JEE Advanced Mix Test 71

Result

JEE Advanced Mix Test 71

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Weekly Quiz Competition

Question 1
4 / -1

A solid cube is placed on a horizontal surface. The coefficient of friction between them is μ, where μ < 1/2 . A variable horizontal force is applied on the cube’s upper face, perpendicular to one edge and passing through the mid-point of that edge. The maximum acceleration with which it can move without toppling is

A
μg

B
2μg

C
g/2(1 - 2μ)

D
(μ + 1/2)

Solution
Question 2
4 / -1

A spherical body of mass m, radius r and moment of inertia I about its centre moves along the x-axis. Its centre of mass moves with velocity = v₀ and it rotates about its centre of mass with angular velocity ω₀.L_O = lω₀ + mv_or . The angular momentum of the body about the origin O is

A
L₀, only if v₀ = rω₀

B
greater than L₀ if v₀ > ω₀r

C
less than L₀, if v₀> ω₀r

D
L_o for all values of ω₀ and v₀

Solution

As we know

L₀ = L₁ + L₂

L₁ = due to rotational motion

L₂ = due to linear motion.
Question 3
4 / -1

The base of a hollow right cone of semi vertical angle 30^o is fixed to a horizontal plane. Two particle each of mass m are connected by a light inextensible string which passes through a small hole in the vertex of the cone. One particle A hangs at rest inside the cone. The other particle B moves on the outer smooth surface of the cone at a distance ℓ from vertex in a horizontal circle with centre at A. Neglecting friction, now answer the following.

The tention in the string is

A
√3/2 mg

B
1/2mg

C
2/√3mg

D
none of these

Solution
Question 4
4 / -1

The base of a hollow right cone of semi vertical angle 30^o is fixed to a horizontal plane. Two particle each of mass m are connected by a light inextensible string which passes through a small hole in the vertex of the cone. One particle A hangs at rest inside the cone. The other particle B moves on the outer smooth surface of the cone at a distance ℓ from vertex in a horizontal circle with centre at A. Neglecting friction, now answer the following.

The angular velocity of B is

A

B

C

D

Solution
Question 5
4 / -1

Where X is a compound that forms azodye with benzene diazonium chloride in faintly basic medium.

Hence the products P, X and Y are respectively.

A

B

C

D

Solution
Question 6
4 / -1

A white compound (A) on strong heating decomposes to produce two products (B) and (C). (B) on reaction with white phosphorus produces (D), which is a strong dehydrating agent. (D) on reaction with perchloric acid converts it to its anhydride.

The compound (A) is

A
NH₄ NO₂

B
NH₄ ClO₄

C
NH₄)₂ Cr₂o₇

D
NH₄ NO₃

Solution
Question 7
4 / -1

A white compound (A) on strong heating decomposes to produce two products (B) and (C). (B) on reaction with white phosphorus produces (D), which is a strong dehydrating agent. (D) on reaction with perchloric acid converts it to its anhydride.

The product/s obtained on hydrolysis of (D) is

A
Mixture of H₃PO₃ and H₃PO₄

B
only PH3

C
only H₃PO₃

D
Mixture of H₃PO₃ and H₃PO₂

Solution
Question 8
4 / -1

PQ is the double ordinate of the parabola y2 = 4x which passes through the focus S. ΔPQA is an isosceles right angle triangle, where A is on the axis of the parabola. Line PA meets the parabola at C and QA meets the parabola at B.

The area of trapezium PBCQ is

A
96 sq units

B
64 sq units

C
72 sq units

D
48 sq units

Solution

end point of latus rectum P(1, 2) & Q(1, -2) ΔPAQ is isosceles right angled

∴ slope of PA is – 1

In equation y – 2 = - (x – 1)

x + y – 3 = 0

similarly equation of line QB

x – y – 3 = 0

solving x + y – 3 = 0 with parabola y² = 4x

(3-x)2 = 4x

x = 1,9

∴ co-ordinate of B & C are (9, -6) & (9, 6) respectively

Area of trapezium

= 1/2 x (12 + 4) x 8

= 64 sq units
Question 9
4 / -1

PQ is the double ordinate of the parabola y2 = 4x which passes through the focus S. ΔPQA is an isosceles right angle triangle, where A is on the axis of the parabola. Line PA meets the parabola at C and QA meets the parabola at B.

The circumradius of trapezium PBCQ is

A
6√5

B
3√6

C
2√10

D
5√3

Solution
Question 10
4 / -1

Let z be a complex number satisfying z² + 2αz + 1 = 0 where α is a parameter which can take any real value.

The roots of this equation lie on a certain circle if

A
-1<α<1

B
α >1

C
α <1

D
none of these

Solution

one root lies inside the unit circle and other will outside the unit circle case||| where α is very large then