A)
\[\frac{14}{3}\]
done
clear
B)
\[\frac{56}{3}\]
done
clear
C)
\[\frac{8}{3}\]
done
clear
D)
\[\frac{32}{3}\]
done
clear
View Answer play_arrow
A)
\[3\sqrt{3}\pi \]
done
clear
B)
\[6\pi \]
done
clear
C)
\[2\sqrt{3}\pi \]
done
clear
D)
\[\frac{4}{3}\pi \]
done
clear
View Answer play_arrow
A)
\[\text{lo}{{\text{g}}_{e}}\left| \text{sec}\left( \frac{{{x}^{2}}-1}{2} \right) \right|+\text{c}\]
done
clear
B)
\[\text{lo}{{\text{g}}_{e}}\left| \frac{1}{2}\text{se}{{\text{c}}^{2}}({{x}^{2}}-1) \right|+\text{c}\]
done
clear
C)
\[\frac{1}{2}\text{lo}{{\text{g}}_{e}}\left| \text{se}{{\text{c}}^{2}}\left( \frac{{{x}^{2}}-1}{2} \right) \right|+\text{c}\]
done
clear
D)
\[\frac{1}{2}{{\log }_{e}}\left| \sec ({{x}^{2}}-1) \right|+c\]
done
clear
View Answer play_arrow
A)
512
done
clear
B)
\[-\,512\]
done
clear
C)
\[-\,256\]
done
clear
D)
256
done
clear
View Answer play_arrow
A)
\[\frac{7}{64}\]
done
clear
B)
\[\frac{13}{16}\]
done
clear
C)
\[\frac{49}{16}\]
done
clear
D)
\[\frac{1}{4}\]
done
clear
View Answer play_arrow
A)
\[2\sqrt{3}y=12x+1\]
done
clear
B)
\[2\sqrt{3}y=-x-12\]
done
clear
C)
\[\sqrt{3}y=x+3\]
done
clear
D)
\[\sqrt{3y}=3x+1\]
done
clear
View Answer play_arrow
A)
200
done
clear
B)
300
done
clear
C)
500
done
clear
D)
350
done
clear
View Answer play_arrow
A)
\[\frac{1}{\sqrt{a}}=\frac{1}{\sqrt{b}}+\frac{1}{\sqrt{c}}\]
done
clear
B)
a, b, c are in A.P
done
clear
C)
\[\sqrt{a},\sqrt{b},\sqrt{c}\] are in A.P D.
done
clear
D)
\[\frac{1}{\sqrt{b}}=\frac{1}{\sqrt{a}}=+\frac{1}{\sqrt{c}}\]
done
clear
View Answer play_arrow
A)
14
done
clear
B)
6
done
clear
C)
4
done
clear
D)
8
done
clear
View Answer play_arrow
A)
\[(4-4)\]
done
clear
B)
\[(5,2\sqrt{6})\]
done
clear
C)
(8, 6)
done
clear
D)
\[(6,4\sqrt{2})\]
done
clear
View Answer play_arrow
A)
\[(-\,3,0,-1)\]
done
clear
B)
\[(3,3,-1)\]
done
clear
C)
\[(3,2,1)\]
done
clear
D)
\[(-\,3,1,1)\]
done
clear
View Answer play_arrow
A)
4
done
clear
B)
\[\,-\,3\]
done
clear
C)
\[-\,2\]
done
clear
D)
2
done
clear
View Answer play_arrow
A)
The lines are all parallel
done
clear
B)
Each line passes through the origin.
done
clear
C)
The lines are concurrent at the point
done
clear
D)
\[\left( \frac{3}{4},\frac{1}{2} \right)\]
done
clear
View Answer play_arrow
The system of linear equations. \[x+y+z=2\] \[2x+3y+2z=5\] \[2x+3y+({{a}^{2}}-1)z=a+1\]
A)
has infinitely many solutions for \[a=4\]
done
clear
B)
is inconsistent when \[\left| a \right|=\sqrt{3}\]
done
clear
C)
is inconsistent when \[a=4\]
done
clear
D)
has a unique solution for \[\left| a \right|=\sqrt{3}\]
done
clear
View Answer play_arrow
A)
\[\frac{19}{2}\]
done
clear
B)
8
done
clear
C)
\[\frac{17}{2}\]
done
clear
D)
9
done
clear
View Answer play_arrow
A)
57
done
clear
B)
47
done
clear
C)
42
done
clear
D)
52
done
clear
View Answer play_arrow
A)
22
done
clear
B)
20
done
clear
C)
16
done
clear
D)
18
done
clear
View Answer play_arrow
A)
\[\frac{52}{169}\]
done
clear
B)
\[\frac{25}{169}\]
done
clear
C)
\[\frac{49}{169}\]
done
clear
D)
\[\frac{24}{169}\]
done
clear
View Answer play_arrow
A)
\[{{f}_{3}}(x)\]
done
clear
B)
\[{{f}_{1}}(x)\]
done
clear
C)
\[{{f}_{2}}(x)\]
done
clear
D)
\[\frac{1}{x}{{f}_{3}}(x)\]
done
clear
View Answer play_arrow
A)
\[\frac{5\pi }{6}\]
done
clear
B)
\[\frac{2\pi }{3}\]
done
clear
C)
\[\frac{3\pi }{4}\]
done
clear
D)
\[\pi \]
done
clear
View Answer play_arrow
A)
10 V
done
clear
B)
5 V
done
clear
C)
15 V
done
clear
D)
20 V
done
clear
View Answer play_arrow
A)
0
done
clear
B)
\[\sqrt{\frac{2\,\sigma qd}{m{{\in }_{0}}}}\]
done
clear
C)
\[\sqrt{\frac{\sigma qd}{m{{\in }_{0}}}}\]
done
clear
D)
none of these
done
clear
View Answer play_arrow
A)
the magnet does not rotate
done
clear
B)
the magnet rotates clockwise as seen by observer from below
done
clear
C)
the magnet rotates anti-clockwise as seen form below
done
clear
D)
none of the above.
