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The \( 4^{t h} \) and \( 10^{t h} \) terms of an AP are 13 and 25 respectively. Find the first term and the common difference of the AP. Also, find its \( 17^{t h} \) term.
2
Maths
The slope and y-intercept of the following line are respectively \( 4 x-y=0 \) A. slope \( =m=4 \) and \( y- \) intercept \( =0 \) B. slope \( =m=-4 \quad \) and \( \quad y- \) intercept \( =0 \) C \( . \) slope \( =m=1 / 4 \) and \( y- \) intercept \( =0 \) D. slope \( =m=0 \) and \( y- \) intercept \( =1 / 4 \)
2
Maths
If \( \boldsymbol{y}=\tan ^{-1}\left(\frac{1+\boldsymbol{x}^{2}}{1-\boldsymbol{x}^{2}}\right) \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=? \) A. \( \frac{2 x}{\left(1+x^{4}\right)} \) B. \( \frac{-2}{\left(1+x^{4}\right)} \) c. \( \frac{x}{\left(1+x^{4}\right)} \) D. none of these
2
Maths
Polyphosphates are used as water softening agents because they: A. form soluble complexes with anionic species B. precipitate anionic species C. form soluble complexes with cationic species D. precipitate cationic species
1
Chemistry
In the manufacture of acetic acid from aerial oxidation of acetaldehyde, the catalyst used is : A . acidified \( K_{2} C r_{2} O_{7} \) в. \( \left(C H_{3} C O O\right)_{2} M n \) \( \mathrm{c} \cdot \mathrm{HgSO}_{4} \) D. \( N i \)
1
Chemistry
The oscillations about a systems equilibrium position that occur in the absence of an external excitation are This question has multiple correct options A. free vibrations B. damped vibrations c. natural vibrations D. None of these
3
Physics
Arrange the following in increasing order of their acidic strength. \( \mathbf{A} \cdot I I I<I<I V<I I \) В . \( I I<I<I V<I I I \) \( \mathbf{c} \cdot I<I I I<I V<I I \) D . \( I I<I I I<I<I V \)
1
Chemistry
Match the column:
1
Chemistry
\( 20 \mathrm{ml} \) of \( H_{2} O_{2} \) after acidification with \( \operatorname{dil} H_{2} S O_{4} . \) required \( 30 \mathrm{ml} \) of \( \mathrm{N} / 2 \) \( K M n O_{4} \) for complete oxidation Calculate the \( \% \) of \( H_{2} O_{2} \) in g/lit. A . 10.75 g/lit B. 11.75 g/lit c. \( 12.75 \mathrm{g} / \) lit D. 13.75 g/lit
1
Chemistry
Find the maximum and minimum distances between the bars during the subsequent motion of the system, if the masses of the bars are equal to \( m_{1} \) and \( m_{2}, \) and the force \( F \) is applied to the bar of mass \( \boldsymbol{m}_{2} \)
3
Physics
Copper and Germanium are cooled from room temperature to \( 100 K . \) Then the resistance of A. Germanium decreases, Copper increases B. Germanium decreases, Copper decreases c. Germanium increases, Copper decreases D. Germanium increases, Copper increases
3
Physics
Statement I : Ammonia has a trigonal pyramidal molecular geometry. Statement II : Ammonia has a tetrahedral electron pair geometry with the three atoms bonded to the central atom A. true, true, correct explanation B. true, true, not correct explanation c. true, false \( \mathbf{D} \cdot \) false, true
1
Chemistry
Calculate the distance between the points (-3,6,7) and (2,-1,4) in \( 3 D \) space. A . 4.36 в. 5.92 c. 7.91 D. 9.11 E . 22.25
2
Maths
A field is \( 225 m \) long and \( 175 m \) wide. It has two roads in its centre of uniform width of \( 5 m \), one parallel to its length and the other parallel to its breadth. Find the cost of levelling the roads at Rs.3 per square metre. A \( . \) Rs. 1975 в. \( R s .1125 \) c. \( R s .592 \) D. Rs.6125
2
Maths
