JEE MAIN 9

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2016 JEE Mains Test - 9

main: Engineering Test Code: TST2002RCfI21366 Course: IITJEE 2016

tal Questions: 90 Total Time: 180 min. Maximum Marks: 360.0

ection Details:

hemistry

bjects: Chemistry

pics: Qualitative Analysis, Introduction To Organic Chemistry, Isomerism

tal Questions: 30

hysics

bjects: Physics

pics: Electrostatics

tal Questions: 30

athematics

bjects: Mathematics

pics: Mixed Topics, Differential calculus-1

tal Questions: 30

neral Instructions:This Test contains 90 questions spread across 3 Section(s).There are No Sectional Cut-Offs but the Student is expected to display his/her performance across all the sections.Section Wise time indicates the Ideal Time which should be given to a particular section. You are free to give more or less time than what is mentioned for a Section, but the Test should be Finished within the Specified time.The Test is to be given in One Single Attempt. Once the Test is Started, it can't be Paused for any Breaks.If the Test is Not completed before the Test Time, then as soon as the Time for the Test is completed, the Test would Automatically End and its Answer file would be generated.Use of Calculators and Log Tables is Not Permitted.Use of Unfair means during the Test is Strictly Prohibited.For fair Result and Performance evaluation, Please Do Not discuss the Test with your peers.Result for the Test can also be accessed on Vidyamandir Website.

Chemistryction Title: Chemistry

tal No. of Questions: 30

Subjects:Chemistry

What is the decreasing stability order of the following carbocations as per inductive effect only ?

(A). (B).

(C). (D).

Correct

Answer B

Explanation Order of stability of carbocation is 3o > 2o > 1o

(Subject: Chemistry, Topic : Introduction To Organic Chemistry).(Marks: 4.0, Negative Marks : 1.0).

Match the foll owing elements with colour their complexes/compounds produce for quantitat ive/qualitative determinat ion as per Lassaigne's test :

(A). (B).

(C). (D).

Correct

Answer D

Explanation

(Subject: Chemistry, Topic : Qualitative Analysis).(Marks: 4.0, Negative Marks : 1.0).

Select the response that correctly identif ies the number of carbon atoms of each hybridization in the compound shown.

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(A). (B).

(C). (D).

Correct

Answer A

Explanation NA


Which of the foll owing compounds is not constitutional/ structural isomer of three others?

(A). Methylcyclohexane (B). 1, 1, 2-Trimethylcyclobutane

(C). Cyclopropyl cyclobutane (D). 1-Heptene

Correct

Answer C

Explanation Cyclopropyl cyclobutane is while others have molecular formula .(Subject: Chemistry, Topic : Isomerism).

(Marks: 4.0, Negative Marks : 1.0).

Which of the following compounds is/are aromatic ?

The correct choice is :

(A). I and III (B). Only I

(C). Only III (D). III and IV

CorrectAnswer

C

Explanation Cyclic compounds having delocalized in close loop are aromatic compounds.


Which of the following resonating structure of diazomethylene , is most stable ?

(A). (B).

(C). (D).

Correct

Answer A

Explanation Structure having complete octet and negative charge on more electronegative atom is most stable.


How many optically active forms are present for the formula : ?

(A). 2 (B). 3

(C). 1 (D). 4

Correct

Answer A

Explanation two active forms & one meso form

(Subject: Chemistry, Topic : Isomerism).(Marks: 4.0, Negative Marks : 1.0).

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Which of the following show geometrical isomerism ?


(A). Only I (B). I and III

(C). I, III and IV (D). I, II and IV

Correct

Answer

D

Explanation


In which of the fol lowing compounds K Jeldahl's method can't be used :


(A). I & III (B). II & III

(C). III only (D). None of the above

Correct

Answer B

Explanation Kjeldahl's method can't be used for compounds which produce on heating such as N in ring, Nitro compounds, compounds.


