JEE Main Practice Test- 26 - JEE

The correct option is C.
Since.a, band c are in HP. Then 1/a, 1/b and 1/c are in AP. 2/b = 1/a + 1/c ⇒ 1/a - 2/b + 1/c = 0 Hence, straight line x/a + y/b + 1/c = 0 always passes through a fixed point (1, -2).

D is the correct option.sin⁻1(4/21)

D is the correct option.a.(b-c)=a.b-a.c is correct if a,b,c are any three vectors.

The correct option is C.
The equilibrium constant in a reversible reaction at a given temperature. Solution : Equilibrium constant is independent of original concentration of reactant.

C is the correct option.The structure of white phosphorus is tetrahedral.
White phosphorus, yellow phosphorus or simply tetraphosphorus (P4) exists as molecules made up of four atoms in a tetrahedral structure. The tetrahedral arrangement results in ring strain and instability. The molecule is described as consisting of six single P–P bonds.

The correct is C.
Isopropyl chloride undergoes hydrolysis via both SN-1 and SN-2 mechanisms. Both of them yield the same result/ products. Since, isopropyl chloride is a secondary alkyl halide.

The correct option is C.

(z₁-z₂)/(z₂-z₃)= cos(-60)+sin(-60)=e-i60

taking mode on both sides

Absolute value of(z₁-z₂/z₂-z₃)=1

Therefore |z₁-z₂|=|z₂-z₃|

Also angle between z₁-z₂ & z₂-z₃ is 60

So given triangle is equilateral triangle.

Given y = cot^-1 (1+x)/(1-x)

Put x = tan θ

θ = tan^{-1 x}

Then y = cot^-1 (1 + tan θ)/(1- tan θ)

y = cot^-1 (tan π/4 + tan θ)/(1- tan π/4 tan θ)

= cot^-1 tan (π/4 +θ)

= cot^-1 cot (π/2 – (π/4 +θ))

= π/4 – θ

= π/4 – tan^-1 x

dy/dx = -1/(1+x²)

A statement is logically equivalent to its contrapositive.

To form the contrapositive, switch the "If" and  "then" sections

of the statement AND insert "NOTs" into each section.

Notice in this situation, that inserting

"NOTs" turns the thoughts positive (you are negating negative thoughts).

The correct option is Option C.

When f(x) = g(x)

Then the range includes 1. 

But it is already given that 1 is excluded.

Hence, the assertion is correct but the reason behind it is false.

Since A+B is defined, A and B are matrices of the same type,
say m×n; Also, AB is defined.
So, the number of columns in A must be equal to the number of rowsin B ie. n=m.
Hence, A and B are square matrices of the same order.

f ′ (x)   = 4 So, for 0 ≤ x < 1, we get f ′ x < 0, i . e . , f x is m.d. and for 1 < x ≤ 2 we get f ′ (x)   > 0, i . e . , f (x)    is m.i .

∴ min f (x)   =

It is given that the parabola passes through the point (2,-6)
Length of its latus rectum is 4a
y² = 4ax
i.e. 

(-6)² = 4a(2)
⇒a = 9/2
∴ Length of the latus rectum is 4 x 9/2 = 18

We know that ,
1) ⁿP_r. = n!/( n - r )!
2) ⁿC_r = n!/ [ ( n - r )! r ! ]
3) r! = ( ⁿP_r )/ ⁿC_r 

It is given that ,

nPr = 840 ---( 1 )

nCr = 35 ---( 2 )

r! = ( nPr )/ ( nCr )

= 840/35

= 24

r! = 4 × 3 × 2 × 1

r ! = 4!
Therefore,

r = 4

Substitute r value in equation ( 1 ),

We get

n!/ ( n - 4 ) ! = 840

n( n - 1 )( n - 2 )( n - 3 ) = 840

n( n - 1 )( n - 2 )( n - 3 ) = 7× 6 × 5 × 4

Therefore ,

n = 7

Let n be successive independent trials and p the probability of getting a success.