Which of the following is not optically active? \( \mathbf{A} \cdot\left[\operatorname{Co}(e n)_{3}\right]^{3+} \) B . \( \left[C r(o x)_{3}\right]^{3} \) c. \( \operatorname{cis}-\left[\operatorname{CoCl}_{2}(e n)_{2}\right] \) D. \( \operatorname{trans}-\left[\operatorname{CoCl}_{2}(e n)_{2}\right]^{+} \)
1
Chemistry
If the first term of a GP is 729 and \( 7^{t h} \) term is \( 64, \) then the sum of its first seven terms is A . 2187 в. 2059 \( c .1458 \) D. 2123 E . 1995
2
Maths
A physical balance has its arms of length \( 60 \mathrm{cm} \) and \( 40 \mathrm{cm} . \) What weight kept on pan of longer arm will balance an object of weight \( 100 g f \) kept on other pan? A. \( 33.33 g f \) \( f \) в. \( 66.67 g f \) \( c .50 g f \) D. \( 16.67 g f \)
3
Physics
Verify Lagrange's mean value theorem for the following function on the indicated interval. In each case find a point \( ^{\prime} c^{\prime} \) in the indicated interval as stated by the Lagrange's mean value theorem: \( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x}-\sin 2 \boldsymbol{x}-\boldsymbol{x} \) on \( [\mathbf{0}, \boldsymbol{\pi}] \)
2
Maths
As the temperature of a conductor increases, its resistivity and conductivity change. The ratio of resistivity to conductivity A. increases B. decreases c. remains constant D. may increase or decrease depending on the actual temperature
3
Physics
\( \cos \left[\pi^{2}\right] \theta-\sin [e] \theta=? \)
2
Maths
Find the value of \( \mathrm{m} \) and \( \mathrm{n} \) using cross multiplication method: \( 3 m+n=15 \) and \( m+2 n=10 \) \( A \cdot(4,3) \) B. (-4,3) \( c \cdot(-4,-3) \) D. (4,-3)
2
Maths
Based on above isomers answer the following. Which isomers on dehydration with conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) give alkene which is capable to show geometrical isomerism? \( A \cdot g, h, f \) B. b, d, a \( c \cdot a, b, c \) \( D \) of these
1
Chemistry
Choose the incorrect statement: A. Flemings right-hand rule is a simple rule to know the direction of induced current B. The right-hand thumb rule is used to find the direction of magnetic fields due to current carrying conductors C. The difference between the direct and alternating currents is that the direct current always flows in one direction, whereas the alternating current reverses its direction periodically D. In India the AC changes direction after every \( \frac{1}{50} \) second
3
Physics
From three men and two women, environment committee of two person to be formed. Condition for event \( \boldsymbol{A} \) : There must be at least one woman member. Condition for event \( B: \) One man, one woman committee to be formed. Condition for event \( C \) : There should not be a woman member.
2
Maths
n the figure, an ideal gas changes its state from state \( A \) to state \( C \) by two paths \( A B C \) and \( A C \) The internal energy of gas of \( A \) is \( 30 J \) and the amount of heat supplied to change its state to \( C \) through path \( A C \) is \( 210 J . \) Calculate the internal energy of gas at \( C \)
3
Physics
In an average soil, the percentage of organic matter is about A . 20 B. 30 \( c \cdot 45 \) D.
0
Biology
Name two chemicals used to disinfect water
0
Biology
The velocity of a particle moving along a straight line increases according to the linear law \( v=v_{0}+k x, \) where \( k \) is a constant. Then This question has multiple correct options A. the acceleration of the particle is \( k\left(v_{0}+k x\right) \) B the particle takes a time \( \frac{1}{k} \log _{e}\left(\frac{v_{1}}{v_{0}}\right) \) to attain a velocity \( v_{1} \) c. velocity varies linearly with displacement with slope of velocity displacement curve equal to \( k \). D. the acceleration of the particle is zero.
