SAT (Stage-1) Mock Test - 67

The given circuit can be redrawn as:

For the upper arm, 6Ω and 2Ω resistance are connected in parallel and their parallel combination is in series with 1.5Ω resistance, hence its equivalent resistance is:

This resistance is in parallel with another 3Ω resistance, hence equivalent resistance of the circuit is equal to

Current supplied by the battery is:

Let two resistances be R₁ and R₂
Resistance will be maximum when they are connected in series
R₁ + R₂ = 16Ω ...1
Resistance will be minimum when they are connected in parallel.

R₁R₂ = 3 × 16 = 48 Ω ...2
Hence we can conclude R₁ = 4Ω and R₂ = 12Ω or R₁ = 12Ω and R₂ = 4Ω

Since specific resistance or resistivity depends upon material of wire, so specific resistance wil be same for both the wires. Hence, ratio will be 1 : 1.

As the observer is in denser medium and the object is in rare medium, hence ray of light travelling from denser medium to rare medium will bend away from the normal.
Apparent height of the person = Refractive index × Actual height
So, the man will appear taller than he actually is.

As the near point is greater than 25 cm, person suffering from hypermetropia. Hence, convex lens is used to correct the defect.

u = -25 cm; v = -50 cm

Power of the lens combination is

The refractive index of glass is greater than that of air, the speed of light is less in glass than in air.
The frequency of light never changes due to reflection or refraction.

wavelength decreases because speed  decreases.

Let the angle between the two mirrors be θ. The ray of light striking the first mirror is parallel to second mirror, hence, ∠BAC = θ.
The ray after reflection from second mirror becomes parallel to the first mirror, hence it will make angle θ with the mirror, so, ∠BCA = θ.
Hence, in triangle ABC, all the angles are same and equal to θ.
Hence 3θ = 180°
Or θ = 60°

Power of each bulb = 60 W
When three bulbs are connected in series, power drawn will be

Refractive index is defined as the ratio of the speed of the light in vacuum to the speed of light in medium.

Or, we can say that greater is the refractive index, lesser is the speed.
Refractive index of the diamond is maximum and the refractive index of the water is minimum in the given mediums.
So, the speed of the light is the maximum in water and the minimum in diamond.
v_water > v_glass > v_diamond

The resistance of the metal wire increases with the increase in the temperature as

Where, α is the temperature coefficient and R₀ is the resistance of the wire at temperature T₀, and R_t is the resistance of the wire at temperature T.

From ohm's law, the ratio  is defined as the resistance.

Hence, we can say that as the temperature of the metallic wire increases, the ratio  will also increase.

According to Fleming's left hand rule, if we stretch - the thumb, the first finger and the second finger - such that they are perpendicular to each other, then the first finger gives the direction of the magnetic field, the second finger gives the direction of the motion of the positive charge particle and the thumb gives the direction of the force exerted by the magnetic field on the positive charge particle. So, when a proton is projected horizontally eastwards in a uniform magnetic field, which is horizontal and southwards in direction, the proton will be deflected downwards.

The chemical reaction between barium hydroxide and ammonium chloride to form barium chloride, ammonia and water is an endothermic reaction.
This is a double displacement reaction and forms NH₄OH initially which decomposes to produce NH₃ gas and water.
All decomposition processes are endothermic.

Raw materials required for the preparation of soaps are vegetable oil, sodium hydroxide and sodium chloride.
Vegetable oil + NaOH → Soap + Glycerol
NaCl helps to precipitate out the soap once it is formed.