SRMJEE Mock Test - 1 (Engineering) - JEE MCQ

This is a balanced Wheatstone's bridge.
Therefore,
10/40 = 7/X
This gives X = 28 Ω.
Hence, the correct choice is (4).

Coin will revolve with the record if

So, the coin placed at 4 cm will revolve with the record.

In classical mechanics, when any charged particle will be in acceleration, it will radiate energy in form of electromagnetic waves and will lose its energy.
In Rutherford's model, electron revolves around the nucleus and will be in accelerated motion. So it will lose kinetic energy in form of electromagnetic waves and will cause decrease in radius.

For a square loop of side l, perimeter = 4l, current = i. Magnetic field at the center:

For a circular loop with the same perimeter (4l), radius  Magnetic field at the center:

Ratio:

The filament of the incandescent lamp is of tungsten material.  Since the filament is a metallic conductor so when the lamp is switched on, heat generation takes place which drastically increases the resistance of the incandescent lamp. As the temperature rises, the conductor's resistance increases.
Thus, the resistance of the incandescent lamp is greater when switched on.

The reactivity series of metals is:

It is clear that hydrogen is present above Cu in the reactivity series i.e., it is more reactive than Cu. So, Cu cannot displace hydrogen from dilute acids.

According to Raoult's law, relative lowering of vapour pressure ∝ mole fraction of solute.
Thus, mole fraction of solute = 0.0125
Mole fraction of a solute is related to the molality by the following expression.


where, X = mole fraction of solute
m_B = moleular weight of solvent
m = molality

= 0.70

Due to resonance, the C-Cl has double bond characteristic and thus, it becomes difficult to break that bond. Hence, vinyl chloride will not react with phenol to give ethers

Schizophrenia is a type of psychosis characterised by alterations in thought, perception, emotions, language, sense of self, and behaviour.

Aldehydes and ketones containing no α-H-atom on reaction with 50% NaOH or KOH, undergo disproportionation to give an alcohol and Na or K salt of an acid. This reaction is called Cannizaro reaction.
Acetaldehyde does not show Cannizaro reaction due to presence of α-hydrogen atom.
Rather, they undergo aldol condensation reaction with dilute base.

2A + B → product
[B] is doubled, half-life did not change.
Half-life is independent of change in concentration of reactant i.e., the first order.
First order w.r.t. B:

When [A] is doubled, the rate increased by two times.
First order w.r.t. A:
Hence, net order of reaction = 1 + 1 = 2
Unit for the rate constant = concentration⁽¹⁻ⁿ⁾t⁻¹
=(mol.L⁻¹)⁻¹ s⁻¹
= L mol⁻¹ s⁻¹

In triangle ABC, ∠A = 60°
We know that cos A =
cos 60° =
Since, cos 60° = 1/2


⇒ 6c = 18 + 2c² - 32
⇒ 2c² - 6c - 14 = 0
⇒ c² - 3c - 7 = 0

So, required equation is c² - 3c - 7 = 0.

Given line: y = mx + c ... (1)
Suppose the line in (1) touches the ellipse (x²/a²) + (y²/b²) = 1. ... (2)
Eliminating 'y' from (1) and (2),
x²(b² + a²m²) + 2a²mcx + a²(c² - b²) = 0 ... (3)
If (1) touches (2), then the roots of (3) must be coincident, i.e. D = 0.
i.e. (2a²mc)² = 4(b² + a²m²) a²(c² - b²)
Solving this, we get c = +
So, the equation of the tangent is y = mx + for all real m.
c² = a²m² + b²

(i) Since f(2 + 3i) = f(2 - 3i), f is many-one.
(ii) Since the modulus of a complex number can never be negative, range(f) ≠ R. So, f is into.

Let,

Now,

Also,

hence, 

or

Let 

By multiplying each element a_ij by k^i−j we get,

Taking 1/k common out of R₁ and k common out of R₃ we get,

Taking k common out of C₁ and 1/k common out of C₃ we get,

⇒ |B| = |A|

Given, k₁|A| + k₂|B| = 0 

We have x = 2y + 3, a straight line

Required area = Area of shaded region

= 6 sq. units.

In the question, the equation of directrix and tangent with the point of contact is given.

We need to find the length of the semi latus rectum.

We know that the semi-latus rectum is the perpendicular distance of focus from the directrix. So, we need to find the focus.

