JEE Main Part Test - 2 - JEE MCQ

A uniform ring of mass M and radius R is placed directly above uniform sphere of mass 8M and of same radius R. The centre of the ring is at a distance of d = √3R from the centre of sphere. The gravitational attraction between the sphere and the ring is

A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container.
As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20 mm and 1 mm respectively. The upper end of the container is open to the atmosphere.

Q. If the piston is pushed at a speed of 5 mms^–1, the air comes out of the nozzle with a speed of

If the elastic limit of copper is 1.5 × 10⁸ N/ m², determine the minimum diameter a copper wire can have under a load of 10.0 kg if its elastic limit is not to be exceeded.

A circular steel wire 2.00 m long must stretch no more than 0.25 cm when a tensile force of 400 N is applied to each end of the wire. What minimum diameter is required for the wire? ( Given Young's Modulus for steel is 20 × 10¹⁰ Pa.)

Water is flowing continuously from a tap having an internal diameter 8 × 10^-3m. The water velocity as it leaves the tap is 0.4 ms^-1. The diameter of the water stream at a distance 2 × 10^-1 m below the tap is close to

[AIEEE 2011]

There are two identical small holes on the opposite sides of a tank containing a liquid. The tank is open at the top. The difference in height between the two holes is h. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to  

Two soap bubbles with radii   come in contact. Their common surface has a radius of curvature r. Then

At what temperature is the r.m.s velocity of a hydrogen molecule equal to that of an oxygen molecule at 47°C?

The oxidation number of P in Ba(H₂PO₂)₂, Ba(H₂PO₃)₂ and Ba(H₂PO₄)₂ are respectively

How much heat will be required at constant pressure to form 1.28 kg of CaC₂ from CaO(s) & C(s) ?

Given :

Δ_fH°(CaO, s) = -152 kcal/mol

Δ_fH°(CaC₂, s) = -14 kcal/mol

Δ_fH°(CO, g) = -26 kcal/mol

From the following data, the heat of formation of Ca(OH)_2(s) at 18°C is ………..kcal:

How many litres of water must be added to litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with pH of 2? 

 [AIEEE-2013]

For the following electrochemical cell reaction at 298 K,
 
E^°cell = 1.10 V

A 0.10 M solution of a weak acid, HX, is 0.059% ionized. Evaluate K_a for the acid.

AgCI(s)is sparingly soluble salt,

AgCl (s)  Ag⁺(aq) + Cl^-(aq)

There is

If the coefficients of (r +1)th term and (r + 3)th term in the expansion of (1+x)²ⁿ be equal then

In the expansion of (1+x)⁶⁰, the sum of coefficients of odd powers of x is

The middle term in the expansion of (1+x)²ⁿ is

The mid points of the sides of a triangle are (5, 0), (5, 12) and (0, 12), then orthocentre of this triangle is

Area of a triangle whose vertices are (a cos q, b sinq), (–a sin q, b cos q) and (–a cos q, –b sin q) is

If A(cosa, sina), B(sina, – cosa), C(1, 2) are the vertices of a ΔABC, then as a varies, the locus of its centroid is

The locus of a variable point whose distance from the point (2, 0) is 2/3 times its distance from the line x = 9/2 is

The locus of a point such that two tangents drawn from it to the parabola y² = 4ax are such that the slope of one is double the other is

T is a point on the tangent to a parabola y² = 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Then

The focus of the parabola x²−8x+2y+7 = 0 is

The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one-year old child. If the average age of the family now is λ, then the number of divisors of λ are