3
Physics
Statement 1: In simple harmonic motion, the motion is to and fro and periodic. Statement 2: Velocity of the particle \( (v)=\omega \sqrt{k^{2}-x^{2}} \) (where \( x \) is the displacement). A. Statement 1 is false, Statement 2 is true B. Statement 1 is true, Statement 2 is true; Statement 2 is the correct explanation for Statement 1 c. statement 1 is true, Statement 2 is true; Statement 2 is not the correct explanation for Statement D. Statement 1 is true, Statement 2 is false
3
Physics
In mammals, the teeth are (i) Of different types (ii) Embedded in the cup-like socket of the jaw bones (iii) Only two sets, present throughout life These conditions are referred as A. Heterodont, thecodont and diphyodont B. Thecodont, heterodont and diphyodont c. Diphyodont, thecodont and heterodont D. Heterodont, diphyodont and thecodont E. Thecodont, diphyodont and heterodont
0
Biology
The given figure shows the plant for the formation of an important compound \( \mathbf{X} \) Identify \( X \) A. Washing soda B. Common salt c. Baking powder D. Bleaching powder
1
Chemistry
The vertical component of earth's magnetic field is zero at A. magnetic equator B. magnetic poles c. geographical poles D. everywhere
3
Physics
A value of \( C \) for which the conclusion of Mean Value Theorem holds for the function \( f(x)=\log _{e} x \) on the interval [1,3] is \( \mathbf{A} \cdot 2 \log _{3} e \) B. \( \frac{1}{2} \log _{3} e \) \( \mathbf{c} \cdot \log _{3} e \) D. \( 2 \log _{e} 3 \)
2
Maths
Match the Column-I and Column-II:
1
Chemistry
The speed-time graph for a car is shown in Fig. (a) Find how far does the car travel in the first 4 seconds. Shade the area on the graph that represents the distance travelled by the car during the period. (b) Which part of the graph represents uniform motion of the car?
3
Physics
Can you remove the shell of an unboiled egg without boiling, keeping the egg's thin membrane intact? If yes, explain.
1
Chemistry
If energy( \( E \) ), velocity \( (V) \) and force \( (F) \) be taken as fundamental quantity, then what are the dimension of mass? A \( . E V^{2} \) B. \( E V^{-2} \) \( \mathbf{c} \cdot F V^{-1} \) D. \( F V^{-2} \)
3
Physics
In an alkaline solution, the following equilibrium exists. \( S^{2-}+S \leftrightharpoons S_{2}^{2-}, K_{1}=12 \) \( \boldsymbol{S}_{2}^{2-}+\boldsymbol{S} \leftrightharpoons \boldsymbol{S}_{3}^{2-}, \boldsymbol{K}_{2}=\mathbf{1 1} \) What is the equilibrium constant for the given equilibrium? \( S_{3}^{2-} \leftrightharpoons S^{2-}+2 S \) A \( \cdot 23 \) в. 132 \( c \cdot 1 / 132 \) D. \( 1 / 32 \)
1
Chemistry
What is the type of reaction? \( \boldsymbol{C H}_{2}-\boldsymbol{C H}-\boldsymbol{C H}_{3}+\boldsymbol{H B r} \rightarrow \) \( \boldsymbol{C H}_{3} \boldsymbol{C H B r} \boldsymbol{C H}_{3} \) A. Nucleophilic addition B. Electrophilic substitution c. Electrophilic addition D. Free radial addition
1
Chemistry
The \( 100^{t h} \) element is named in honor of A. Einstein B. Bohr c. Fermi D. Curie
1
Chemistry
A point at a distance of \( \sqrt{6} \) from the origin which lies on the straight line \( \frac{x-1}{1}=\frac{y-2}{2}=\frac{z+1}{3} \) will be \( \mathbf{A} \cdot(1,-1,2) \) В. (1,2,-1) C \( \cdot\left(\frac{5}{7}, \frac{10}{7}, \frac{-13}{7}\right) \) D. \( \left(\frac{5}{7}, \frac{2}{7}, \frac{-6}{7}\right) \)
2
Maths
Find the missing number: \( (+6) \times-----(-42) \)
2
Maths