Now to find focus, let's consider foot of the perpendicular from point (2, 1) on the directrix of the parabola to be (α, β).

Now as we know image of point (α, β) w.r.t. tangent is focus which is let's say (γ, δ).

Since, equation of directrix is x + y + 2 = 0

Semi-latus rectum = Distance of focus from directrix

Here, we are only concerned with the slopes of the given pair of straight lines.

So, take the homogeneous part of the equation.

The homogeneous part of the given equation is y² + 3xy = 0, which represents the straight lines y = 0 and y + 3x = 0, both passing through the origin.

Now, the lines perpendicular to these lines are x = 0 and x - 3y = 0, both passing through the origin.

So, the combined equation of these lines is:

x(x - 3y) = 0

⇒ x² - 3xy = 0.

Let I = ∫1 ⋅ f⁻¹(x) dx.

Applying integration by parts, we get:

∫(u × v) dx = u ∫v dx − ∫((d/dx(u))(∫v dx)) dx

Thus,

I = f⁻¹(x) ∫1 dx − ∫(d/dx(f⁻¹(x)) ∫1 dx) dx

This simplifies to:

I = f⁻¹(x) ⋅ x − ∫x ⋅ (f⁻¹(x))' dx

Let f⁻¹(x) = t.
Then x = f(t), and we have dx = f'(t) dt.

Also, (f⁻¹(x))' dx = dt.

Thus, we can rewrite I as:

I = f⁻¹(x) ⋅ x − ∫f(t) ⋅ dt

Given that ∫f(x) dx = g(x), we have:

I = f⁻¹(x) ⋅ x − g(t) + C

So, we obtain:

∫f⁻¹(x) dx = x ⋅ f⁻¹(x) − g(f⁻¹(x)) + C.

Here, it is given that, a man standing on the bank of river and the angle of elevation of the top of the tower on the opposite bank is 45°.
Let h be the height of the tower and x be the breadth of the river
So from right angle triangle tanθ = P/B
Now, tan45° = h / x ⇒  x = h.

Let the numbers be x, x + 2, and x + 4.

Given:
The sum of three consecutive odd numbers is 1383.

x + (x + 2) + (x + 4) = 1383

3x + 6 = 1383

Solving for x:

3x = 1383 - 6

3x = 1377

x = 1377 ÷ 3 = 459

Thus, the three consecutive odd numbers are 459, 461, and 463.

Conclusion: The required largest number is 463.

Let y = (x − a)(x − c) / (x − b) = (x² − (a + c)x + ac) / (x − b)

Rearranging, we get:
y(x − b) = x² − (a + c)x + ac

Expanding further:
x² − (a + c + y)x + ac + by = 0 ----(1)

Since x is real, the discriminant of equation (1) must be non-negative:

(a + c + y)² − 4(ac + by) ≥ 0

Expanding:
y² + 2(a + c)y + (a + c)² − 4ac − 4by ≥ 0

Rearranging:
y² + 2(a + c − 2b)y + (a − c)² ≥ 0 ----(2)

Since y takes all real values, inequality (2) must hold for all y. This is possible only if:

4(a + c − 2b)² − 4(a − c)² < 0 (since the coefficient of y² is positive)

Factorizing:
(a + c − 2b + a − c)(a + c − 2b − a + c) < 0

Simplifying:
(2a − 2b)(2c − 2b) < 0

Dividing by 4:
(a − b)(c − b) < 0

Thus, b lies between a and c. One possible ordering is a < b < c.

Let the C.P. of each article be x.

C.P. of 15 articles = 15x
S.P. of 15 articles = C.P. of 10 articles = 10x

Loss = 15x - 10x = 5x

Loss% = (Loss / C.P.) × 100
= (5x / 15x) × 100 = 33.33%

If we read the above word carefully, we will find that it is made with two different words. We can make two independent words using POSTSCRIPT without changing order of letters are as following-
'POST' and 'SCRIPT'
So, the answer will be two.

The line "With an increase in competition and marketing efforts, poverty-alleviation experts are concerned that people will be talked into loans they wouldn't otherwise want" suggests the answer. So, option 2 is the correct answer.
Option 1 presents the competition in a positive light, which is not the case. Nothing about micro-financing firms' marketing funds has been mentioned, so option 3 is incorrect. As the writer does not mention anything about the loan recovery means of the micro-financing firms, option 4 is also incorrect.