The given figure represents two isobaric processes for the same mass of an ideal gas, then
a.
π $_{2}$ $\geq$π $_{1}$
b.
π $_{2}$ > π $_{1}$
c.
π $_{1}$ = π $_{2}$
d.
π $_{1}$ > π $_{2}$
Correct Answer
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Q2mcq
The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ
pipe. If length of the open pipe is 60 cm, the length of the closed pipe will be :
a.
60 cm
b.
45 cm
c.
30 cm
d.
15 cm
Correct Answer
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Q3nat
Two waves of intensity ratio 1 : 9cross each other at a point. The resultant intensities at the point, when (a)
Waves are incoherent is πΌ $_{1}$ πWaves are coherent is πΌ $_{2}$ and differ in phase by 60 $^{o}$ . If $\frac{πΌ1}{πΌ2}$ = $\frac{10}{π₯}$ , then π₯=
_________.
✓ Accepted Answer:13
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Q4nat
A body starts falling freely from height π»hits an inclined plane in its path at height β. As a result of this
perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of $\frac{π»}{β}$ for which
the body will take the maximum time to reach the ground is _____.
✓ Accepted Answer:2
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Q5mcq
In a plane EM wave, the electric field oscillates sinusoidally at a frequency of 5 $\times$ 10 $^{10}$ Hzand an amplitude
of 50 V m $^{- 1}$ . The total average energy density of the electromagnetic field of the wave is : [Use
π $_{0}$ = 8 . 85 $\times$ 10 $^{- 12}$ C $^{2}$ N $^{-1}$ m $^{-2}$ ]
Two charges πand 3πare separated by a distance βπβ in air. At a distance π₯from charge π, the resultant electric
field is zero. The value of π₯is :
Identify the logic operation performed by the given circuit.
a.
NAND
b.
NOR
c.
OR
Correct Answer
d.
AND
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Q8mcq
The parameter that remains the same for molecules of all gases at a given temperature is :
a.
kinetic energy
Correct Answer
b.
momentum
c.
mass
d.
speed
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Q9nat
A parallel plate capacitor with plate separation 5 mmis charged up by a battery. It is found that on
introducing a dielectric sheet of thickness 2 mm, while keeping the battery connections intact, the capacitor
draws 25%more charge from the battery than before. The dielectric constant of the sheet is ____.
✓ Accepted Answer:2
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Q10nat
The mass defect in a particular reaction is 0 . 4 g. The amount of energy liberated is π$\times$ 10 $^{7}$ kW h, where
π= _____. (speed of light = 3 $\times$ 10 $^{8}$ m s $^{-1}$ )
✓ Accepted Answer:1
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In the given arrangement of a doubly inclined plane two blocks of masses πand πare placed. The blocks are
connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface
of the plane and the blocks is 0 . 25. The value of π, for which π= 10 kgwill move down with an
acceleration of 2 m s $^{-2}$ , is: (take π= 10 m s $^{-2}$ and tan 37$^{\circ}$ = $\frac{3}{4}$ )
a.
9 kg
b.
4 . 5 kg
c.
6 . 5 kg
d.
2 . 25 kg
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A coin is placed on a disc. The coefficient of friction between the coin and the disc is π. If the distance of the
coin from the center of the disc is π, the maximum angular velocity which can be given to the disc, so that the
coin does not slip away, is :
a.
$\frac{ππ}{π}$
b.
$\sqrt$ $\frac{π}{ππ}$
c.
$\sqrt$ $\frac{ππ}{π}$
d.
$\frac{π}{$\sqrt{\,}$ππ}$
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A solid circular disc of mass 50 kgrolls along a horizontal floor so that its center of mass has a speed of
0 . 4 m s $^{-1}$ . The absolute value of work done on the disc to stop it is ______ J.
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A small square loop of wire of side πis placed inside a large square loop of wire of side πΏπΏ= π $^{2}$ . The loops are
coplanar and their centers coincide. The value of the mutual inductance of the system is $\sqrt$π₯$\times$ 10 $^{-7}$ H, where
π₯=______.
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A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct
representation of the velocity time graph for the transit of the ball?
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The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by 0 . 02%is
_____ m.
(Take density of sea water = 10 $^{3}$ kg m $^{-3}$ , Bulk modulus of rubber = 9 $\times$ 10 $^{8}$ N m $^{-2}$ , and
π= 10 m s $^{-2}$ )
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When a metal surface is illuminated by light of wavelength π, the stopping potential is 8 V. When the same
surface is illuminated by light of wavelength 3π, stopping potential is 2 V. The threshold wavelength for this
surface is :
a.