0.A racemic mixture is an :

(A). Equimolar mixture of tautomers (B). Equimolar mixture of enantiomers

(C). Equimolar mixture of diastereomers (D). Equimolar mixture of cis and trans-isomers

Correct

Answer B

Explanation NA


1.Which one of the following has three hybridized carbon atoms ?

(A). Toluene (B). Xylene

(C). Mesitylene (D). None of these

Correct

Answer C

Explanation Mesitylene is 1, 3, 5-Trimethyl benzene.

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2.Which of the following is not correct for tartaric acid, HOOCCH(OH)CH(OH)COOH ?

(A). It exist in four stereoisomeric forms (B). It contains two chiral carbon atoms

(C). It has two optically active isomers (D). Its meso form is optically inactive

Correct

Answer A

ExplanationOnly three stereoisomeric forms are possible for tartaric acid : d, and meso


3.Planar cyclic compound is aromatic if it contains.

(A).A close loop of localized electrons where

(B).A close loop of delocalized electrons where

(C).A close loop of delocalized electrons where

(D). A close loop of localized electrons where

Correct

Answer C

Explanation NA


4.Arrange following species in decreasing order of stability ?


(A). Q > R > P

(B). R > P > Q

(C). R > Q > P (D). P > Q > R

CorrectAnswer

B

ExplanationFor cyclic compounds order of stability is Aromatic > Non aromatic > Anti aromatic


5.

For the estimation of nitrogen, 1.4 g organic compound was digested by Kjeldahl method and the evolved ammonia was absorbed in 60 mL of sulphuric acid.

The unreacted acid required 20 mL of sodium hydroxide for complete neutralization. The percentage of nitrogen in the compound is :

(A). 5 % (B). 6 %

(C). 10 % (D). 3 %

Correct

Answer C

Explanation


6.Which of the following statement is correct for cyclooctatetraene ?

(A). It is planar compound (B). It is non planar compound

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(C). It has delocalized electrons (D). It has delocalized electrons

CorrectAnswer

B

ExplanationCyclooctatetraene is non planar tub shape molecule


7.Which of the following is correct for intermediate species given below.

(A).X is destabilized by effect of group while Y is

stabilized by effect of group

(B).X is stabilized by +M effect of group while Y is stabilized

by +H effect of group

(C).X is destabilized by effect of group while Y is

stabilized by +H effect of group

(D). X is less stable than Y.

Correct

Answer B

ExplanationAlkyl carbocations are stabilized by hyperconjugation


8.Which of the foll owing compounds can exist in three stereoisomeric forms, two optically active and one optically inactive ?


(A). Only II (B). Only I

(C). I and II (D). I, II and III

Correct

Answer A

Explanation NA


9.Which of the following structural features is correct for intermediates methyl free radical, methyl carbocation and methyl carbanion respectively ?

(A). (B).

(C). (D).

Correct

Answer B

ExplanationFree radical is odd electron species hence it is paramagnetic. Carbon in carbocation is hybridized so it is planar but in carbanion it ishybridized with one lone pair.


0.Which of the following compounds can show tautomerism (keto-enol isomerism) ?

(A). Only II (B). I and II

(C). II and III (D). I, II and III

Correct

Answer B

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ExplanationAll enols show keto-enol i somerism while ketone and aldehyde having alpha H atom on hybridized alpha carbon atom can show keto-enolisomerism.


1.For which of the following compounds, both metamers and tautomers are possible ?

I. II. III.


(A). Only II (B). Only I

(C). I and II (D). II and III

Correct

Answer B

Explanation NA


2.How many isomeric structures are possible for organic compound having molecular formula ?

(A). 6 (B). 7

(C). 8 (D). 9

Correct

Answer D

Explanation

Compound has two degree of unsaturation so following structural formulas are possible.


3.Select the order of stability of the following carbocations :


(A). I > II > III > IV (B). III > II > I > IV

(C). IV > III > II > I (D). II > III > I > IV

Correct

Answer C

ExplanationOrder of stability of cations is explained by hyperconjugation i.e. more the -hydrogen, more the hyperconjugative structures, stable is thecarbocation. Resonance stabilized is even better.


