Two infinitely large charged planes having uniform surface charge density \[+\sigma \] and \[-\sigma \] are plane along x-y plane and \[yz\] plane respectively as shown in the figure. Then the nature of electric lines of forces in x-z plane is given by :
Radius of a circular ring is changing with time and the coil is placed in uniform constant magnetic field perpendicular to its plane. The variation of \['r'\] with time \['t'\] is shown in the figure. Then induced e.m.f. \[\varepsilon \] with time will be best represented by.
Three identical capacitors are given a charge Q each and they are then allowed to discharge through resistance \[{{R}_{1}},\] \[{{R}_{2}}\] and \[{{R}_{3}}\] separately. Their charges, as a function of time are shown in the graph below. The smallest of the three resistances is:
AB is small object dipped in water at a depth of d. Its length is \[\ell .\] It is seen from air at near normal incidence. The length of the image is :
Two coherent light sources P and Q each of wavelength \[\lambda \] are separated by a distance \[3\lambda \] as shown. The maximum number of minima formed on line AB which runs from \[-\,\infty \] to \[\varphi \phi \] is:
A rod of length \[\ell \] is in motion such that its ends A and B are moving along x-axis and y-axis respectively. It is given that \[\frac{d\theta }{dt}=2\] rad/s always. P is a fixed point on the rod. Let \[M\] be the projection of \[P\] on x-axis. For the time interval in which \[\theta \] changes from 0 to \[\frac{\pi }{2}\] choose the correct statement:
A)
The acceleration of \[M\] is always directed towards right
A small uniform tube is bent into a circular tube of radius R and kept in the vertical plane. Equal volumes of two liquids of densities \[\rho \] and \[\sigma \,\,(\rho >\sigma )\] fill half of the tube as shown. \[\theta \] is the angle which the radius passing through the interface makes with the vertical:
A point mass \['m'\] and charge \['q'\]is projected with a velocity v towards a stationary charge \[{{Q}_{0}}\] from a distance of \[2\text{ }m.\] The closest distance that q can approach is: \[\left[ k=\frac{1}{4\pi {{\varepsilon }_{0}}} \right]\]
In an acid-base titration, \[0.1\text{ }M\text{ }HCl\] solution was added to the\[NaOH\] solution of unknown strength. Which of the following correctly shows the change of pH of the titration mixture in this experiment?
Identification and arrangement of organisms on the basis of their cytological characteristics.
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B)
The classification of organisms based on broad morphological characters.
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C)
Delimiting various taxa of organisms and establishing their relationships.
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D)
The classification of organisms based on their evolutionary history and establishing their phylogeny on the totality of various parameters from all fields of studies.
(il) area bounded by\[y=f(x),\text{ }y={{x}^{4}}-4{{x}^{2}},\], y - axis and line \[x=t(0\,\,\le \,\,t\,\,\le \,\,2)\] is k times the area bounded by\[y=f(x),\,\,y=2{{x}^{2}}-{{x}^{3}}\], y - axis and line \[x=t(0\le t\le 2)\], is given as
In the figure given below, the end B of the rod AB which makes angle \[\theta \] with the floor is pulled with a constant velocity \[{{v}_{0}}\] as shown. The length of rod is \[\ell .\] At an instant when \[\theta =37{}^\circ \]
A)
Velocity of end A is \[\frac{4{{v}_{0}}}{3}\]
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B)
Angular velocity of rod is \[\frac{5{{v}_{0}}}{6\ell }\]
A solid sphere of mass M and radius R is placed on a smooth horizontal surface. It is given a horizontal impulse J at a height h above the centre of mass and sphere starts rolling then, the value of h and speed of centre of mass are -
A)
\[h=\frac{2}{3}R\] and \[v=\frac{J}{M}\]
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B)
\[h=\frac{2}{5}R\] and \[v=\frac{2}{5}\frac{J}{M}\]
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C)
\[h=\frac{7}{5}R\] and \[v=\frac{7}{5}\frac{J}{M}\]
In the diagram shown, the charge +Q is fixed. Another charge +2q, is projected from a distance R from the fixed charge. Minimum separation between the two charges if the velocity becomes \[\frac{1}{\sqrt{3}}\] times of the projected velocity, at this moment is (Assume gravity to be absent) -
A container of dimension \[4m\,\,\times \,\,3m\,\,\times \,\,2m\] starts to move with uniform acceleration \[a=1.25\text{ }m/{{s}^{2}}\] at t = 0. The volume of liquid in vessel is \[18\text{ }{{m}^{3}}.\] The speed of liquid coming out from a very small orifice made at bottom of right side wall just after acceleration of container -
A researcher was investigating the substrate specificity of two different enzymes, X and Y, on the same substrate. Both the enzymes were subjected to treatment with either heat or an inhibitor which inhibits the enzyme activity. Following are the results obtained where
a=inhibitor treatment, b=heat treatment and c=control.