5π
b.
3π
c.
9π
d.
4 . 5π
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An artillery piece of mass π $_{1}$ fires a shell of mass π $_{2}$ horizontally. Instantaneously after the firing, the ratio of
kinetic energy of the artillery and that of the shell is :
a.
$\frac{π1}{( π1+ π2)}$
b.
$\frac{π2}{π1}$
c.
$\frac{π2}{( π1+ π2)}$
d.
$\frac{π1}{π2}$
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A particle performs simple harmonic motion with amplitude π΄. Its speed is increased to three times at an
instant when its displacement is $\frac{2π΄}{3}$ . The new amplitude of motion is $\frac{ππ΄}{3}$ . The value of πis _____.
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A rigid wire consists of a semicircular portion of radius π and two straight sections. The wire is partially
immerged in a perpendicular magnetic field π΅= π΅ $_{0}^{^}$ jas shown in figure. The magnetic force on the wire if it
has a current πis :
a.
-ππ΅π $^{^}$ j
b.
2ππ΅π $^{^}$ j
c.
ππ΅π $^{^}$ j -2ππ΅π j $^{^}$
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A coil is placed perpendicular to a magnetic field of 5000 T. When the field is changed to 3000 Tin 2 s,
an induced emf of 22 Vis produced in the coil. If the diameter of the coil is 0 . 02 m, then the number of
turns in the coil is:
a.
7
b.
70
c.
35
d.
140
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The relation between time βπ‘β and distance βπ₯β is π‘= πΌπ₯ $^{2}$ + π½π₯, where πΌand π½are constants. The relation
between acceleration πand velocity π£is:
a.
π= - 2πΌπ£ $^{3}$
b.
π= - 5πΌπ£ $^{5}$
c.
π= - 3πΌπ£ $^{2}$
d.
π= - 4πΌπ£ $^{4}$
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A force is represented by πΉ= ππ₯ $^{2}$ + ππ‘ $\frac{1}{2}$ , where π₯=distance and π‘=time. The dimensions of $\frac{π2}{π}$ are :
a.
[ππΏ $^{3}$ π $^{- 3}$ ]
b.
[ππΏπ $^{- 2}$ ]
c.
[ππΏ $^{- 1}$ π $^{- 1}$ ]
d.
[ππΏ $^{2}$ π $^{- 3}$ ]
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Two conductors have the same resistances at 0 $^{\circ}$Cbut their temperature coefficients of resistance are πΌ $_{1}$ and πΌ $_{2}$
. The respective temperature coefficients for their series and parallel combinations are :
Four identical particles of mass πare kept at the four corners of a square. If the gravitational force exerted on
one of the masses by the other masses is $\frac{2$\sqrt{\,}$2+ 1}{32} \frac{πΊπ2}{πΏ2}$ , the length of the sides of the square is
a.
$\frac{πΏ}{2}$
b.
4πΏ
c.
3πΏ
d.
2πΏ
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An electron moves through a uniform magnetic field $^{$\rightarrow$}$ π΅= π΅ $_{0}^{^}$ i + 2π΅ $_{0}^{^}$ j T. At a particular instant of time, the
velocity of electron is $^{$\rightarrow$}$ π’= 3 $^{^}$ i + 5 $^{^}$ j m s $^{-1}$ . If the magnetic force acting on electron is πΉ= 5π $^{$\rightarrow$}$ k N $^{^}$ , where πis
the charge of electron, then the value of π΅ $_{0}$ is ____ T.
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The correct statements from the following are:
A. The strength of anionic ligands can be explained by crystal field theory.
B. Valence bond theory does not give a quantitative interpretation of kinetic stability of coordination
compounds.
C. The hybridization involved in formation of [Ni ( CN ) $_{4}$ ] $^{2 -}$ complex is dsp $^{2}$ .
D. The number of possible isomer(s) of cis-[PtCl $_{2}$ ( en ) $_{2}$ ] $^{2 +}$ is one
Choose the correct answer from the options given below:
a.
A, D only
b.
A, C only
c.
B, D only
d.
B, C only
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The linear combination of atomic orbitals to form molecular orbitals takes place only when the combining
atomic orbitals
A. have the same energy B. have the minimum overlap C. have same symmetry about the molecular axis D.
have different symmetry about the molecular axis
Choose the most appropriate from the options given below:
a.