done
clear
View Answer play_arrow
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
View Answer play_arrow
A)
P will be at higher potential than Q.
done
clear
B)
Q will be at higher potential than P.
done
clear
C)
Both P and Q will be equipotential.
done
clear
D)
no emf will be developed across rod as it is not crossing / putting any line of force.
done
clear
View Answer play_arrow
A)
\[17{{P}_{0}},\]0, \[-\,2{{R}_{0}}\]
done
clear
B)
\[3{{P}_{0}},\]0, \[-\,2{{R}_{0}}\]
done
clear
C)
\[17.5{{P}_{0}},\]0, \[-\,2{{R}_{0}}\]
done
clear
D)
\[3{{P}_{0}},\]0, \[2{{R}_{0}}\]
done
clear
View Answer play_arrow
A)
2 A
done
clear
B)
\[2\sqrt{2}\,A\]
done
clear
C)
\[0.5\,A\]
done
clear
D)
\[\sqrt{0.4}\,A\]
done
clear
View Answer play_arrow
A)
\[0.2\,\mu \,m\]
done
clear
B)
\[1.0\,\mu \,m\]
done
clear
C)
\[1.4\,\mu \,m\]
done
clear
D)
\[1.6\,\mu \,m\]
done
clear
View Answer play_arrow
A)
a proton and an \[\alpha \]-particle after getting accelerated through same potential difference will have equal penetrating power,
done
clear
B)
penetrating power of \[\alpha \]-particle will be greater than that of proton which have been accelerated by same potential difference.
done
clear
C)
proton's penetrating power will be less than penetrating power of an electron which has been accelerated by the same potential difference.
done
clear
D)
penetrating powers can not be compared as all these are particles having no wavelength or wave nature.
done
clear
View Answer play_arrow
A)
Cut-off wavelength will remain unchanged while characteristic lines will be different.
done
clear
B)
Both cut-off wavelength and characteristic lines will remain unchanged.
done
clear
C)
Both cut-off wavelength and characteristic lines will be different.
done
clear
D)
Cut-off wavelength will be different while characteristic lines will remain unchanged.
done
clear
View Answer play_arrow
A)
110 MeV
done
clear
B)
220 MeV
done
clear
C)
200 MeV
done
clear
D)
Energy is not released
done
clear
View Answer play_arrow
Two point charges \[+\,q\] and \[-\,4\,q\] are placed at \[(-\,a,\,\,0).\] and \[(+\,a,\,\,0).\] Take electric field intensity to be positive if it is along positive x-direction. The variation of the electric field intensity as one moves along the x-axis is
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
View Answer play_arrow
A)
\[\frac{C\varepsilon }{3}\]
done
clear
B)
\[\frac{C\varepsilon }{2}\]
done
clear
C)
\[\frac{C\varepsilon }{4}\]
done
clear
D)
\[C\varepsilon \]
done
clear
View Answer play_arrow
A)
\[{{A}_{1}}/{{A}_{2}}={{K}_{1}}/{{K}_{2}}\]
done
clear
B)
\[{{A}_{1}}/{{A}_{2}}={{K}_{1}}{{C}_{1}}{{\rho }_{1}}/{{K}_{2}}{{C}_{2}}{{\rho }_{2}}\]
done
clear
C)
\[{{A}_{1}}/{{A}_{2}}={{K}_{2}}{{C}_{1}}{{\rho }_{1}}/{{K}_{1}}{{C}_{2}}{{\rho }_{2}}\]
done
clear
D)
\[{{A}_{1}}/{{A}_{2}}={{K}_{2}}/{{K}_{1}}\]
done
clear
View Answer play_arrow
A)
24 N
done
clear
B)
36 N
done
clear
C)
64 N
done
clear
D)
81 N
done
clear
View Answer play_arrow
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
View Answer play_arrow
A)
\[2\vec{a}+\vec{c}=3\vec{b}\]
done
clear
B)
\[\vec{a}+3\vec{c}=2\vec{b}\]
done
clear
C)
\[3\vec{a}+\vec{c}=2\vec{b}\]
done
clear
D)
\[\vec{a}+2\vec{c}=3\vec{b}\]
done
clear
View Answer play_arrow
A)
\[10\sqrt{2}\,\,m/s\]
done
clear
B)
\[10\sqrt{3}\,\,m/s\]
done
clear
C)
20 m/s
done
clear
D)
25 m/s
done
clear
View Answer play_arrow
A)
\[\frac{5}{128}\]
done
clear
B)
10
done
clear
C)
\[\frac{5}{16}\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
Consider the following statements: \[{{S}_{1}}:\] An uncharged conductor kept near a charged body is attracted by that body whether the charge on the body is positive or negative. \[{{S}_{2}}:\] A solid conductor is placed in a uniform electric field. The electric field due to conductor will be same at every point inside the conductor. \[{{S}_{3}}:\] The electric field produced by an infinitely large sheet is same on both sides. \[{{S}_{4}}:\] Intensity of electric field decreases as you go away from the centre of a uniformly charged solid sphere (having uniform volume charge density). State, in order, whether \[{{S}_{1}},\]\[{{S}_{2}},\]\[{{S}_{3}},\]\[{{S}_{4}}\] are true or false
A)
F T F T
done
clear
B)
T F T F
done
clear
C)
F F T F
done
clear
D)
T T F F
done
clear
View Answer play_arrow
A)
\[I_{3}^{+}\] has bent structure
