InterviewSolution
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InterviewSolution
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.
| 1. |
If y=mx+4 is common tangent to parabolas `y^(2)=4x and x^(2)=2by`. Then value of b isA. 128B. `-128`C. `-64`D. `-32` |
| Answer» Correct Answer - B | |
| 2. |
If y=mx+4 is common tangent to parabolas `y^(2)=4x and x^(2)=2by`. Then value of b isA. -64B. -32C. -128D. 16 |
| Answer» Correct Answer - C | |
| 3. |
Evaluate `lim_(x to 2) (3^(x)+3^(x-1)-12)/(3^((-x)/(2))-3^(1-x))` |
| Answer» Correct Answer - 72 | |
| 4. |
If `alpha` and `beta` are the roots of equation (k+1) `tan^(2)x-sqrt2lambda, tan=1-k and tan^(2)(alpha+beta)=50`. Find the value of `lambda`A. 10B. 5C. 7D. 12 |
| Answer» Correct Answer - A | |
| 5. |
Let ` A ( 1, 0 ) , B ( 6, 2 ) ` and ` C (( 3 ) /(2), 6 ) ` be the vertices of a triangle ABC. If P is a point inside the triangle ABC such that the triangles APC, APB and BPC have equal areas , then the length of the line segment PQ, where Q is the point ` ( - ( 7 ) /(6), - ( 1 ) /(3)) , ` is _________. |
| Answer» Correct Answer - `5` | |
| 6. |
If f(x) is continuous and differentiable in `x in [-7,0] and f(x) le 2 AA x in [-7,0]`, also f(-7)=-3 then range of f(-1)+f(0)A. [-5,-7]B. `(-oo,6]`C. `(-oo,20]`D. `[-5,3]` |
| Answer» Correct Answer - C | |
| 7. |
Let P be the set of points `(x, y)` such that `x^2 lt y lt – 2x + 3`. Then area of region bounded by points in set P isA. `29/3`B. `34/3`C. `32/3`D. `31/3` |
| Answer» Correct Answer - `C` | |
| 8. |
A is a `3 xx 3` matrix whose elements are from the set `{ -1, 0, 1}`. Find the number of matrices A such that `tr(AA^T) =3`. Where `tr(A)` is the trace of A. |
| Answer» Correct Answer - 672 | |
| 9. |
Let coefficient of `x^4` and `x^2` in the expansion of `(x+sqrt(x^2-1))^6+(x-sqrt(x^2-1))^6` is `alpha` and `beta` then `alpha-beta` is equal toA. `alpha - beta =-132`B. `alpha + beta =60`C. `alpha - beta =60`D. `alpha+ beta =-30` |
| Answer» Correct Answer - A | |
| 10. |
Pair of tangents are drawn from origin to the circle `x^2 + y^2 – 8x – 4y + 16 = 0` then square of length ofchord of contact isA. `(64)/(5)`B. `(52)/(5)`C. `(56)/(5)`D. `(32)/(5)` |
| Answer» Correct Answer - `A` | |
| 11. |
The area bounded by `x^4 le y le 8x+12` is -A. `(125)/(3)`B. `(124)/(3)`C. `(128)/(3)`D. `(127)/(3)` |
| Answer» Correct Answer - `C` | |
| 12. |
Let `x + 6y = 8` is tangent to standard ellipse where minor axis is `4/sqrt3`, then eccentricity of ellipse isA. `1/2 sqrt(11/3)`B. `sqrt(5/6)`C. `1/3 sqrt(11/3)`D. `1/2 sqrt(5/3)` |
| Answer» Correct Answer - `A` | |
| 13. |
Solution set of `3^x (3^x –1) + 2 = |3^x –1| + |3^x – 2|` containsA. is an empty setB. is a singleton.C. contains at least four elements.D. contains exactly two elements . |
| Answer» Correct Answer - `B` | |
| 14. |
The number of four letter words that can be made from the letters of word "EXAMINATION" is |
| Answer» Correct Answer - 2454 | |
| 15. |
If `f(x) = [x] - [x/4], x in R` where [x] denotes the greatest integer function, thenA. `sqrt(A +1)`B. `sqrt(A + 21)`C. `sqrtA`D. `sqrt(A +5)` |
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Answer» Correct Answer - A |
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| 16. |
Let one end of focal chord of parabola `y^2 = 8x` is (1/2, -2)`, then equation of tangent at other end of this focal chord isA. x+2y+8=0B. x-2y+8 =0C. 2x-y-24=0D. 2x+y-24=0 |
| Answer» Correct Answer - `B` | |
| 17. |
If `f(a+b+1-x)=f(x)`, for all x where a and b are fixed positive real numbers, the `(1)/(a+b) int_(a)^(b) x(f(x)+f(x+1)` dx is equal to :A. `underset(a+1)overset(b+1)int f(x)dx`B. `underset(a+1)overset(b+1)int f(x+1)dx`C. `underset(a-1)overset(b-1)int f(x)dx`D. `underset(a-1)overset(b-1)int f(x+1)dx` |
| Answer» Correct Answer - D | |
| 18. |
If `I= int_(1)^(2)(dx)/(sqrt(2x^3-9x^2+12x+4)),` thenA. `1/9 lt I^2 lt 1/8`B. `1/6 lt I^2 lt 1/2`C. `1/16 lt I^2 lt 1/9`D. `1/8 lt I^2 lt 1/4 ` |