A, B, C only
b.
A and C only
c.
B, C, D only
d.
B and D only
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The number of species from the following in which the central atom uses sp $^{3}$ hybrid orbitals in its bonding is
_________.
NH $_{3}$ , SO $_{2}$ , SiO $_{2}$ , BeCl $_{2}$ , CO $_{2}$ , H $_{2}$ O, CH $_{4}$ , BF $_{3}$
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The product (C) in the below mentioned reaction is:
KOHalc HBr β
CH $_{3}$ - CH $_{2}$ - CH $_{2}$ - Br $\rightarrow$ $_{β}$ A $\rightarrow$ B $\rightarrow$ $_{KOHaq}$ C
a.
Propan-1-ol
b.
Propene
c.
Propyne
d.
Propan-2-ol
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The ionization energy of sodium in kJ mol $^{- 1}$ . If electromagnetic radiation of wavelength 242 nmis just
sufficient to ionize sodium atom is ______.(nearest integer)
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The 'Spin onlyβ Magnetic moment for [Ni ( NH $_{3}$ ) $_{6}$ ] $^{2 +}$ is______$\times$ 10 $^{- 1}$ BM. (given = Atomic number of
Ni : 28)
Round off your answer to the nearest integer.
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Identify correct statements from below:
A. The chromate ion is square planar.
B. Dichromates are generally prepared from chromates.
C. The green manganate ion is diamagnetic.
D. Dark green coloured K $_{2}$ MnO $_{4}$ disproportionates in a neutral or acidic medium to give permanganate.
E. With increasing oxidation number of transition metal, ionic character of the oxides decreases.
Choose the correct answer from the options given below:
a.
B, C, D only
b.
A, D, E only
c.
A, B, C only
d.
B, D, E only
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Consider the oxides of group 14elements πππ $_{2}$ , πΊππ $_{2}$ , πππ $_{2}$ , πππ $_{2}$ , πΆπand πΊππ. The amphoteric
oxides are
a.
GeO, GeO $_{2}$
b.
SiO $_{2}$ , GeO $_{2}$
c.
SnO $_{2}$ , PbO $_{2}$
d.
SnO $_{2}$ , CO
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Molar mass of the salt from NaBr, NaNO $_{3}$ , KIand CaF $_{2}$ which does not evolve coloured vapours on heating
with concentrated H $_{2}$ SO $_{4}$ is ____ g mol $^{- 1}$ , (Molar mass in
g mol $^{- 1}$ : Na : 23, N : 14, K : 39, O : 16, Br : 80, I : 127, F : 19, Ca : 40
)
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Match List I with List II
List-I List-II
A. Glucose/NaHCO $_{3}$ / β I. Gluconic acid
B. Glucose/HNO $_{3}$ II. No reaction
C. Glucose/HI / β III. n-hexane
D. Glucose/Bromine water IV. Saccharic acid
Choose the correct answer from the options given below:
a.
A-IV, B-I, C-III, D-II
b.
A-II, B-IV, C-III, D-I
c.
A-III, B-II, C-I, D-IV
d.
A-I, B-IV, C-III, D-II
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Integrated rate law equation for a first order gas phase reaction is given by (where π $_{π}$ is initial pressure and π $_{π‘}$
is total pressure at time π‘)
Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R:
Assertion A: ππΎ $_{π}$ value of phenol is 10 . 0while that of ethanol is 15 . 9.
Reason R: Ethanol is stronger acid than phenol.
In the light of the above statements, choose the correct answer from the options given below:
a.
A is true but R is false
b.
A is false but R is true
c.
Both A and R are true and R is the correct
explanation of A
d.
Both A and R are true but R is NOT the correct
explanation of A.
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For the given reaction, choose the correct expression of K $_{C}$ from the following:
Fe $^{3 +}_{aq}$ + SCN $^{-}_{aq}$ $\rightleftharpoons$(FeSCN ) $^{2 +}_{aq}$
Give below are two statements:
Statement-I : Noble gases have very high boiling points.
Statement-II: Noble gases are monoatomic gases. They are held together by strong dispersion forces. Because
of this they are liquefied at very low temperature. Hence, they have very high boiling points.
In the light of the above statements. choose the correct answer from the options given below:
a.
Statement I is false but Statement II is true
b.
Both Statement I and Statement II are true
c.