The value of \( \int \frac{x^{2}+1}{x^{4}-x^{2}+1} d x \) is A \( \cdot \tan ^{-1}\left(2 x^{2}-1\right)+C \) B. \( \tan ^{-1}\left(\frac{x^{2}-1}{x}\right)+C \) \( ^{\mathrm{c}} \cdot \sin ^{-1}\left(x-\frac{1}{x}\right)+C \) D. \( \tan ^{-1} x^{2}+C \)
2
Maths
The total intensity of the earth's magnetic field at equator is 5 units. What is its value at the poles? A . 5 B. 4 \( c .3 \) D. 2
3
Physics
The intercept on the line \( y=x \) by the \( \operatorname{circle} x^{2}+y^{2}-2 x=0 \) is \( A B \) Equation of the circle with \( A B \) as a diameter is A \( \cdot x^{2}+y^{2}+x+y=0 \) B . \( x^{2}+y^{2}-x-y=0 \) c. \( x^{2}+y^{2}+x-y=0 \) D. None of these
2
Maths
What is the main function of lightning conductor? A. To capture lightning stroke and conduct discharge current safely to the ground B. To capture lightning stroke and conduct discharge current safely to the cloud C. To capture lightning stroke and conduct discharge current safely to the building D. None
3
Physics
The velocity of a particle moving in straight line depends on its position \( x \) w.r.t. to fixed origin according to the relation \( 16 x^{2}+4 v^{2}=9 . \) The acceleration of particle when it is at \( x=2 m \) is: A \( .-2 m / s^{2} \) B. \( -8 m / s^{2} \) c. \( -6 m / s^{2} \) D. Not defined
3
Physics
Find the value of \( \cos \left(\sec ^{-1} x+\right. \) \( \left.\operatorname{cosec}^{-1} x\right),|x| \geq 1 \)
2
Maths
Which of the two tautomers is more stable? \( A \) \( B \) c. \( I=I I \) D. None of these
1
Chemistry
Choose the correct answers from the alternatives given The prokaryotic genetic system contains: A. either DNA or histones B. DNA but no histones c. neither DNA nor histones D. DNA and histones
0
Biology
Paramagnetism of oxygen is explained on the basis of which of the following electronic configuration? A \( \cdot\left(2 \pi^{*} p y\right)^{1}\left(2 \pi^{*} p z\right)^{1} \) B . \( \left(2 \pi^{*} p x\right)^{1}\left(2 \pi^{*} p y\right)^{1} \) C \( \cdot(2 \sigma p x)^{1}(2 \pi p y)^{1} \) D. \( (2 \sigma p y)^{1}(2 \pi p y)^{1} \)
1
Chemistry
In Boolean algebra \( \boldsymbol{A} . \boldsymbol{B}=\boldsymbol{Y} \) implies that: A. product of \( A \) and \( B \) is \( Y \) B. \( Y \) exists when \( A \) exists or \( B \) exists c. \( Y \) exists when both \( A \) and \( B \) exist but not when only \( A \) or \( B \) exists D. \( Y \) exists when \( A \) or \( B \) exists but not both \( A \) and \( B \) exist
3
Physics
In a geometric progression with common ratio 'q', the sum of the first 109 terms exceeds the sum of the first 100 terms by \( 12 . \) If the sum of the first nine terms of the progression is \( \frac{\boldsymbol{\lambda}}{\boldsymbol{q}^{100}} \) then the value of \( \lambda \) equals to A . 10 B. 14 c. 12 D. 22
2
Maths
The number of \( U^{238} \) nuclei in a rock sample is equal to the number of \( \mathrm{Pb}^{206} \) atoms. The half-life of \( \mathrm{U}^{238} \) is \( 4.5 \times 10^{9} \) years.The age of the rock is A \( \cdot 4.5 \times 10^{9} y \) B. \( 9 \times 10^{9} y \) C. \( 13.5 \times 10^{9} y \) D. \( 18 \times 10^{9} y \)
3
Physics
A dynamo A. Creates mechanical energy B. Creates electrical energy C. Converts electrical energy into mechanical energy D. Converts mechanical energy into electrical energy
3
Physics
If \( 72 K \) is a perfect cube, find the value of \( \boldsymbol{K} \) \( \mathbf{A} \cdot \mathbf{1} \) B . 2 \( c .3 \) D.