4.In the structure of 4, 4-di isopropyl-2, 6-dimethylheptane, number of 3oH atoms are :

(A). 18 (B). 5

(C). 3 (D). 4

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CorrectAnswer

D

Explanation


5.Out of the following, the alkene(s) that exhibits both optical isomerism and geometrical isomerism is/are :

I. 4-Methylhex-2-ene II. 3-Ethylpent-1-ene III. 3-Methylpent-1-ene


(A). I and III (B). Only I

(C). II and III (D). I, II and III

Correct

Answer B

Explanation


6.In which of the following resonating structure polar contributing structure is more stable than the non-polar contributing structure.

(A). (B).

(C). (D). None of these

Correct

Answer C

ExplanationBecause of aromatic character in three membered ring of polar contributing structure.


7.Total number of stereoisomers of following compound are :

(A). 3 (B). 2

(C). 4 (D). 6

Correct

Answer C

ExplanationTwo geometric isomers two optical isomers hence total 4 stereoisomers.


8.Which of the following has same physical properties (such as boiling point) ?

(A). Constitutional isomers (B). Enantiomers

(C). Diastereomers (D). None of these

Correct

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Answer B

ExplanationEnantiomers have same physical properties expect sign of angle of optical rotation.


9.Arrange the following carbocations in the decreasing order of number of hyper-conjugative structures :

I. II. III.


(A). I > II > III (B). II > I > III

(C). III > II > I (D). I > III > II

Correct

Answer D

Explanation


0.Which one of the following has the largest dipole moment ?

(A). (B).

(C). (D).

Correct

Answer B

ExplanationSymmetrical molecules have zero dipole moment.


PhysicsSection Title: Physics

Total No. of Questions: 30

Subjects:Physics

31.

The electric field in a region is given by the vector . The maximum drop in potential will bealong :

(A). X - axis (B). Y - axis

(C). the line 4y =x (D). the line 3y = 4x

Correct

Answer C

Explanation The potential drops maximum along the resultant electric field.

(Subject: Physics, Topic : Electrostatics).(Marks: 4.0, Negative Marks : 1.0).

32. An equilateral triangle wire frame of side L having 3 point charges at its vertices is kept in x-y plane as shown.Component of electric field due to the configuration inx direction at origin is : [Origin is centroid of triangle]

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(A). (B). Zero


CorrectAnswer

B

Explanation

(Subject: Physics, Topic : Electrostatics). (Marks: 4.0, Negative Marks : 1.0).

33. The variation of electric field between the two charges q1 and q2 along the line joining the charges is plotted againstdistance from q1}

(taking rightwards direction of field as positive) as shown, then the correct statement is :

(A). q1 and q2 are positive and q1 < q2 (B). q1 and q2 are positive and q1 > q2

(C). q1 is positive and q2 is negative and q1 < q2 (D). q1 and q2 are negative and q1 < q2

Correct

Answer A

Explanation Since field between the charges is zero, so they must be of same sign. Also, the net field is zeronear q1 so its magnitude should be smaller than q2.


34.In a region of space, the electric field is in the x direction and is given as . Consider an imaginary cubicalvolume of edge a, with a its edges parallel to the axes of coordinates. The net charge inside this volume is :

(A). Zero (B).

(C). (D).

Correct

Answer A

Explanation (inside)


35. In the figure below, a point charge +Q1 is at the centre of an imaginary spherical Gaussian surface and another pointcharge +Q2 is outside of the Gaussian surface. Point P is on the surface of the sphere. Which one of the following

statements is true?

(A). Both charges contribute to the net electric fluxthrough the sphere but only charge +Q1contributes to the electric field at point P onthe sphere.

(B). Both charges contribute to the net electric fluxthrough the sphere but only charge +Q2contributes to the electric field at point P onthe sphere.

(C). Only the charges +Q1 contributes to the netelectric flux through the sphere but bothcharges +Q1 and +Q2 contribute to the

electric field at point P.