Statement I is true but Statement II is false
d.
Both Statement I and Statement II are false
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Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R:
Assertion A: Alcohols react both as nucleophiles and electrophiles.
Reason R: Alcohols react with active metals such as sodium, potassium and aluminum to yield corresponding
alkoxides and liberate hydrogen.
In the light of the above statements, choose the correct answer from the options given below:
a.
A is false but R is true.
b.
A is true but R is false.
c.
Both A and R are true and R is the correct
explanation of A
d.
Both A and R are true but R is NOT the correct
explanation of A
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The correct sequence of electron gain enthalpy of the elements listed below is
A. Ar B. Br C. F D. S
Choose the most appropriate from the options given below:
a.
C > B > D > A
b.
A > D > B > C
c.
A > D > C > B
d.
D > C > B > A
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Consider the following reaction at 298 K.
$\frac{3}{2}$ O $_{2g}$ $\rightleftharpoons$O $_{3g}$ . K $_{p}$ = 2 . 47 $\times$ 10 $^{-29}$
β $_{r}$ G $^{0}$ for the reaction is _________ kJ. (Given R = 8 . 314 JK $^{- 1}$ mol $^{- 1}$ )
Round off your answer to the nearest integer.
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Match List I with List II
LIST I (Technique) LIST II (Application)
A. Distillation I. Separation of glycerol from spent-lye
B. Fractional distillation II. Aniline - Water mixture
C. Steam distillation III. Separation of crude oil fractions
D. Distillation under reduced pressure IV. Chloroform-Aniline
Choose the correct answer from the options given below:
a.
A-IV, B-I, C-II, D-III
b.
A-IV, B-III, C-II. D-I
c.
A-I. B-II, C-IV, D-III
d.
A-II, B-III. C-I, D-IV
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Given below are two statements:
Statement I: IUPAC name of HO - CH - ( CH ) - COCH is 7-hydroxyheptan-2-one.
$^{2}^{2}_{3}$ - CH $^{2}^{3}$
Statement II: 2-oxoheptan-7-ol is the correct IUPAC name for the above compound.
In the light of the above statements, Choose the most appropriate answer from the options given below:
a.
Statement I is correct but Statement II is
incorrect.
b.
Both Statement I and Statement II are incorrect.
c.
Both Statement I and Statement II are correct.
d.
Statement I is incorrect but Statement II is
correct.
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Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable π₯to be the
number of rotten apples in a draw of two apples, the variance of π₯is
a.
$\frac{37}{153}$
b.
$\frac{57}{153}$
c.
$\frac{47}{153}$
d.
$\frac{40}{153}$
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Let πbe the sum of all coefficients in the expansion of ( 1 - 2π₯+ 2π₯ $^{2}^{2023}$ ( 3 - 4π₯ $^{2}$ + 2π₯ $^{3}^{2024}$ and
) )
π₯ log1 + π‘
$\int$ ππ‘
π= $_{π₯$\rightarrow$0}$ lim $\frac{0π‘2024+ 1}{π₯2}$ . If the equations ππ₯ $^{2}$ + ππ₯+ π= 0and 2ππ₯ $^{2}$ + ππ₯+ 4 = 0have a common root, where
π, π, π$\in$π , then π : π : πequals
a.
2 : 1 : 4
b.
4 : 1 : 4
c.
1 : 2 : 4
d.
1 : 1 : 4
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Let πand π be the feet of perpendiculars from the point ππ, π, πon the lines π₯= π¦, π§= 1and
π₯= -π¦, π§= -1respectively. If $\angle$πππ is a right angle, then 12π $^{2}$ is equal to ________
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Let πΌ, π½, πΎ, πΏ$\in$πand let π΄πΌ, π½, π΅1, 0, πΆπΎ, πΏand π·1, 2be the vertices of a parallelogram π΄π΅πΆπ·.
If π΄π΅= $\sqrt$10and the points π΄and πΆlie on the line 3π¦= 2π₯+ 1, then 2πΌ+ π½+ πΎ+ πΏis equal to
a.
10
b.
5
c.
12
d.
8
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For πΌ, π½, πΎ$\neq$0. If sin $^{-1}$ πΌ+ sin $^{-1}$ π½+ sin $^{-1}$ πΎ= πand πΌ+ π½+ πΎπΌ-πΎ+ π½= 3πΌπ½, then πΎequal to
a.
$\frac{$\sqrt{\,}$3}{2}$
b.
