rise in temperature. This is mainly because (A) the collision frequency increases with temperature (B) the fraction of molecules having energy in excess of the activation energy increases with temperature (C) the activation energy decreases with temperature (D) the average kinetic energy of molecules increases with temperature |
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Answer» Correct Option :- (B) the fraction of molecules having energy in excess of the activation energy increases with temperature |
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| 349. |
Ants locate sucrose by (A) Using a strong sense of smell (B) Using a keen sense of vision (C) Physical contact with sucrose (D) Sensing the particular wave length of light emitted reflected by sucrose |
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Answer» Correct Option :- (C) Physical contact with sucrose |
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| 350. |
A majority of the tree species of penensular Indian origin fruit in the months of (A) April – May (B) December – January (C) August – September (D) All months of the year |
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Answer» Correct Option :- (A) April – May |
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