(D). Only the charges +Q2 contributes to the netelectric flux through the sphere but bothcharge contribute to the electric field at pointP.

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Correct

AnswerC

Explanation NA


36. A charge q is placed at the centroid of an equilateral triangle. Three charges equalQ are placed at the vertices of thetriangle. The system of four charges will be in equilibrium if q is equal to :

(A). (B).

(C). (D).

Correct

Answer C

Explanation

For Equation of system net force on Q = 0


37. Figure shows a circular surface and a paraboloidal surface. It is placed in a uniform electric field of m agnitude E suchthat the circular surface is oriented at right - angles to the direction of field. Electric flux through the paraboloidal

surface is :

(A). zero (B).

(C). (D).

Correct

Answer D

Explanation


38.The linear charge density on a dielectric ring of radius R is varying with .The potential at the centre of the ring is :

(A). Zero (B).

(C). (D).

Correct

Answer A

Explanation

(Subject: Physics, Topic : Electrostatics).


39. An infinite plane sheet of aluminium of areaA has total charge Q uniformly distributed over its surfaces. The electric

field hear its surface is . The same charge is spread uniformly on one surface of glass slab having same face

area. The electric field intensity near its surface is .

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(A). (B).

(C). (D). Cannot say anything

Correct

Answer A

Explanation


40.Two infinit e sheets having charge densities are placed in two perpendicular planes whose twodimensional view is shown in the figure. The charges are distributed uniformly on sheets. Four points are marked I,

II, III and IV the electric field intensities at these points are , respectively. Choose the correctoption.

(A). (B).

(C). (D). None of the above

Correct

Answer C

Explanation

Electric fields at all the points due to both the sheets are mutually perpendicular

.


41. Three concentric spherical conductorsA, B and C are arranged as shown in the figure. If they are given charges Q1,Q2, Q3 respectively, the potential at point P will be :

(A). (B).

(C). (D).

Correct

Answer B

Explanation

Point P is outside the spheresA andB and inside C. By applying principle of superposition,

potential of point P,

.


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42. Two small spheres with mass m1 and m2 hang from massless, insulating threads of length l1 and l2. The twospheres carry charges q1 and q2 respectively. The spheres hang such that they are on same horizontal level and the

threads are inclined to the vertical at angle . Which of the condition is required if :

(A). m1 =m2 (B). | q1 | = | q2|

(C). l1 = l2 (D).

Correct

Answer A

Explanation

Since both the small spheres are at same horizontal level, the electrostatic forces on both spheresare in horizontal direction. The FBD of left sphere is shown in figure.

The magnitude of electrostatic force on each spheres is same irrespective of its charge


43. Two concentric conducting thin shells of radiusR and 2R carry charges +Q, +3Q respectively.The magnitude of electric field at a distance x outside and inside from the surface of outer sphere is same. Then thevalue ofx is:

(A). (B).

(C). (D).

Correct

Answer B

Explanation

Electric field at a distancex outside from surface of outer shell =

Electric field at a distancex inside from surface of outer shell =

.


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44. A thin, metall ic spherical shell contains point charge q placed at the centre and another point charge q1 is placedoutside it as shown in figure. Both the charges are positive. The force on the central charge due to the shell is:

(A). Towards left (B). Towards right

(C). Upward (D). Zero

Correct

Answer B

ExplanationNet force on q is zero. Due to q1 it is towards left to make net force zero due to the shell it is

towards right.


45.A thin semicircular ring of radius r has a positive charge 'q' distributed uniformly over it. The net field at thecentre O is :

(A). (B).

(C). (D).

Correct

Answer

D

Explanation


46.

Let there be a spherically symmetric charge distribution with charge density varying as upto r

= R and for r >R, where r is the distance from the origin. The electric field at a distance r (r < R) fromthe origin is given by :

(A). (B).

(C). (D).

CorrectAnswer C

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Explanation


47. A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other twocorners. If the net electrical force on Q is zero, theQ/q equals :

(A). 1 (B).