$\frac{1}{$\sqrt{\,}$2}$
c.
$\frac{$\sqrt{\,}$3- 1}{2$\sqrt{\,}$2}$
d.
$\sqrt$3
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Let πbe the set of positive integral values of πfor which $\frac{ππ₯2+ 2π+ 1π₯+ 9π+ 4}{π₯2- 8π₯+ 32}$ < 0, $\forall$π₯$\in$β. Then, the number
of elements in πis:
a.
1
b.
0
c.
$\infty$
d.
3
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If πΌdenotes the number of solutions of 1 -π $^{π₯}$ = 2 $^{π₯}$ and π½= $\frac{π§}{argπ§}$ , where π§= $\frac{π}{4}$ 1 + π $\frac{41 -$\sqrt{\,}$πΒ· π}{π+ π}$ + $\frac{$\sqrt{\,}$π-π}{1 + $\sqrt{\,}$πΒ· π}$ ,
$\sqrt$
π= $\sqrt$-1, then the distance of the point πΌ, π½from the line 4π₯-3π¦= 7is ______
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ππ₯, π₯$\leq$0
Let ππ₯be a linear function and ππ₯= $\frac{1}{π₯}$ , is continuous at π₯= 0. If π $'$ 1 = π-1, then the value of
$\frac{1 + π₯}{2 + π₯}$ , π₯> 0
π3is
a.
$\frac{1}{3}$ log $_{π}\frac{4}{1}$
9π3
b.
$\frac{1}{3}$ log $_{π}\frac{4}{9}$ + 1
c.
log $_{π}\frac{4}{9}$ -1
d.
log $_{π}\frac{4}{1}$
9π3
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Let $^{$\rightarrow$}$ πand $^{$\rightarrow$}$ πbe two vectors such that $^{$\rightarrow$}$ π= 1, $^{$\rightarrow$}$ π= 4and $^{$\rightarrow$}$ π$\cdot$ $^{$\rightarrow$}$ π= 2. If $^{$\rightarrow$}$ π= 2 $^{$\rightarrow$}$ π$\times$ $^{$\rightarrow$}$ π-3 $^{$\rightarrow$}$ πand the angle between
$^{$\rightarrow$}$ πand $^{$\rightarrow$}$ πis πΌ, then 192sin $^{2}$ πΌis equal to _________
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The distance of the point π( 0, 2, - 2 ) form the line passing through the point π( 5, - 4, 3 ) and
perpendicular to the lines $^{$\rightarrow$}$ π= -3 $^{^}$ π+ 2π+ π2 $^{^}^{^}$ π+ 3 $^{^}$ π+ 5π, $^{^}$ π$\in$βand
$^{$\rightarrow$}$ π= $^{^}$ π-2 $^{^}$ π+ π+ π- $^{^}^{^}$ π+ 3 $^{^}$ π+ 2π, $^{^}$ π$\in$βis
a.
$\sqrt$86
b.
$\sqrt$20
c.
$\sqrt$54
d.
$\sqrt$74
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If the foci of a hyperbola are same as that of the ellipse $\frac{π₯2}{9}$ + $\frac{π¦2}{25}$ = 1and the eccentricity of the hyperbola is $\frac{15}{8}$
times the eccentricity of the ellipse, then the smaller focal distance of the point $\sqrt$2, $\frac{14}{3} \frac{2}{5}$ on the hyperbola,
$\sqrt$
is equal to
a.
7$\sqrt$ $\frac{2}{5}$ - $\frac{8}{3}$
b.
14$\sqrt$ $\frac{2}{5}$ - $\frac{4}{3}$
c.
14$\sqrt$ $\frac{2}{5}$ - $\frac{16}{3}$
d.
7$\sqrt$ $\frac{2}{5}$ + $\frac{8}{3}$
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Two marbles are drawn in succession from a box containing 10red, 30white, 20blue and 15orange marbles,
with replacement being made after each drawing. Then the probability, that first drawn marble is red and
second drawn marble is white, is
a.
$\frac{2}{25}$
b.
$\frac{4}{25}$
c.
$\frac{2}{3}$
d.