The the mean and variance of a binomial distribution is given by :

Mean = np

Variance = np(1 - p)

In this case we have :

p = 1/4

Variance = (standard deviation) ²

Variance = 3² = 9

From this we can get the value of n as follows :

Variance = np(1 - p)

Doing the substitution we have

9 = 1/4n( 1 - 1/4)

9 = 1/4n(3/4)

9 = 3/16n

n = 16/3 × 9

n = 48

Mean = np

Mean = 48 × 1/4 = 12

The mean of the binomial distribution is equal to 12.

A-B=π/4

Which implies A=B+π/4

Taking tan on both sides

tanA=tan(B+π/4)

tanA=(tanB + tan(π\4))/(1- tanB.tan(π/4))

tanA=(tanB+1)/(1-tanB)

Substituting the value of tanA in

(1+tanA).(1-tanB) we get

(1+(tanB+1)/(1-tanB)).(1-tanB)

= (1-tanB+tanB+1)/(1-tanB).(1-tanB)

=2

Formation of a π - bond occurs by the sideways overlap of p-orbitals of two C-atoms.The molecular plane does not have any π - electron density since the p-orbitals are perpendicular to the plane containing the ethene molecule.The nodal plane in the π-bond of ethene is located in the molecular plane.

Fats and oils
1. Fats and oils are a concentrated source of energy.
2. Fats and oils are essential for the transport and storage of fat-soluble vitamins in the body.
3. Fats and oils are tri- esters formed from the condensation of glycerol (propane1,2,3-triol) and three carboxylic acid molecules.
4. The hydrolysis products of a fat or oil can be identified from the structure of the fat or oil.

Outer electronic configuration of Li^-1 (2s² most stable)
Be ^– ( 2s² 2p¹ less stable) than Be (2s² most stable)
B ^– (2s² 2p² stable) ; C ^– (2s² 2p³ most  stable)
As Be ^– is formed from highly stable configuration it tries to loose electron and form Be.

According to Molecular Orbital theory,

CN⁻,CO and NO⁺ are isoelectronic (14e⁻) and bond order is 3.

Define all the terms to find the correct answer:
(a) Entropy : It is the measurement of randomness or disorder of system.
(b) Enthalpy : It is the total heat content of system or it is the heat which is exchanged in a chemical reaction at constant temperature andpressure.
(c) Free energy : It is the energy of system which can be converted into useful work. 
(d) Internal energy : It is the energy stored within a substance.

The anticonformation is most stable in which F and OH groups are far apart as possible and minimum repulsion between two groups occurs.

In fully eclipsed conformation F and OH groups are so close that the steric strain is maximum .

Hence this conformation is most unstable.

The order of stability of these conformations is anti > gauche > partially eclipsed > fully eclipsed.

Hence a is the correct answer.

Gallium and Germanium were unknown at the time when Mendeleev's periodic table was formulated. But Mendeleev's predicted the properties of these elements and named them eka-aluminium and eka-silicon. Later when these elements were discovered, their properties were found to be similar to those of aluminium and silicon.

As we move from left to right in a period, the ionisation potential increases with increasing atomic number and the ionisation potential keeps on decreasing regularly as we move down a group. Thus the first ionisation potential of Li is less than Be and higher than Na.

CFSE = [− 0.4p + 0.6q]Δ₀
= [− 4p + 6q]Dq
p = electrons in e_g orbitals
q = electrons in t_2g orbitals
For d₁ (high spin) configuration
CFSE = [- 0.4 x + 0.6 x 0]Δ₀
=[−0.40 + 0]Δ₀ = − 0.4 Δ
= 4Dq.
(Configuration of d¹ in high spin or low spin is same).