(C). (D).

Correct

Answer C

Explanation


48.Electric flux through a surface of area 100 m2 lying in thexy plane is if

(A). 100 (B). 141.4

(C). 173.2 (D). 200

Correct

Answer C

Explanation

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49.The maximum magnitude of electric field due to a ring of Radius 5 m and charge per unit length of at apoint on the axis of the ring is :

(A). (B).

(C). (D).

Correct

Answer C

Explanation


50. The variation of electric field through a solid sphere of radiusRand having net charge Q is shown is :

(A). (B).

(C). (D).

Correct

Answer A

Explanation


51. A -veQ charge is placed at and a +veQ charge is placed at . A separate chargeQ is first brought

at where the force experienced by it is F1 and then brought at R (y = a) where the force experienced

by it is F2. Then F1/F2 is :

(A). (B).

(C). (D).

Correct

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Answer B

Explanation


52. A point chargeq is placed inside a conducting spherical shell of inner radius 2R and outer radius 3R at a distance ofR from the centre of the shell. The electric potential at the centre of shell will be :

(A). (B).

(C). (D).

Correct

Answer C

Explanation

Net potential at the centre is due to potential contribution from all surfaces.


53. The electric field due to a point charge at distanceR isE1 and the electric field due to a ring carrying same charge at

a distance R on the axis of ring is E2. Then, is :

(A). (B).

(C). (D).

Correct

Answer A

Explanation

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54.The potential at the centre of the solid sphere having total charge uniformly distributed over the sphere ofradius 2 units is :

(A). (B).

(C). (D).

Correct

Answer B

Explanation


55. Two solid spheres of radius 2m and 4m have charges 6C and 3C respectively. They are placed at infinite distanceand joined by a conducting wire. Finally, they attain the equal potential which is :

(A). (B).

(C). (D).

Correct

Answer D

Explanation



56. Six charges are placed at the corner of a regular hexagon as shown. If an electron is placed at its centreO, force onit will be :

(A). Zero (B). AlongOF

(C). AlongOC (D). None of these

Correct

Answer D

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Explanation


57.An infinite non-conducting sheet of charge has a surface charge density of . The separation betweentwo equipotential surfaces near the sheet whose potential differ by 5 V is:

(A). 0.88 cm (B). 0.88mm

(C). 0.88m (D).

Correct

Answer B

Explanation



58. Potential diff erence between centre & the surface of sphere of radius R and uniform volume charge densitywithin it will be :

(A). (B).

(C). 0 (D).

Correct

Answer A

Explanation


59. A charge 3 coulomb experiences a force 3000 N when placed in a uniform electric field. The potential differencebetween two points separated by a distance of 1 cm along the field lines is :

(A). 10V (B). 90V

(C). 1000 V (D). 9000 V

Correct

Answer A

Explanation


60. Two concentric conducting shells of radii R and 3R carrying charges Q and 2Q respectively. If the charge on innershell is doubled. How many times will the potential difference between inner and outer shells become?

(A). 2 (B). 4

(C). 1/2 (D). 1/4

Correct

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Answer A

Explanation

If Q1 is doubled, becomes two times.

(Subject: Physics, Topic : Electrostatics). (Marks: 4.0, Negative Marks : 1.0).

MathematicsSection Title: Mathematics

Total No. of Questions: 30

Subjects:Mathematics

61.

If , then :

(A). (B).

(C). (D).

Correct

Answer C

Explanation

(Subject: Mathematics, Topic : Differential calculus-1).(Marks: 4.0, Negative Marks : 1.0).

62.

Given the function (where a > 2). Then f (x + y) + f (x - y) =

(A). (B).


Correct

Answer A

Explanation

We get

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63.The range of the function , is :

(A). [1, 3] (B). [1, 5]

(C). [3, 5] (D). None of these

Correct

Answer B

Explanation


64.The period of the function , where [.] denotes the greatest integer function, is :

(A). 1 (B).

(C). 2 (D). None of these

Correct

Answer C

Explanation

(Subject: Mathematics, Topic : Differential calculus-1).