done
clear
B)
\[Xe{{F}_{2}}\] and \[C{{O}_{2}}\] has same shape
done
clear
C)
\[S{{F}_{4}}\] is sea-saw structure whereas \[IC{{l}_{3}}\] is T-shaped
done
clear
D)
All of these
done
clear
View Answer play_arrow
A)
D-glucose units joined by \[\alpha \]-glycosidic linkage
done
clear
B)
D-glucose units joined by \[\beta \]-glycosidic linkage
done
clear
C)
D-galactose units joined by \[\alpha \]-glycosidic linkage
done
clear
D)
D-galactose units joined by \[\beta \]-glycosidic linkage
done
clear
View Answer play_arrow
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
View Answer play_arrow
A)
p-chloro phenol is more acidic than p-flouro phenol
done
clear
B)
\[-\overset{\oplus }{\mathop{N}}\,M{{e}_{3}}\] is stronger -I group than \[-\overset{\oplus }{\mathop{N}}\,{{H}_{3}}\]
done
clear
C)
Acidity order: o-nitrobenzoic acid > p-nitrobenzoic acid > m-nitrobenzoic acid
done
clear
D)
Acidity order:\[{{H}_{3}}C-COOH<{{H}_{3}}Si-\overset{O}{\mathop{\overset{\parallel }{\mathop{C}}\,}}\,-OH\]
done
clear
View Answer play_arrow
A)
\[X\,\,is\,\,C{{H}_{3}}-C\equiv C-H\]
done
clear
B)
\[Y\,\,is\,\,C{{H}_{3}}-\underset{\underset{O}{\mathop{\parallel }}\,}{\mathop{C}}\,-{{C}_{2}}{{H}_{5}}\]
done
clear
C)
\[Z\,\,is\,\,C{{H}_{3}}-\underset{{}}{\mathop{\overset{\overset{O}{\mathop{\parallel }}\,}{\mathop{C}}\,}}\,-C{{H}_{3}}\]
done
clear
D)
\[Y\,\,is\,\,C{{H}_{3}}-C{{H}_{2}}-CHO\]
done
clear
View Answer play_arrow
A)
5 : 1
done
clear
B)
25 : 4
done
clear
C)
20 : 1
done
clear
D)
8 : 4
done
clear
View Answer play_arrow
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
View Answer play_arrow
A)
91
done
clear
B)
92
done
clear
C)
93
done
clear
D)
94
done
clear
View Answer play_arrow
A)
\[[PtC{{l}_{2}}{{(N{{H}_{3}})}_{2}}]\]
done
clear
B)
\[{{[CoC{{l}_{2}}{{(N{{H}_{3}})}_{4}}]}^{+}}\]
done
clear
C)
\[[Co{{(N{{O}_{2}})}_{3}}{{(N{{H}_{3}})}_{3}}]\]
done
clear
D)
\[{{[Co{{(en)}_{3}}]}^{3+}}\]
done
clear
View Answer play_arrow
A)
\[\frac{1}{n-1}\left( \frac{{{2}^{n-1}}-2}{{{a}^{n-1}}} \right)\frac{1}{k}\]
done
clear
B)
\[\frac{1}{n-1}\left( \frac{{{2}^{n-2}}-2}{{{a}^{n-1}}} \right)\frac{1}{k}\]
done
clear
C)
\[\frac{1}{n-1}\left( \frac{{{2}^{2n-2}}-1}{{{a}^{n-1}}} \right)\frac{1}{k}\]
done
clear
D)
\[\frac{1}{n-2}\left( \frac{{{2}^{2n-2}}-1}{{{a}^{2n-1}}} \right)\frac{1}{k}\]
done
clear
View Answer play_arrow
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
View Answer play_arrow
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
View Answer play_arrow
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
View Answer play_arrow
A)
done
clear
B)
\[Me-\overset{\overset{O}{\mathop{\parallel }}\,}{\mathop{C}}\,-\overset{\overset{O}{\mathop{\parallel }}\,}{\mathop{C}}\,-Ph\]
done
clear
C)
\[Me-\overset{\overset{OH}{\mathop{|}}\,}{\mathop{\underset{\underset{Ph}{\mathop{|}}\,}{\mathop{C}}\,}}\,-COOH\]
done
clear
D)
\[Ph-\overset{\overset{O}{\mathop{\parallel }}\,}{\mathop{C}}\,-\overset{\overset{O}{\mathop{\parallel }}\,}{\mathop{C}}\,-O-Me\]
done
clear
View Answer play_arrow
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
View Answer play_arrow
A)
A > B > C > D
done
clear
B)
C > B > D > A
done
clear
C)
D > C > A > B
done
clear
D)
D > C > B > A
done
clear
View Answer play_arrow
An aromatic compound \[A({{C}_{8}}{{H}_{10}}O)\] gives following tests with the given reagents. Identify 'A'
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
View Answer play_arrow
A)
\[0.142\text{ }c{{m}^{-1}}\]
done
clear
B)
\[0.918\text{ }c{{m}^{-1}}\]
done
clear
C)
\[1.12\text{ }c{{m}^{-1}}\]
done
clear
D)
\[0.616\text{ }c{{m}^{-1}}\]
done
clear
View Answer play_arrow
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
View Answer play_arrow
What is correct for stability order- of isomers (I) Cyclohexan 1, 3 diol aa > ee conformer conformer (II) Cylco octene cis > trans isomer Isomers (III) 1, 2 dimethyl cyclobutane trans > cis isomer Isomer (IV) Ethan-1, 2 diol anti form > gauch form (V) Methyl cyclohexan Axial conformer > equatorial conformer
A)
I, III, IV, V only
done
clear
B)
I, II, III only
done
clear
C)
I, III, IV only
done
clear
D)
All are correct
done
clear
View Answer play_arrow
A)
Chemiosmosis
done
clear
B)
phosphorylation
done
clear
C)
Fermentation
done
clear
D)
glycolysis
done
clear
View Answer play_arrow
A)
About 25 bp upstream of the transcription start site.