CoCl₂ is a weak Lewis acid, reacting with chloride ion to produce salt containing the tetrahedral [CoCl₄]^2- ion. CoCl₂ is blue when anhydrous, and a deep magneta colour when hydrated, for this reason it is widely used as an indicator for water.

Oxidation state of N in HNO3 is +5---

OS of H= +1, & O = -2

H = +1
O x 3 = -2 x 3
= -6
net charge on molecule = 0

So +1 -6 +N = 0
=> N = 0+6-1
= +5

Hydrogen is a non-metal while all other members of group 1 (alkali metals) are metals.

if bromine water is added to a solution of phenol in water.

the bromine water is decolourised and a white precipitate is formed which smells of antiseptic .

The precipitate is 2,4,6- tribromophenol

Notice the multiple substitution around the ring - into all the activated positions.

Conformational isomerism is a form of stereoisomerism in which the isomers can be interconverted exclusively by rotations about formally single bonds. Such isomers are generally referred to as conformational isomers or conformers and, specifically, as rotamers.

 Mass of H2 nucleus =mass of proton =1 amu energy equivalent to 1 amu is 931 MeV so correct option is (b).

de Broglie wavelength for a particle is given by λ = h/p = h/mv, where m, v and p are the mass, velocity and momentum respectively. it is Planck's constant. Now, since all the particles are moving with same velocity, the particle with least mass will have maximum de-Broglie wavelength. Out of the given four particles (proton, α -particles, i.e. He nucleus and β-particles. i.e. electrons) β-particles has the lowest mass and therefore it has maximum wavelength.

For photoemission to take place from metal the wavelength of incident ray will be less than threshold value. For photoelectric emission from given metal plate, the incident wavelength must be less than that of ultraviolet rays assuming the wavelength of ultraviolet rays as the threshold value. Out of the given radiations, X-rays have wavelength less than that of ultraviolet rays. Thus, X-rays can cause photoelectric emission.

When you draw the electric field lines for these 2 charges they will starts from the positive charge and end at the negative charge. And when they pass through the Y axis they will be perpendicular to the Y axis, since both the charges are at equal distance and equal in magnitude. The direction of electric field is found by the tangents to the electric field at that point, since the line is parallel to x axis it's slope will also be zero, So the direction of the electric field line will be along the x axis.

If the value of potential on each small drop be V and potential on each small drop be V ^'

Since the Earth is flattened at the poles and bulges at the equator, an oblate spheroid the distance from Earth's center to sea level is roughly 21 kilometers (13 miles) greater at the equator than at the poles. Since the value of g varies inversely with the square of the earth's radius, the shorter radius at the pole will result in a greater value of g. 

The second reason is that at latitudes nearer the Equator, the outward centrifugal force produced by Earth's rotation is larger than at polar latitudes. This counteracts the Earth's gravity to a small degree – up to a maximum of 0.3% at the Equator – and reduces the value of g at the equator.

So as we move from equator to pole value of g will increase. Hence option C is the correct.

Due to higher thermal conductivity of metal than wood, heat begins to flow readily from our body to the metal surface and so we feel colder.

The reading on scale would be 
w= M (g+a)
w=80 ( 10+ 5)
w=1200 

Tension at mean position, 

mg+ 
(i) and if the body displaces by angle q with the vertical then v = 
(ii) Comparing (i) and (ii), 

cosθ = 0 Þ θ = 90º

Since the mass of the earth is infinitely large compared to that of the ball, hence velocity developed in the earth is negligible

 (Y,l and L are constant) If diameter is made four times then force required will be 16 times. i.e. 16 x 10³ N

Explanation: In an adiabatic process,
∆Q=0
∆U=∆Q-∆W=0-W=-W.

When a ray of light falls on sea shell, then its small amount first gets refracted (slightly polarised) and then almost gets reflected back (fully polarised). That is why, view of sea shell is golden due to polarisation.

Calorimeters are made up of metal only because they are good conductor of heat and hence the heat exchange is quick which the basic requirement for the working of calorimeter.