2
Maths
A particle moves in the \( x-y \) plane under the action of a force \( \vec{F} \) such that the value of its linear momentum \( (\vec{P}) \) at anytime \( t \) is \( P_{x}=2 \cos t, P_{y}=2 \sin t \) The angle \( \theta \) between \( \vec{F} \) and \( \vec{P} \) at a given time \( t \) will be \( \mathbf{A} \cdot \theta=0^{\circ} \) B . \( \theta=30 \) c. \( \theta=90 \) D. \( \theta=180^{\circ} \)
3
Physics
State whether True or False: Hysteresis is the number of lines of force per unit area in a magnetic field. A. True B. False
3
Physics
If \( \boldsymbol{A}=\left(\begin{array}{ccc}1 & 2 & 1 \\ -1 & 0 & 3 \\ 2 & -1 & 1\end{array}\right) \) then characteristic equation is given by A. \( -\lambda^{3}+2 \lambda^{2}-4 \lambda+18=0 \) 0 B . \( \lambda^{3}+2 \lambda^{2}+4 \lambda+18=0 \) c. \( 2 \lambda^{3}-\lambda^{2}+6 \lambda-2=0 \) D. None of these
2
Maths
Identify the constituent radiations of electromagnetic spectrum which (a) is obsorbed by ozone layer in the atmosphere (b) i produced by bombarding a metal target by high speed electrons (c) is used in satellite communication (d) has wavelength range between 400 nm to \( 700 \mathrm{nm} \)
3
Physics
Which of the following non-metals belongs to the halogen family? A. Flourine B. Chlorine c. Bromine D. All of the above
1
Chemistry
A uniform ladder of length \( 5 m \) is placed against the wall as shown in the figure. If coefficient of friction \( \mu \) is the same for both the walls, what is the minimum value of \( \mu \) for it not to slip? A \( \cdot \mu=\frac{1}{2} \) B. \( \mu=\frac{1}{4} \) \( c \cdot_{\mu}=\frac{1}{3} \) D. \( \mu=\frac{1}{5} \)
3
Physics
Methanol is a: A. yellow coloured liquid B. brown coloured liquid C . colourless liquid D. blue coloured liquid
1
Chemistry
Which element is not present in chlorophyll? A. carbon B. Calcium c. Magnesium D. Hydrogen
1
Chemistry
Catenation is defined as: A. formation of double bond between carbon atoms. B. linking of carbon atoms with of atoms other elements. C . indefinite linking of carbon atoms D. the formation of four covalent bonds by a carbon atom.
1
Chemistry
End product of fermentation of sugars is A. Water and carbon dioxide B. Alcohol and carbon dioxide c. Carbon dioxide D. Alcohol
0
Biology
When a horse pulls a cart, the force that helps the horse to move forward is the force exerted by A. the cart on the horse B. the ground on the horse c. the ground on the carttt D. the horse on the ground
3
Physics
The order of \( [x, y, z]\left[\begin{array}{lll}a & h & g \\ h & b & f \\ g & f & c\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right] \) is \( A \cdot 3 \times 1 \) B. \( 1 \times 1 \) c. \( 1 \times 3 \) D. \( 3 \times 3 \)
2
Maths
The n-side of the depletion layer of a p-n junction. A. Always has same width as of the p-side B. Has no bound charges c. Is negatively charged D. Is positively chargedd
3
Physics
If the equation \( a x^{2}+2 b x+c=0 \) has real roots, \( a, b, c \) being real numbers and if \( m \) and \( n \) are real number such that \( m^{2}>n>0 \) then show that the equation \( a x^{2}+2 m b x+n c=0 \) has real roots.