| Answer» Correct Answer - A | |
| 19. |
If `lim_(x rarr 0)x[4/x]= A`, then the value of x at which `f(x) = [x^2]sinpix` is discontinuous , (where `[.]` denotes greatest integer function)A. `sqrt(A+1)`B. `sqrt(A+5)`C. `sqrt(A)`D. `sqrt(A+21)` |
| Answer» Correct Answer - A | |
| 20. |
`f(x) : [0, 5] → R, F(x) = int_(0)^(x) x^2 g(x)`, f(1) = 3g(x) = `int_(1)^(x) f(t) dt ` then correct choice isA. `F(x)` has local minimum at `x = 1`B. `F(x)` has local maximum at `x = 1`C. `F(x)` has point of inflection at `x = 1`D. `F(x)` has no critical point |
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Answer» Correct Answer - A |
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| 21. |
`lim_(xto0) (int_(0)^(x)tsin(10t)dt)/(x)` is equal to :A. `-1/5`B. `-1/10`C. 0D. `1/10` |
| Answer» Correct Answer - C | |
| 22. |
`lim_(xto0) (int_(0)^(x)tsin(10t)dt)/(x)` is equal to :A. `-1/5`B. `-1/10`C. 0D. `1/10` |
| Answer» Correct Answer - C | |
| 23. |
Amongst the following , the form of water with the lowest ionic conductance at 298 KA. distilled waterB. saline water used for intravenous injectionC. water from a wellD. sea water |
| Answer» Correct Answer - a | |
| 24. |
Biochemical oxygen demand (BOD) is defined as ............ in ppm of `O_2`.A. Required to sustain lifeB. The amount of oxygen required by bacteria to break down the organic matter present in a certain volume of a sample of waterC. The amount of oxygen required by anaerobic bacteria to break down the inorganic matter present in a certain volume of a sample of waterD. Required photochemical reaction to degrade waste |
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Answer» Correct Answer - B |
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| 25. |
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 currentA. 25 AB. 15 AC. `10 A`D. 20 A |
| Answer» Correct Answer - 4 | |
| 26. |
Consider the following reactions `A underset((ii)H_(3)O^(+))overset((i)CH_(3)MgBr)to B underset(573K)overset(Cu)to 2`-methyl-2-butene the mass percentage of carbon in A is ________. |
| Answer» Correct Answer - 66.67 | |
| 27. |
White phosphorus on reaction with concentrated NaOH solution in an inert atmosphere of `CO_(2)`, gives phosphine and compound (X). (X) on acidification with HCl gives compound (Y). The basicity of compound (Y) is:A. 3B. 2C. 1D. 4 |
| Answer» Correct Answer - C | |
| 28. |
If z = `(3+isintheta)/(4-icostheta)` is purely real and `theta in (pi/2,pi)` ,then `arg(sintheta + i costheta)` is -A. `pi-tan^(-1).((3)/(4))`B. `pi-tan^(-1)((4)/(3))`C. `tan^(-1)((4)/(3))`D. `-tan^(-1)((3)/(4))` |
| Answer» Correct Answer - `B` | |
| 29. |
The equation that is incorrect is :A. `(Lambda_(m)^(0))_(H_(2)O)=(Lambda_(m)^(0))_(HCl)+(Lambda_(m)^(0))_(NaOH)-(Lambda_(m)^(0))_(NaCl)`B. `(Lambda_(m)^(0))_(KCl)-(Lambda_(m)^(0))_(NaCl)=(Lambda_(m)^(0))_(KBr)-(Lambda_(m)^(0))_(NaBr)`C. `(Lambda_(m)^(0))_(NaBr)-(Lambda_(m)^(0))_(NaCl)=(Lambda_(m)^(0))_(KBr)-(Lambda_(m)^(0))_(KCl)`D. `(Lambda_(m)^(0))_(NaBr)-(Lambda_(m)^(0))_(Nal)=(Lambda_(m)^(0))_(KBr)-(Lambda_(m)^(0))_(NaBr)` |
| Answer» Correct Answer - d | |
| 30. |
The correct order of stability for the following alkoxides is : A. `(B) gt (A) gt (C)`B. `(C) gt (A) gt (B)`C. `(C) gt (B) gt (A)`D. `(B) gt (C) gt (A)` |
| Answer» Correct Answer - c | |
| 31. |
In the following reaction sequence, structures of A and B, respectively well be : A. B. C. D. |
| Answer» Correct Answer - c | |
| 32. |
Identify (A) in the following reaction sequence : A. B. C. D. |
| Answer» Correct Answer - a | |
| 33. |
Number of common terms in both sequence 3, 7, 11,...., 407 and 2, 9, 16,....,905 is |
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Answer» Correct Answer - 14 |
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| 34. |
The major product Z obtained in the following reaction scheme is: A. B. C. D. |