Which of the following statements is correct?
A)
Only protein X is specific for the substrate, S.
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B)
Only protein Y is specific for the substrate, S.
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C)
Both X and Y are specific for the substrate, S.
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D)
Both X and Y are non-specific for the substrate, S.
The \[{{C}_{4}}\] carbon cycle is a \[C{{O}_{2}}\] concentrating mechanism evolved to reduce photorespiration. The followings are stated as important features of the \[{{C}_{4}}\] pathway:
(i) The leaves of \[{{C}_{4}}\] plants have Kranz anatomy that distinguishes mesophyll and bundle sheath cells.
(ii) In the peripheral mesophyll cells, atmospheric \[{{\operatorname{CO}}_{2}}\] is fixed by phosphoenol pyruvate carboxylase yielding a four-carbon acid.
(iii) In the inner layer of mesophyll, NAD-malic enzyme decarboxylates four-carbon acid and releases\[{{\operatorname{CO}}_{2}}\].
(iv) \[{{\operatorname{CO}}_{2}}\] is again re-fixed through Calvin cycle in the bundle sheath cells.
Which one of the following combinations is correct?
Choose the correct statement from the codes given below.
(i) Separation from extracellular medium allows the cells to maintain its chemical pool, orderliness of structure and reactions in contrast to disorderly distribution and randomly interacting molecules in the extracellular medium.
(ii) Cells are unable to recognise one another due to the presence of specific chemicals on their surface.
(iii) Cells of plant tissue are often connected with one another through cytoplasmic bridges called plasmodesmata.
(iv) Different cells of an organism communicate as well as exchange materials with one another.
A sample of enzyme lactase was isolated from the intestinal lining of a calf. Assays were undertaken to evaluate the activity of enzyme sample. The substrate of lactase is the disaccharide lactose. Lactase breaks a lactose molecule in two, producing a glucose molecule and a galactose molecule.
The results of two assays are:
Assay 1
Lactose Concentration (\[%\]w/v)
15
15
15
15
15
15
Concentration of enzyme sample (\[%\]v/v)
0
5
10
15
20
25
Rate of reaction (\[\mu \] mole glucose \[{{\sec }^{-1}}\]\[{{\operatorname{ml}}^{-1}}\])
0
25
50
75
100
125
Assay 2
lactone concentration (\[%\]w/v)
0
5
15
20
25
30
Concentration of enzyme sample (\[%\]v/v)
5
5
5
5
5
5
Rate of reaction (\[\mu \]mole glucose \[{{\sec }^{-1}}\]\[{{\operatorname{ml}}^{-1}}\])
0
15
25
35
40
40
Which of the following statements can be concluded from two assays?
A)
The reaction rate of lactase assay is always proportional to the amount of enzyme present.
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B)
The amount of lactose in an assay has no effect on the rate of reaction.
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C)
The reaction rate of the lactase assay is proportional to the amount of lactose present.
doneclear
D)
The reaction rate is proportional to the amount of enzyme present at a lactose concentration of \[15%\]w/v.