2
Maths
The interparticle forces between linear chains in Nylon - 6,6 are A. hydrogen bonds B. covalent bonds c. ionic bonds D. coordinate bonds
1
Chemistry
If \( \boldsymbol{y}=\log _{e}\left(\frac{\boldsymbol{x}^{2}}{e^{2}}\right), \) then \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}} \) equals \( A \cdot-\frac{1}{x} \) B. \( -\frac{1}{x^{2}} \) c. \( \frac{2}{x^{2}} \) D. \( -\frac{2}{x^{2}} \)
2
Maths
\( \$ \$ \operatorname{lint}|,| \operatorname{left}\left[x \sin ^{\wedge}\{-1\} x \mid, \text { lleft } \mid\{1\right. \) \( \left|\operatorname{sqrt}\left\{\left(1|,-|, \mathbf{x}^{\wedge} 2\right\}|,| r i g h t \mid\right\} \wedge\{-1\}\right| \) |right \( ] \wedge \mid, \$ \$ d x \)
2
Maths
The metal oxide which cannot be reduced to metal by carbon is A \( . Z n O \) в. \( F e_{2} O_{3} \) \( c . P b O \) D. \( A l_{2} O_{3} \)
1
Chemistry
Which of the following property is not a thermodynamic property of the system? A. pressure B. temperature c. specific volume D. heat
1
Chemistry
Differentiate with respect to \( x \) : \( \frac{3 x^{2} \sin x}{\sqrt{7-x^{2}}} \)
2
Maths
An artificial satellite in the presence of frictional forces will move into an orbit closer to the earth and may have increased kinetic energy. Explain this.
3
Physics
Which of the following compound cannot be thermally decomposed even at high temperature? A. \( C s H C O_{3} \) в. \( R b_{2} C O_{3} \) \( \mathrm{c} \cdot L i_{2} \mathrm{CO}_{3} \) D. \( \left(N H_{4}\right)_{2} C O_{3} \)
1
Chemistry
Find the equation of all lines having slope 2 and being tangent to the curve \( \boldsymbol{y}+\frac{\mathbf{2}}{\boldsymbol{x}-\mathbf{3}}=\mathbf{0} \)
2
Maths
Which of the following processes produces a decrease of the entropy of the system? A. Dissolving sodium chloride in water B. Sublimation of naphthalene c. Dissolving oxygen in water D. All of these
1
Chemistry
The real part of \( \left(\frac{1+i}{3-i}\right)^{2}= \) \( \mathbf{A} \cdot \mathbf{1} \) B . 16 \( c \cdot 16 \omega^{2} \) D. \( \frac{-3}{25} \)
2
Maths
When potassium chloride and lead \( (I I) \) nitrate react in an aqueous solution, which of the following terms will be present in the balanced molecular equation? A \( \cdot P b C l_{s} \) B \( \cdot P b_{2} C l_{(s)} \) \( \mathbf{c} \cdot K N O_{3(a q)} \) D. \( 2 K N O_{3(a q)} \) E \( \cdot 2 K C l_{2(s)} \)
1
Chemistry
The radius of hydrogen atom, when it is in its second excited state, becomes: A . half B. double c. four times D. nine times
3
Physics
Which of the following is an antifreeze? A. water B. ether c. ethyl alcohol D. aniline
1
Chemistry
Assertion \( N H_{3} \) and \( C H_{3}^{-} \) both have pyramidal shape. Reason \( \mathrm{N} \) in \( N H_{3} \) and \( \mathrm{C} \) in \( C H_{3}^{-} \) both have \( s p^{3} \) hybridisation with one lone pair of electron on each. A. Assertion is true, Reason is true and Reason is correct explanation for Assertion. B. Assertion is true, Reason is true and Reason is NOT the correct explanation for Assertion. c. Assertion is true, Reason is false. D. Assertion is false, Reason is true
1
Chemistry
When sodium hydroxide solution is added to a freshly prepared solution of ferrous sulphate, a green precipitate of ferrous hydroxide is formed which on standing turns brown because: A. ferric salts are unstable B. the mixture becomes dirty c. ferrous hydroxide becomes ferric oxide D. green ferrous hydroxide oxidises to brown ferric hydroxide
1
Chemistry
Renewable sources of energy are produced in nature: A. biennial B. annually c. continuously D. quarterly
1
Chemistry