done
clear
B)
About 50 bp upstream of the transcription start site.
done
clear
C)
About 75 bp upstream of the transcription start site.
done
clear
D)
About 200 bp upstream of the transcription start site.
done
clear
View Answer play_arrow
A)
Shortest fragments of DNA.
done
clear
B)
Longest fragments of DNA.
done
clear
C)
Restriction enzyme used to cut the DNA into fragments.
done
clear
D)
Ligase used to bind the DNA fragments together.
done
clear
View Answer play_arrow
A)
Kinetic energy (K.E.) of \[{{H}_{2}}O\] in A solution > K.E. of water in B solution
done
clear
B)
K.E. of water in B solution >K.E. of water in A solution
done
clear
C)
K.E. of water in A solution \[=K.E.\,of\,{{H}_{2}}O\] in b solution
done
clear
D)
Water potential has nothing to do with K.E
done
clear
View Answer play_arrow
Which of the following events is involve in the transfer of information across a chemical synapse? [A] Neurotransmitters bind to the postsynaptic receptors. [B] Calcium channels open in the presynaptic [C] Ion channels open in the postsynaptic membrane. [D] Direct flow of ions from one neuron to the next.
A)
[A] and [B] only
done
clear
B)
[A], [B] and [C] only
done
clear
C)
[B], [C] and [D] only
done
clear
D)
All of these
done
clear
View Answer play_arrow
A)
Bud and shoot formation; rapid cell expansion; increased cell division.
done
clear
B)
Bud and shoot formation; slow cell expansion; increased cell division
done
clear
C)
Bud and shoot formation; rapid cell expansion; increased cell division.
done
clear
D)
Root formation; rapid cell expansion; decreased cell division.
done
clear
View Answer play_arrow
A)
11
done
clear
B)
33
done
clear
C)
333
done
clear
D)
1
done
clear
View Answer play_arrow
Which of the following statement (s) is /are incorrect? [A] light is essential for life to exist on the earth. [B] Many species of small plant under the canopy of tall trees in forest show optimal use of available light due to having large sized antenna and higher number of thylakoids. [C] UV-rays is not harmful for many organisms. [D] Photoperiodic requirement is not essential for many plants for flowering. [E] Red algae can live in deeper water of sea because of having pigments, phycoerythrin.
A)
Only [A]
done
clear
B)
Only [B]
done
clear
C)
Only [C]
done
clear
D)
[D] and [E]
done
clear
View Answer play_arrow
A)
Use and disuse of organs
done
clear
B)
Adaptation to living in burrows
done
clear
C)
Natural selection
done
clear
D)
Inheritance of acquired characters
done
clear
View Answer play_arrow
A)
Target tissue 1 had fewer hormone receptors
done
clear
B)
Target tissue 2 and 3 had hormone receptors with a higher hormone affinity than 1.
done
clear
C)
Target tissue 1 had hormone affinity than 2 and 3.
done
clear
D)
The hormone was released only in the vicinity of target tissue 1.
done
clear
View Answer play_arrow
A)
Are active forms of antigen
done
clear
B)
Are the least active forms.
done
clear
C)
Contain antibodies formed for coat proteins only.
done
clear
D)
Contain antibodies against whole antigen.
done
clear
View Answer play_arrow
A)
Linear chain of alternating NAG and Nam linked by \[\alpha (1-4)\] linkage.
done
clear
B)
Linear chains of alternating NAG and NAM linked by \[\beta (1-4)\] linkage.
done
clear
C)
Linear chain of glucose linked by \[\beta (1-4)\] linkage.
done
clear
D)
Linear chain of glucose linked by \[\alpha (1-4)\] linkage
done
clear
View Answer play_arrow
A)
Pyramid of number in a forest
done
clear
B)
Pyramid of biomass in a follow land
done
clear
C)
Pyramid of biomass in a lake
done
clear
D)
Energy pyramid in a lake
done
clear
View Answer play_arrow
A)
3
done
clear
B)
51
done
clear
C)
17
done
clear
D)
20
done
clear
View Answer play_arrow
A)
It can occur in both somatic and sex cells.
done
clear
B)
It can cause down?s syndrome in humans.
done
clear
C)
It can change a dominant allele into a recessive one.
done
clear
D)
It can be brought about by exposure to ionizing radiation.
done
clear
View Answer play_arrow
A)
3
done
clear
B)
2
done
clear
C)
4
done
clear
D)
1
done
clear
View Answer play_arrow
A)
Period with clear cut observable symptoms.
done
clear
B)
stage, which has highest % of antibodies blood
done
clear
C)
period in which infected person is tested negative when subjected to antibody blood test.
done
clear
D)
Stage when the person is not infected identify the correct statements.
