VITEEE PCME Mock Test - 7 - JEE MCQ

Height of two tower are 20 m and 80 m



5h = 80 ⇒ h = 16 m

P(X = k) =
Now, P(X = k + 1) = r(k) P(X = k)
⇒
⇒ r(k) = λ/(k+1)

Given, Mean = 4, Variance = 3
np = 4, npq = 3

Mode is an integer x such that

⇒ 3.25 < x < 4.25
∴ x = 4

Let α, β be the roots of x² + bx + c = 0, and γ, δ be the roots of x² + qx + r = 0.

For the first equation: α + β = -b, αβ = c

For the second equation: γ + δ = -q, γδ = r

Given that αβ = γδ (i.e., c = r), we can proceed with the following relationship:

(α - β)²(α + β)² = (γ - δ)²(γ + δ)²
(Squaring both sides and applying components and division)

Then, αβ(α + β)² = γδ(γ + δ)²
(After subtracting -1 from both sides)

This simplifies to:
c * b² = r * q²

Hence, the correct answer is D) b²r = q²c.

Let O be the center of the circle.

Since the hexagon is regular, we have:
∠A₀OA₁ = 360° / 6 = 60°

Thus, △A₀OA₁ is an equilateral triangle. From the unit circle, A₀O = 1.

Hence, A₀A₁ = 1.

Also, A₀A₂ = A₀A₄.

We know that a perpendicular drawn from the center bisects the chord, so:

A₀A₂ = A₀A₄ = 2 × A₀D
= 2 (OA₀ sin 60°)
= 2 × (1) × (√3/2) = √3

Thus,
(A₀A₁) × (A₀A₂) × (A₀A₄) = (1) × (√3) × (√3) = 3

Let, g(x) = ax + b

Now at x = 0, equating both L.H.L and R.H.L we get

now for

Taking log both side we get,

arg = arg(z + i) - arg(z - i) = tan^-1- tan^-1 = tan^-1 = , i.e. x² + y² - 2x = 1 is the equation of a circle.

The given lines are coplanar if the normal to the plane containing these lines is perpendicular to both of them.
Since the given lines are parallel to the vectors and ,
so, the normal to the plane is parallel to , which is perpendicular to the line joining the points on the plane with position vectors and
⇒ , which is the required condition for the given lines to be coplanar.

The phase angle between voltage V and current I is π/2.
Power factor,

Hence, the power consumed is zero.

In beta decay, atomic number increases by 1 whereas the mass number remains the same. Therefore, following equation can be possible.

The slope of the (I-V) graph is given by 1/R. In the CD region, the slope of the I-V curve is negative, meaning R is negative. Therefore, the portion corresponding to negative resistance is the CD region.

The radio waves are part of electromagnetic waves. They have the longest wavelength in the electromagnetic spectrum. Their size can vary from a foot to a few miles long. They are used to transmitting data for all sorts of things; radios, satellites, radar etc.

The separation between the images formed by extreme wavelengths of the visible range is called the longitudinal chromatic aberration.

It is given by the formula:

Longitudinal chromatic aberration = Dispersive power (ω) × Mean focal length (fy)

Given:

• Dispersive power (ω) = 0.02
• Mean focal length (fy) = 20 cm

Substituting the values:

Longitudinal chromatic aberration = 0.02 × 20 = 0.40 cm

When object is placed between F and pole of a convex lens then a virtual, erect and magnified image will be formed on the same side behind the object.

Given,

m = 25 kg,
v_initial = 2 m/s.

So, the initial kinetic energy of the body:

KE_initial = (1/2) m v²
KE_initial = (1/2) × 25 × 4 = 50 J.

Here, work done = area of F−x graph.

⇒ W = area of triangle

⇒ W = (1/2) × base × height
⇒ W = (1/2) × 4 × 20 = 40 J.
Since the force is resistive, W = −40 J.

By the work-energy theorem,
Work done = change in kinetic energy.

W = KE_final − KE_initial
−40 = KE_final − 50
KE_final = 10 J.

For polyfunctional acids, pI is also the pH midway between the pK_a values on either side of the isoionic species. For example, the pI of aspartic acid is 2.95.
pI = (pK₁ + pK₃)/2 = (2.0 + 3.9)/2 = 2.95

From FLOT, ΔU = q + W
For adiabatic process, q = 0
∴ ΔU = w

Since only 50% of the expected product is obtained:
5 L of N₂ reacts with 15 L of H₂ to form 10 L of NH₃.
used = 5 L, left = 30 - 5 = 25 L
used = 15 L, left = 30 - 15 = 15 L
NH₃ formed: 10 L

Carbohydrates are polyhydroxy aldehydes or polyhydroxy ketones. >C=O and −OH are functional groups of typical ketose, while −CHO and −OH are functional groups of typical aldose. Both aldose and ketose contain a carbonyl group. Carbohydrates are polyhydroxy aldehydes or polyhydroxy ketones, which give aldehydic as well as ketonic groups upon hydrolysis.

It is example of intramolecular aldol condensation.

'Dig into' means to find out her past to know the reality.

We cannot use 'Smoke' as a subject to the verb. The correct way to use it as a noun/subject is by converting it to a gerund.
Gerund is a verb form which functions as a noun. Thus, 'smoke' will get converted to 'smoking.'

In the given sentence, we have to find what will be best suited in place of the underlined part in the sentence.
My opinion for the film is that it will bag the national award.
Here, ''opinion for'' should be replaced with ''opinion about''. ''Opinion about'' means ''any judgement or view about something or place or person''. In this sentence, it is about the National award.
Hence, 'opinion about' is the correct answer. 

The passage sums up one main thought - lawlessness and social non-conformity during the twenties as it mentions Law was a bad joke … organized crime ruled the cities … America's break with the past. It is best illustrated by option 2.

As per the given above table, we see

In school A, income from grants = ₹60 thousands.

Income from tuition fee = ₹120 thousands.

School A = 60/120 = 0.5

In school B, income from grants = ₹54 thousands.

Income from tuition fee = ₹60 thousands.

School B = 54/60 = 0.9
In school C, income from grants = ₹120 thousands.

Income from tuition fee = ₹210 thousands.

School C = 120/210 = 0.57

In school D, income from grants =₹42 thousands.

Income from tuition fee =₹90  thousands.

School D = 42/90 = 0.47

In school E, income from grants = ₹55 thousands.

Income from tuition fee = ₹120 thousands.

School E = 55/120 = 0.46 lowest ratio income)

Therefore, school E has the lowest ratio of income by way of grants and tuition fees.

Given that ∠A = 90° in △ABC and P is a point on side AC, we use the Pythagoras' theorem to find AB:

AB² = BC² - AC²
AB² = 10² - 8²
AB² = 100 - 64
AB² = 36
AB = 6 cm

Now, applying Pythagoras' theorem in △ABP:

AP² = BP² - AB²
AP² = 9² - 6²
AP² = 81 - 36
AP² = 45
AP = √45 = 3√5 cm

Final Answer:
AP = 3√5 cm (Option D).