$\frac{4}{75}$
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Let π¦= π¦( π₯) be the solution of the differential equation $\frac{ππ¦}{ππ₯}$ = $\frac{tanπ₯+ π¦}{sinπ₯secπ₯- sinπ₯tanπ₯}$ , π₯$\in$0, $\frac{π}{2}$ satisfying the
condition π¦ $\frac{π}{4}$ = 2. Then, π¦ $\frac{π}{3}$ is
π₯
Let π= -1, $\infty$and π: π$\rightarrow$βbe defined as ππ₯= $\int$ π $^{π‘}$ -1 $^{11}$ 2π‘-1 $^{5}$ π‘-2 $^{7}$ π‘-3 $^{12}$ 2π‘-10 $^{61}$ ππ‘. Let π=Sum
-1
of square of the values of π₯, where ππ₯attains local maxima on π. and π=Sum of the values of π₯, where ππ₯
attains local minima on π. Then, the value of π $^{2}$ + 2πis ________
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$\frac{π}{2} \frac{1}{2}$
If the integral 525 $\int$ sin2π₯ cos $\frac{11}{2}$ π₯1 + cos $\frac{5}{2}$ π₯ ππ₯is equal to π$\sqrt$2 -64, then πis equal to ________
0
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π1 -π
Let π: β$\rightarrow$βbe a function defined by ππ₯= $\frac{4π₯}{4π₯+ 2}$ and π= $\int$ π₯sin $^{4}$ π₯1 -π₯ππ₯,
ππ
π1 -π
π= $\int$ sin $^{4}$ π₯1 -π₯ππ₯; π$\neq$ $\frac{1}{2}$ . If πΌπ= π½π, πΌ, π½$\in$β, then the least value of πΌ $^{2}$ + π½ $^{2}$ is equal to ______
ππ
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If the system of linear equations
π₯- 2π¦+ π§= - 4
2π₯+ πΌπ¦+ 3π§= 5
3π₯- π¦+ π½π§= 3
has infinitely many solutions, then 12πΌ+ 13π½is equal to
a.
60
b.
64
c.
54
d.
58
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In the expansion of 1 + π₯1 -π₯ $^{2}$ 1 + $\frac{3}{π₯}$ + $\frac{3}{π₯2}$ + $\frac{1}{π₯3}^{5}$ , π₯$\neq$0, the sum of the coefficient of π₯ $^{3}$ and π₯ $^{-13}$ is equal to
______
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Let the foci and length of the latus rectum of an ellipse $\frac{π₯2}{π2}$ + $\frac{π¦2}{π2}$ = 1, π> πbe $\pm$5, 0and $\sqrt$50, respectively.
Then, the square of the eccentricity of the hyperbola $\frac{π₯2}{π2}$ - $\frac{π¦2}{π2π2}$ = 1equals
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The total number of words (with or without meaning) that can be formed out of the letters of the word
"DISTRIBUTION" taken four at a time, is equal to ______.
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The solution curve of the differential equation π¦ $\frac{ππ₯}{ππ¦}$ = π₯log $_{π}$ π₯- log $_{π}$ π¦+ 1, π₯> 0, π¦> 0passing through the
point ( π, 1 ) is
a.
log $_{π}\frac{π¦}{π₯}$ = π₯
b.
log $_{π}\frac{π¦}{π₯}$ = π¦ $^{2}$
c.
log $_{π}\frac{π₯}{π¦}$ = π¦
d.
2log $_{π}\frac{π₯}{π¦}$ = π¦+ 1
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If one of the diameters of the circle π₯ $^{2}$ + π¦ $^{2}$ - 10π₯+ 4π¦+ 13 = 0is a chord of another circle πΆ, whose center
is the point of intersection of the lines 2π₯+ 3π¦= 12and 3π₯- 2π¦= 5, then the radius of the circle πΆis
a.
$\sqrt$20
b.
4
c.
6
d.
3$\sqrt$2
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Let π΄= 1, 2, 3, 4and π = ( 1, 2 ) , ( 2, 3 ) , ( 1, 4 ) be a relation on π΄. Let πbe the equivalence
relation on π΄such that π $\subset$πand the number of elements in πis π. Then, the minimum value of πis _______
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For 0 < π< π< π, let ( π+ π- 2π) π₯ $^{2}$ + ( π+ π- 2π) π₯+ ( π+ π- 2π) = 0and πΌ$\neq$1be one of its root.
Then, among the two statements
(I) If πΌ$\in$-1, 0, then πcannot be the geometric mean of πand π.
(II) If πΌ$\in$0, 1, then πmay be the geometric mean of πand π.
a.
Both (I) and (II) are true
b.
Neither (I) nor (II) is true
c.
Only (II) is true
d.
Only (I) is true
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