done
clear
View Answer play_arrow
Identify the correct statement. [A] The first recombinant DNA was constructed by using a piece of DNA from a plasmid carrying antibiotic resistance gene in the bacterium Salmo \[typhimurium\] and linked it to the plasmid of E.coli. [B] Cohen and Boyer are known as Father of genetic engineering. [C] When cut by the same restriction enzyme, the resultant DNA fragments have the same kind of sticky ends and these can be joined together using DNA ligase. [D] Endonucleases remove nucleotides from the ends of the DNA whereas exonucleases make cuts at specific positions within the DNA. [E] Presence of more than one recognition sites within the vector will generate several fragments which will complicate the gene cloning. [F] Humulin was the first recombinant DNA based product, produced and marketed [G] YAC vectors contain the telomeric sequence, the centromere and autonomously replicating sequence yeast chromosomes. [H] Alkaline phosphatase is used to prevent unwanted self-ligation of the vector DNA molecules in procedures of DNA technology [I] \[pBR322\] vector was the first artificial ideal vector constructed by Bolivar and Rodriguez [J] Plasmid DNA is coated with histone proteins and can act as genetic factor.
A)
[B], [D], [F] and [J]
done
clear
B)
[B], [D], [E] and [J]
done
clear
C)
[A], [C], [F], [G], [H] and [I]
done
clear
D)
[A], [B], [D], [F] and [J]
done
clear
View Answer play_arrow
A)
Muscles in the back of the lower leg are contracting but that in the front are relaxing.
done
clear
B)
Muscles in the front of the lower leg are contracting but that in the back are relaxing.
done
clear
C)
Muscles in the back of the thigh are contracting but that in the front are relaxing.
done
clear
D)
Muscles in the front of the thigh are contracting but that in the back are relaxing.
done
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View Answer play_arrow
A)
Estrogen
done
clear
B)
Progesterone
done
clear
C)
Luteinising hormone
done
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D)
Follicular stimulating hormone
done
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View Answer play_arrow
A)
\[-\,3\,\,\le \,\,m\,\,<-1\]
done
clear
B)
\[6\,\,\le \,\,m\,\,<\,\,8\]
done
clear
C)
\[4\,\,\le \,\,m\,\,<\,\,6\]
done
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D)
\[2\,\,\le \,\,m\,\,<\,\,4\]
done
clear
View Answer play_arrow
Let \[\,M\,=\,\left[ \begin{matrix} {{\sin }^{4}}\theta & -1-{{\sin }^{2}}\theta \\ 1+{{\cos }^{2}}\theta & {{\cos }^{4}}\theta \\ \end{matrix} \right]=\alpha I+\beta {{M}^{-1}}\] where \[\alpha \,=\alpha \,(\theta )\] and \[\beta =\,\beta \,(\theta )\] are real numbers, and I is the \[2\times 2\]identity matrix. If \[{{\alpha }^{*}}\] is the minimum of set and \[\{a\,(\theta ):\theta \in [0,2\pi )\}\]\[\beta *\] is the minimum of the set \[\{\beta \,(\theta ):\,\theta \,\in [0,2\pi )\}\] then the value of \[\alpha *+\beta *\]
A)
\[\frac{-\,29}{16}\]
done
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B)
\[-\,\frac{37}{16}\]
done
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C)
\[\,-\,\frac{17}{16}\]
done
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D)
\[-\,\frac{31}{16}\]
done
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View Answer play_arrow
Let S be the set of all complex numbers z satisfying \[\left| z\,-\,2+i \right|\,\le \,\sqrt{5}.\] If the complex number \[{{z}_{0}}\] is such that \[\frac{1}{\left| {{z}_{0}}\,-\,1 \right|}\] is the maximum of the set \[\left\{ \frac{1}{\left| z-1 \right|}:z\,\in \,\text{S} \right\},\] then the principal argument of \[\frac{4\,\,-\,\,{{z}_{0}}-\,\bar{z}}{{{z}_{0}}\,-\,{{{\bar{z}}}_{0}}+2i}\] is:
A)
\[\frac{\pi }{2}\]
done
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B)
\[\frac{3\pi }{4}\]
done
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C)
\[\frac{\pi }{4}\]
done
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D)
\[-\,\frac{\pi }{2}\]
done
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View Answer play_arrow
The area of region \[(x,y):\,\]\[xy\,\le \,8,\]\[\,1\,\le \,y\,\le \,{{x}^{2}}\] is:
A)
\[16\,\,\text{lo}{{\text{g}}_{e}}\,2\,\,-\,\frac{14}{3}\]
done
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B)
\[\text{lo}{{\text{g}}_{e}}\,2\,\,-\,\frac{7}{3}\]
done
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C)
\[8\,\,\text{lo}{{\text{g}}_{e}}\,2\,-\,\frac{14}{3}\]
done
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D)
\[8\,\,\text{lo}{{\text{g}}_{e}}\,2\,-\,6\]
done
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View Answer play_arrow
A)
\[xy'-\,\sqrt{1-{{x}^{2}}}=\,0\]
done
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B)
\[y\,=\,-\,\text{lo}{{\text{g}}_{e}}\,\left( \frac{1+\sqrt{1-{{x}^{2}}}}{x} \right)+\,\sqrt{1-{{x}^{2}}}\]
done
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C)
\[xy'+\sqrt{1-{{x}^{2}}}=\,0\]
done
clear
D)
\[y\,=\,\text{lo}{{\text{g}}_{e}}\,\left( \frac{1+\sqrt{1\,\,-\,{{x}^{2}}}}{x} \right)-\,\sqrt{1-{{x}^{2}}}\]
done
clear
View Answer play_arrow
Define the collections \[\{{{\text{E}}_{1}},{{\text{E}}_{2}},\,{{\text{E}}_{3}},\,....\}\]of ellipse and \[\{{{\text{R}}_{1}},\,{{\text{R}}_{2}},\,{{\text{R}}_{3}},\,.....\}\]of rectangles as follows:
\[{{\text{E}}_{1}}\,:\,\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}\,=\,1\]
\[{{\text{R}}_{1}}\,:\] rectangle of largest area, with sides parallel to the axes, inscribed in \[{{\text{E}}_{1}};\]
\[{{E}_{n}}\ :\]ellipse \[\frac{{{x}^{2}}}{a_{n}^{2}}+\frac{{{y}^{2}}}{b_{n}^{2}}=\,1\]of largest area inscribed in
\[{{\text{R}}_{n-1}},\,n\,>\,1\,;\]
\[{{\text{R}}_{n}}\,:\] rectangle of largest area, with sides parallel to the axes inscribed in \[{{\text{E}}_{n}},\,n\,>\,1\]
Then which of the following options is/are correct?