Distance of the center of mass of a solid uniform cone from its vertex is \( z_{0} . \) If the radius of its base is \( R \) and its height is \( h \) then \( z_{0} \) is equal to: A \( \cdot \frac{h^{2}}{4 R} \) в. \( \frac{3 h}{4} \) \( c \cdot \frac{5 h}{8} \) D. \( \frac{3 h^{2}}{8 R} \)
3
Physics
When hydrogen sulphide gas is passed through a blue solution of copper sulphate, a black precipitate of copper sulphide is obtained and the sulphuric acid so formed remains in the solution. The reaction is an example of: A. a combination reaction B. a displacement reaction c. a decomposition reaction D. a double displacement reaction
1
Chemistry
Find the radian measures corresponding to \( 5^{0} 37^{\prime} 0^{\prime \prime} \)
2
Maths
Nodal planes of \( \pi \) bonds in benzene are located in: A. molecular plane B. one in a molecular plane and two in a plane perpendicular to the molecular plane which contains C one in the molecular plane and two in the plane perpendicular to the molecular plane which contains Cone in the molecular plane and two in plane perpendicular to molecular plane which contains \( \mathrm{C} \mathrm{C} \sigma \) bonds C. one in molecular plane and two in plane perpendicular to molecular plane which contain \( \mathrm{C} \mathrm{C} \sigma \) bond and \( \mathrm{C}-\mathrm{H} \) \( \sigma \) bond. D. perpendicular to molecular plane which bisect benzene ring in two equal half
1
Chemistry
If \( f(x) \) is a polynomial satisfying \( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}\left(\frac{1}{x}\right)=\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}\left(\frac{1}{x}\right), \operatorname{and} \boldsymbol{f}(\boldsymbol{3})=\mathbf{8} \mathbf{2} \) then \( \int \frac{f(x)}{x^{2}+1} d x= \) A \( \cdot x^{3}-x+2 \tan ^{-1} x+c \) B. \( \frac{1}{3} x^{3}-x+\tan ^{-1} x+c \) c. \( \frac{x^{3}}{3}-x+2 \tan ^{-1} x+c \) D. \( \frac{1}{3} x^{3}+x+2 \tan ^{-1} x+c \)
2
Maths
Na \( C l \) and \( C a C l_{2} \) are added to fused \( M g C l_{2} \) in the electrolysis of \( M g C l_{2} \) so that A. melting point is decreased and conductivity is increased B. melting point is increased and conductivity is decreased c. melting point and conductivity both are decreased D. melting point and conductivity both are increased
1
Chemistry
In an AC generator, maximum number of lines of force pass though the coil when the angle between the plane of coil and lines of force is : A \( \cdot 0^{\circ} \) B. 60 \( c \cdot 30 \) D. \( 90^{\circ} \)
3
Physics
Condensed solid produced during sublimation is: A. crystals B. sublimate c. residue D. insoluble
3
Physics
The wavelength of light visible to eye is of the order of \( \mathbf{A} \cdot 10^{-4} m \) B. \( 10^{-8} \mathrm{m} \) \( \mathbf{c} \cdot 10^{-10} m \) D. \( 10^{-7} m \)
3
Physics
A condenser is charged and then battery is removed. A dielectric plate is put between the plates of condenser, then correct statement is A. Q is constant, v and U decrease B. Q is constant, V increases U decreases c. Q increases, v decreases U increases D. \( Q, v \) and \( U \) increase
3
Physics
Histone proteins are associated with A. DNA B. mRNA c. rRNA D. snRNA E. tRNA
0
Biology
When two coins are tossed and a cubical dice is rolled, then the total outcomes for the compound event is A . 48 B. 52 \( c .36 \) D. 24
2
Maths
Two positive charges \( q \) and \( q \) are placed at the diagonally opposite corners of a square and two negative charges \( -q \) and \( -q \) are placed at the other two corners of the square. Then at the centre of the square the resultant electric intensity and the net electric potential Vare A. \( E \neq 0, V=0 \) в. \( E=0, V=0 \) c. \( E=0, V \neq 0 \) D. \( E \neq 0, V \neq 0 \)
3
Physics