| Answer» Correct Answer - c | |
| 35. |
In the following reaction sequence, the major product B is :A. B. C. D. |
| Answer» Correct Answer - a | |
| 36. |
The major product in the following reaction is : A. B. C. D. |
| Answer» Correct Answer - d | |
| 37. |
An EM wave is travelling in `(hati+hatj)/sqrt(2)` direction. Axis of polarization of EM wave is found to be `hat k` . Then equation of magnetic field will beA. `(hati+hatj)/sqrt(2) cos[omega t+k((hati+hatj)/sqrt(2))]`B. `(hati-hatj)/sqrt(2) cos[omega t-k((hati+hatj)/sqrt(2))]`C. `(hati-hatj)/sqrt(2) cos[omega t+k((hati+hatj)/sqrt(2))]`D. `hatk cos[omega t+k((hati+hatj)/sqrt(2))]` |
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Answer» Correct Answer - B |
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| 38. |
Bond order and magnetic nature of `CN^-` are respectivelyA. 3, paramagneticB. 3, diamagneticC. `2(1)/(2),` paramagneticD. `2(1)/(2),` diamagnetic |
| Answer» Correct Answer - 2 | |
| 39. |
Which of the following statements is correct ?A. Gluconic acid can form cyclic (acetal/hemiacetal ) strucutreB. Gluconic acid is a partial oxidation product of glucoseC. Gluconic acid is obtained by oxidation of glucose with `HNO_(3)`D. Gluconic acid is a dicarboxylic acid |
| Answer» Correct Answer - b | |
| 40. |
Half life of 90Sr is 6.93 years. In a child body 1g of 90Sr dopped in place of calcium, how many years will it take to reduce its concentration by 90% (Assume no involvement of Sr in metabolism) |
| Answer» Correct Answer - 23.03 years | |
| 41. |
Half life of 90Sr is 6.93 years. In a child body 1 g of 90Sr dopped in place of calcium, how many years will it take to reduce its concentration by 90% (Assume no involvement of Sr in metabolism) |
| Answer» Correct Answer - B::C | |
| 42. |
Each of solution A and B of 100 L containing 4 g NaOH and 9.8 g H2SO4. Find pH of solution which is obtain by mixing 40 L solution of A and 10 L solution of B. |
| Answer» Correct Answer - 10.60 | |
| 43. |
`"Hex-3-ynal" overset((1)NaBH_(4))to overset((2)PBr_(3))to overset((3)"Mg/Ether")to overset((4)CO_(2))to overset((5)H^(oplus))to(X)`, formed product X will be:A. B. C. D. |
| Answer» Correct Answer - A | |
| 44. |
Match the following : A. (i) -(c ), (ii) - (d) , (iii) - (a), (iv) - (b)B. (i) - (a), (ii) - (d), (iii) - (c ) , (iv) - (b)C. (i) - (d) , (ii) - (b) , (iii) - (a) , (iv) - (c )D. (i)- (c ) , (ii) - (a), (iii) - (d) , (iv) - (b) |
| Answer» Correct Answer - D | |
| 45. |
`"Hex-3-ynal" overset((1)NaBH_(4))to overset((2)PBr_(3))to overset((3)"Mg/Ether")to overset((4)CO_(2))to overset((5)H^(oplus))to(X)`, formed product X will be:A. B. C. D. |
| Answer» Correct Answer - D | |
| 46. |
Oxidation number of potassium in ` K _ 2 O`, ` K_2 O _ 2 and K O _ 2 ` , respectively, is :A. ` + 1 ,+2 and + 4 `B. ` + 1, + 1 and +1 `C. `+1,+4 and +2`D. ` + 2, + 1 and + ( 1 ) /(2) ` |
| Answer» Correct Answer - B | |
| 47. |
In zeolites & synthetic resin method which will be more efficient in removing premanent hardness of water :A. Synthetic resin method as it exchange only cationB. Zeolite resin method as it exchange only cationC. Synthetic resin method as it exchange only anion.D. Synthetic resin is harmful for nature |
| Answer» Correct Answer - A | |
| 48. |
Oxidation state of potassium in K2O, K2O2 & KO2 are respectivelyA. `+1, +1, +1`B. `+1, +2, +4`C. `+1, +2, +2`D. `+1, +4, +2` |
| Answer» Correct Answer - A | |
| 49. |
Compound X will be : A. B. C. D. |
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Answer» Correct Answer - D |
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| 50. |
The order of basic character is A. `I gt II gt III gt IV`B. `IV gt III gt I gt II`C. `II gt I gt II gt IV`D. `IV gt I gt III gt II` |
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Answer» Correct Answer - B |
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