A)
The eccentricities of \[{{\text{E}}_{18}}\] and \[{{\text{E}}_{19}}\] are not equal
done
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B)
The distance of a focus from the centre in \[{{\text{E}}_{9}}\] is \[\frac{\sqrt{5}}{32}\]
done
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C)
\[\sum\limits_{n\,=\,1}^{\text{N}}{{}}\]\[(area\,of\,{{\text{R}}_{n}})\,<24,\] for each positive integer N
done
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D)
The length of latus rectum of \[{{\text{E}}_{9}}\] is \[\frac{1}{6}\]
done
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View Answer play_arrow
\[\text{Let}\,\,\text{M}\,=\,\left[ \begin{matrix} 0 & 1 & a \\ 1 & 2 & 3 \\ 3 & b & 1 \\ \end{matrix} \right]\,\,\text{and}\,\,\,\text{adj}\,\,\text{M}\,=\,\left[ \begin{matrix} -1 & 1 & -1 \\ 8 & -6 & 2 \\ -5 & 3 & -1 \\ \end{matrix} \right]\] Where a and b are real numbers. Which of the following .options is/are correct?
A)
\[\text{det}\,(adj\,\,{{\text{M}}^{2}})\,=\,81\]
done
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B)
\[a+b=3\]
done
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C)
\[(adj\,{{\text{M}}^{-1}})\,+\,adj\,\,{{\text{M}}^{-1}}=\,-\text{M}\]
done
clear
D)
\[\text{M}\left[ \begin{matrix} \alpha \\ \beta \\ \gamma \\ \end{matrix} \right]\,=\,\left[ \begin{matrix} 1 \\ 2 \\ 3 \\ \end{matrix} \right]\,,\,\text{the}\,\,\alpha \,-\,\beta +\,\gamma \,=\,3\]
done
clear
View Answer play_arrow
Let \[\alpha \] and \[\beta \] be the roots of \[{{x}^{2}}-x-1=0,\] with \[\alpha \,>\,\beta .\] For all positive integer n, define \[{{a}_{n}}\,=\,\frac{{{\alpha }^{n}}\,-\,{{\beta }^{n}}}{\alpha \,-\,\beta },\,n\ge \,1\], \[{{b}_{1}}\,=\,1\] and \[{{b}_{n}}\,=\,{{a}_{n-1}}\,+\,{{a}_{n}}+{{1}^{,\,}}\,n\,\,\le \,2\]. Then which of the following options is/are correct?
A)
\[{{a}_{1}}+{{a}_{2}}+{{a}_{3}}+{{a}_{n}}={{a}_{n+2}}-\,1\] for all \[n\,\,\ge \,\,1\]
done
clear
B)
\[{{b}_{n}}={{a}^{n}}+{{\beta }^{n}}\] for all \[n\,\ge \,1\]
done
clear
C)
\[\sum\limits_{n\,=\,1}^{\infty }{\frac{{{b}_{n}}}{{{10}^{n}}}\,=\,\frac{8}{89}}\]
done
clear
D)
\[\sum\limits_{n\,=\,1}^{\infty }{\frac{{{a}_{n}}}{{{10}^{n}}}\,=\,\frac{10}{89}}\]
done
clear
View Answer play_arrow
Let f : R\[\to \]R be given by:
\[f\,(x)\left\{ \begin{matrix} {{x}^{5}}+5{{x}^{4}}+10{{x}^{3}}+3x+1 & x\,<\,0 \\ {{x}^{2}}-x+1, & 0\,\,\le \,x\,<\,1; \\ \frac{2}{3}{{x}^{3}}-4{{x}^{2}}+7x-\frac{8}{3}, & 1\,\le \,x\,<\,3 \\ (x\,-\,2)\,{{\log }_{e\,}}\,(x-2)\,-\,x+\frac{10}{3}, & x\,\,\ge \,3 \\ \end{matrix} \right.\]
Then which of the following options is/are correct?