65.

Evaluate

(A). 1 (B). 2


Correct

Answer C

Explanation


66.

Evaluate :

(A). 1 (B). 2

(C). 3 (D). 0

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Correct

Answer

B

ExplanationPut


67.

Find the integer value of n for which is a finite nonzero number.

(A). 4 (B). 5


Correct

Answer A

Explanation


68.

The value of is equal to :

(A). e (B).


Correct

Answer C

Explanation


69.

The value of , equals :

(A). (B).

(C). (D).

Correct

Answer C

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Explanation


70.

If exists and is equal to 0, then :

(A). a = -3 and b = 9/2 (B). a = 3 and b = 9/2

(C). a = -3 and b = - 9/2 (D).

Correct

Answer A

Explanation


71.

If , where a is a finite number, then the value of a + b is :

(A). 1 (B). 2(C). 3 (D). None of these

Correct

Answer B

Explanation


72.

. Then :

(A). (B).

(C). (D).

Correct

Answer

B

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Explanation


73.Which of the following functions have finite number of points of discontinuity in R ([.] represents the greatest integerfunction) :

(A). (B).

(C). (D).

Correct

Answer C

Explanation


74.

The function is :

(A). Discontinuous at only one point (B). Discontinuous exactly at two points

(C). x discontinuous exactly at three points (D). Discontinuous exactly at four points

Correct

Answer C

Explanation

We have Clearly, there are three points of discontinuity, viz., 0, 2, .


75.

If , is continuous atx = 0, then :

(Where [.] represents the greatest integer function and {.} represents fractional part of x)

(A). f(0) = 5/2 (B).

(C). (D).

Correct

Answer D

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Explanation


76.

If is continuous atx = 0, then the value of is :

(A). 4loge2 (B). 2loge2

(C). loge2 (D). None of these

Correct

Answer C

Explanation


77.

If is continuous atx = 0, then the ordered pair (a, b) is :

(A). (B).

(C). (D).

Correct

Answer B

Explanation


78.If , then :

(A).f is derivable at

(B).f is continuous but not derivable at

(C).LHD at is 1

(D).RHD at is 1

(-1, -3) (1, 1)

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Correct

Answer A

Explanation



79.Which of the following functions is not differentiable at x = 1?

(A). (B).


Correct

Answer C

Explanation



80.

If , then is :

(A). Differentiable atx = 0 (B). Continuous but not differentiable atx = 0

(C). Discontinuous atx = 0 (D). None of these

Correct

Answer A

Explanation


81.

If , then :

(A). is discontinuous atx = 0

(B). is differentiable atx = 0

(C). is non-differentiable atx = 0, 2

(D). is continuous atx = 0

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Correct

AnswerC

Explanation


PASSAGE

Consider .(Subject: Mathematics, Topic : Differential calculus-1).

82.If is continuous atx = 1, then :

(A). (B).


CorrectAnswer

A

Explanation


83.If is continuous at , then :

(A). (B).


Correct

Answer C

Explanation


84.If is continuous at , then has :

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(A). Imaginary roots (B). Both the roots positive

(C). Both the roots negative (D). Roots of opposite signs

Correct

Answer D

Explanation


85.

. Then at is :

(A). (B).


Correct

Answer B

Explanation


86.If , then at is :

(A). - 4 (B). - 2

(C). - 6 (D). 0

Correct

Answer A

Explanation


87.

If , then is :

-2

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(A). (B).

(C). (D).

Correct

Answer A

Explanation or


88.

If and given that F(5) = 5, then F(10) is :

(A). 5 (B). 10

(C). 0 (D). 15

Correct

Answer A

Explanation


89.

If , then is :

(A). (B).


Correct

Answer A

Explanation

Differentiating both sides w.r.t.x, we get :

Again dif ferentiating w.r.t. x, we get :


90.

If , then find the value of .

(A). 4 (B). 2

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(C). 0 (D). 1

Correct

Answer C

Explanation


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