A)
\[f\] is increasing on \[(-\,\infty ,0)\]
done
clear
B)
\[f\] is onto
done
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C)
\[f\] has a local maximum at \[x=1\]
done
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D)
\[f\] is not differentiable at \[x=1\]
done
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View Answer play_arrow
A)
Probability that the chosen ball is green, given that the selected bag is \[{{\text{B}}_{\text{3}}}\] equals \[\frac{3}{8}\]
done
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B)
Probability that the selected bag is \[{{\text{B}}_{\text{3}}}\] and the chosen ball is green equals \[\frac{3}{10}\]
done
clear
C)
Probability that the selected bag is \[{{\text{B}}_{\text{3}}}\] and the chosen ball is green equals \[\frac{5}{13}\]
done
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D)
Probability that the chosen ball is green equals \[\frac{39}{80}\]
done
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View Answer play_arrow
A)
\[\frac{mg}{k}\]
done
clear
B)
\[\frac{2mg}{k}\]
done
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C)
\[\frac{3mg}{k}\]
done
clear
D)
\[\frac{4mg}{k}\]
done
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View Answer play_arrow
A)
zero
done
clear
B)
\[\frac{Qqd}{2\pi {{\in }_{0}}{{\ell }^{3}}}\]
done
clear
C)
\[\frac{Qqd}{\pi {{\in }_{0}}{{\ell }^{3}}}\]
done
clear
D)
\[\frac{Qqd}{4\pi {{\in }_{0}}{{\ell }^{3}}}\]
done
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View Answer play_arrow
A)
\[\left( \frac{{{v}_{0}}}{2{{B}_{0}}\alpha },\,\,\frac{\sqrt{2}{{v}_{0}}}{\alpha {{B}_{0}}},\,\,\frac{-{{v}_{0}}}{{{B}_{0}}\alpha } \right)\]
done
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B)
\[\left( -\frac{{{v}_{0}}}{2{{B}_{0}}\alpha },\,\,0,\,\,0 \right)\]
done
clear
C)
\[\left( 0,\,\,\frac{2{{v}_{0}}}{{{B}_{0}}\alpha },\,\,\frac{{{v}_{0}}\pi }{2{{B}_{0}}\alpha } \right)\]
done
clear
D)
\[\left( \frac{{{v}_{0}}\pi }{{{B}_{0}}\alpha },\,\,0,\,\,\frac{-\,2{{v}_{0}}}{{{B}_{0}}\alpha } \right)\]
done
clear
View Answer play_arrow
A)
\[\frac{L{{E}^{2}}}{2{{R}_{2}}^{2}}\]
done
clear
B)
\[\frac{L{{E}^{2}}}{2{{R}_{1}}^{2}}\]
done
clear
C)
\[\frac{L{{E}^{2}}}{2{{R}_{1}}{{R}_{2}}}\]
done
clear
D)
\[\frac{L{{E}^{2}}\,{{({{R}_{1}}+{{R}_{2}})}^{2}}}{2{{R}_{1}}^{2}{{R}_{2}}^{2}}\]
done
clear
View Answer play_arrow
Current in an ac circuit is given by \[i=3\,\,\sin \,\,\omega \,\,t+4\,\,\cos \,\,\omega \,\,t\] then:
A)
rms value of current is 5 A.
done
clear
B)
mean value of this current in one half period will be \[6/\pi .\]
done
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C)
if voltage applied is \[V={{V}_{m}}\sin \,\,\omega \,t\] at then the circuit must be containing resistance and capacitance.
done
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D)
if voltage applied is \[V={{V}_{m}}\sin \,\,\omega \,t,\] the circuit may contain only resistance and inductance.
done
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View Answer play_arrow
A)
\[\frac{IAe}{h\nu }\]
done
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B)
\[\frac{IAe}{2h\nu }\]
done
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C)
\[\frac{2IAe}{h\nu }\]
done
clear
D)
none of these
done
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View Answer play_arrow
A)
first increases then decreases
done
clear
B)
continuously decreases
done
clear
C)
continuously increases
done
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D)
first decreases then increases.
done
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View Answer play_arrow
A)
\[\theta \le 37{}^\circ \]
done
clear
B)
\[\theta <37{}^\circ \]
done
clear
C)
\[\theta \le 53{}^\circ \]
done
clear
D)
\[\theta <53{}^\circ \]
done
clear
View Answer play_arrow
A)
\[a+b=2\sqrt{c}\]
done
clear
B)
\[abc=1\]
done
clear
C)
\[{{a}^{2}}=c\]
done
clear
D)
\[a{{b}^{2}}=c\]
done
clear
View Answer play_arrow
A)
5 V
done
clear
B)
10 V
done
clear
C)
25 V
done
clear
D)
70 V
done
clear
View Answer play_arrow
The decomposition \[N{{H}_{3}}\] gas on a heated tungsten surface gave the following results:
Initial pressure (m m)
65
105
y
185
HIf-life (sec)
290
x
670
820
Calculate approximately the values of x and y.
A)
\[x=410\,\,\sec \]
done
clear
B)
\[x=467\text{ }sec\]
done
clear
C)
\[x=490\text{ }sec\]
done
clear
D)
\[x=430\text{ }sec\]
done
clear
View Answer play_arrow
A)
3.37
done
clear
B)
5.26
done
clear
C)
2.56
done
clear
D)
4.62
done
clear
View Answer play_arrow
A)
\[{{[Zn{{(N{{H}_{3}})}_{6}}]}^{2+}}\]
done
clear
B)
\[{{[\,Ni\,{{(N{{H}_{3}})}_{6}}]}^{2+}}\]
done
clear
C)
\[{{[Cr{{(N{{H}_{3}})}_{6}}]}^{3+}}\]
done
clear
D)
\[{{[Co\,{{(N{{H}_{3}})}_{6}}]}^{3+}}\]
done
clear
View Answer play_arrow
A)
290 K
done
clear
B)
285.5 K
done
clear
C)
267.42 K
done
clear
D)
250 K
done
clear
View Answer play_arrow
Consider the following reactions at 300 K.
A\[\to \]B (uncatalysed reaction)
A\[\xrightarrow{catalyst}\]B (catalyst reaction)
The activation energy is lowered by \[8.314\text{ }kJ\text{ }mo{{l}^{-1}}\] for the catalysed reaction. How many times the rate of this catalysed reaction greater than that of uncatalysed reaction? \[(Given\,\,{{e}^{3.33}}=28)\]
A)
15 times
done
clear
B)
38 times
done
clear
C)
22 times
done
clear
D)
28 times
done
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View Answer play_arrow
\[C{{u}^{+}}+{{e}^{-}}\to Cu,E{}^\circ ={{x}_{1}}\] volt;
\[C{{u}^{2+}}+2{{e}^{-}}\to Cu,\] \[E{}^\circ ={{x}_{2}}\] volt, then for
\[C{{u}^{2+}}+{{e}^{-}}\to C{{u}^{+}},\] \[E{}^\circ \](volt) will be -
A)
\[{{x}_{1}}-2{{x}_{2}}\]
done
clear
B)
\[{{x}_{1}}+2{{x}_{2}}\]
done
clear
C)
\[{{x}_{1}}-{{x}_{2}}\]
done
clear
D)
\[2{{x}_{2}}-{{x}_{1}}\]
done
clear
View Answer play_arrow
A)
1-A, 2-C, 3-D, 4-B
done
clear
B)
1-C, 2-A, 3-B, 4-D
done
clear
C)
1-A, 2-C, 3-B, 4-D
done
clear
D)
1-A, 2-B, 3-C, 4-D
done
clear
View Answer play_arrow
A)
Both the compounds form same product on treatment with alcoholic KOH.
done
clear
B)
Both the compounds form same production treatment with aq. NaOH
done
clear
C)
Both the compounds form different product on reduction.
done
clear
D)
Both the compounds are optically active.
done
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View Answer play_arrow
A)
Identical
done
clear
B)
Positional isomers
done
clear
C)
Functional isomers
done
clear
D)
Optical isomers
done
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View Answer play_arrow
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
View Answer play_arrow
A)
\[50\times 1{{0}^{6}} m{{m}^{2}}\]
done
clear
B)
\[200\times 1{{0}^{6}}m{{m}^{2}}\]
done
clear
C)
\[100 \times 1{{0}^{6}}m{{m}^{2}}\]
done
clear
D)
\[1000 \times 1{{0}^{6}}m{{m}^{2}}\]
done
clear
View Answer play_arrow
Given below are some characters of a cell organelle.
(I) It is a membrane bound space found in the Cytoplasm.
(II) It is bound by a single membrane called tonoplast.
(III) It contains water, excretory products and other materials not useful to the cell.
(IV) It has higher concentration of sap than the Cytoplasm.
Identify the correct organelle which shows all the characters described above.
A)
Golgi apparatus
done
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B)
Lysosomes
done
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C)
Endoplasmic reticulum
done
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D)
Vacuoles
done
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View Answer play_arrow
A)
mRNA degradation
done
clear
B)
Alternate splicing
done
clear
C)
Gene amplification
done
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D)
Nonsense mutation
done
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View Answer play_arrow
A)
A-\[Trichoderma\text{ }polysporum\], B-Organ transplants, C-Yeast (fungus), D-lowering of blood cholesterol
done
clear
B)
A-lowering of blood cholesterol, B-\[Trichoderma\text{ p}olysporum\], C- organ transplant patients, D-Yeast (Fungus),
done
clear
C)
A-Yeast (Fungus), B-Lowering of blood cholesterol, C-\[Trichoderma\text{ }Polysporum\], D-organ transplant patients
done
clear
D)
A-organ transplant patients, B-Yeast (fungus), C-lowering of blood cholesterol, D-\[Trichoderma\text{ }Polysporum,\]
done
clear
View Answer play_arrow
Minisatellites are used as marker for identifying Individuals via DNA fingerprinting as the alleles May differ in the number of repeats. From the Southern blot shown below identify the progeny (A, B, C and D) for the given parents
\[\left( M=\text{ }mother,\text{ }F=\text{ }father \right).\]
A)
A, B, C and D
done
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B)
A, B and D
done
clear
C)
A and D only
done
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D)
B, C and D
done
clear
View Answer play_arrow
A)
Increased
done
clear
B)
Decreased
done
clear
C)
Remained the same
done
clear
D)
Been uncertain
done
clear
View Answer play_arrow
A)
\[{{\operatorname{Na}}^{+}}\,and\,\,{{K}^{+}}\] Will increase outside the cell.
done
clear
B)
\[{{\operatorname{Na}}^{+}}\]Outside the nerve will increase.
done
clear
C)
\[{{\operatorname{Na}}^{+}}\]Inside the nerve will increase.
done
clear
D)
\[{{\operatorname{K}}^{+}}\]Inside the nerve will increase.
done
clear
View Answer play_arrow
Dividing chromosomes can be labelled with a thymine analogue, bromodeoxy - uridine. After differential staining, the chromosomes can be seen as darkly stained (old) strands and lightly stained (new) strands. The following chromosomes were observed and photographed while studying division of human blood cells. From the picture, which of the following can be deduced? [A] The chromosomes belong to metaphase stage. [B] The cell division was taking place in mature red blood cells. [C] Parts of the chromatids were exchanged by crossing over. [D] The different colours of the two sister chromatids confirm that DNA replication is semi-conservative.
A)
[A], [B] and [D]
done
clear
B)
[B] and [D]
done
clear
C)
[A] and [D]
done
clear
D)
[A], [B] and [C]
done
clear
View Answer play_arrow
A)
12, 48
done
clear
B)
48, 12
done
clear
C)
24, 12
done
clear
D)
24, 96
done
clear
View Answer play_arrow
A)
Egg production only.
done
clear
B)
Sperm production only.
done
clear
C)
Either egg or sperm production.
done
clear
D)
Both egg and sperm production.
done
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View Answer play_arrow