KVPY (SA) Mock Test - 2

Fifth term of GP is 48
Third term of GP is 12
Second term of GP = ?
T_n = ar^n-1
T₅ = ar^s-1
48 = ar⁴
48 = ar² - r²
48 = 12 - r²
r² = 48/12 = 4
r = 2
T₃ = ar^3-1
12 = ar²
If r = 2 then ar² = 12
a (2)² = 12
a (4) = 12
a = 3
2^nd term, T_n = ar^n-1
T₂ = (3) (2)^2-1
T₂ = 3 (2)¹
T₂ = 6

x +1/x = 5/2
x² + 1 = 5/2 x
2x² + 2 = 5x
2x² - 5x + 2 = 0
2x² - 4x - x + 2 = 0
2x (x - 2) - (x - 2) = 0
(2x - 1) (x - 2) = 0
x = 1/2 and 2

Suppose after 'y' second, two hands of a clock become symmetric.

So, after 'y' second, angle made by hour hand with vertical = 60 - y/120 and angle made by minute hand with vertical = y/10.
So, from the given question, angles are symmetric with vertical.

60 - y/120 = y/10

⇒ 13y/120 = 60

⇒ y = 553.8 second = 9 minutes 14 seconds

Hence, two hands of a clock are symmetric with respect to the vertical line at 10h 9m 14s.

Since the sides are in A.P let the sides be x , x + d and x + 2d.
Now since smallest side is 10

Therefore, x = 10
=> sides are 10, 10 + d and 10 + 2d

We know that sum of any two sides of a triangle is greater than the third side.
=> 20 + d > 10 +2d
=> 10 + d > 2d
Since, we know that the sign of d = +
Therefore, we can subtract d.
10 > d
=> d
Since the sides are positive integers.
Therefore ,
d can hold the values 1 , 2 ,3 …, 9

Therefore, number of triangles which are possible is 9.

Pressure exerted by the liquid column, P = 77000 Nm^–2
Depth or height, h = 7 m
Acceleration due to gravity, g = 10 m/s²
Pressure exerted by liquid column, P = h × d × g
∴ 77000 = 7 × d x 10
77000 = 70 x d
Or d = 1100 kgm^–3

The magnitude of force exerted by the plane on the block will be Mg and components of force are Mg cosθ and Mg sinθ.

The combination of both the prisms will behave like a full slab. So, there would not be any spectrum, but the light will be displaced literally.

Kirchhoff's first law states that at a junction, the sum of incoming currents and outgoing currents is always zero; this is in accordance with conservation of charge. Kirchhoff's second law states that the algebraic sum of all the potential differences in the loop is always zero; this is in accordance with the conservation of energy.

All three objects (1) a metal tray, (2) a block of wood, and (3) a woollen cap will be in thermal equilibrium with the air of room. So, temperatures of the three will be same.

The IUPAC name of acetic acid (CH₃COOH) is ethanoic acid.

Out of sp³, sp and sp² hybridised carbons, sp hybridised carbon is the most electronegative. The larger the 's' character of the atom, the closer the electrons are held to the nucleus. sp³ carbons are the least electronegative as the 'p' character forces the electrons to exist far away from the nucleus, thereby decreasing electronegativity.

Atoms have the outer most electronic configuration 2s², 2p³ has atomic number 7. Nitrogen is the element with atomic number 7.

Since pressures of the gases are the same in both the containers, therefore, the final pressure will not change.

Dipole moment depends on the Electronegativity of the elements as it is the product of charge on one of the ions and distance between them. Dipole moment of CH₃Cl is gretaer than CH₃F due to more charge separation.
CH₃Cl > CH₃ F > CH₃Br > CH₃ I

New volume = 2 + 3 = 5 times
For the gas in the 1^st cylinder,
PV = P'V'
550 × 3 = P' × 5
P' = 330 mm Hg
For the gas in the 2^nd cylinder,
PV = P'V'
800 × 2 = P'5
P'= 320 mm Hg
∴ Final pressure in the two cylinders = 320 + 330 = 650 mm Hg

The reactivity of metals differs from metal to metal. The reactivity series of metals in which metals are arranged in decreasing order of reactivity is as follows:

K > Na > Ca > Mg > Al > Zn > Fe > Pb > [H] > Cu > Hg > Ag > Au

Gold has the least reactivity. So, it cannot react with oxygen present in the air at room temperature.

The correct order of the hydrocarbon compounds in terms of the decrease in the acidic character is ethyne, ethene, ethane.

The urea cycle (also known as the ornithine cycle) is a cycle of biochemical reactions that produces urea ((NH₂)₂CO) from ammonia (NH₃). This cycle occurs in ureotelic organisms. The urea cycle converts highly toxic ammonia to urea for excretion.

Roots show positive geotropism while stems show negative geotropism. Positive geotropism is the growth towards gravity.

It occurs when enough protein is not in the diet.

Anthrax is caused by bacteria.

Penicillin is an antibiotic that works against bacteria. Nystatin and fluconazole are anti-fungal agents whereas oseltamivir is an anti-viral drug.

There are four main blood groups (types of blood) – A, B, AB and O. Your blood group is determined by the genes you inherit from your parents. Each group can be either RhD positive or RhD negative, which means in total there are eight main blood groups.

Birds are warm-blooded. Their body temperature remains the same irrespective of the temperature outside.

Stroma contains DNA, ribosomes and RNA also. Stroma is a structure of chloroplast.

'On the origin of species, by means of Natural selection' was written by Charles Darwin.

Scales cover and provide protection to the body.

The primary difference between flora and fauna is that flora talks about the plant life of a region or a certain period whereas fauna represents the wildlife of a region or specific period.

Deficiency of insulin causes diabetes.

The rate of bacterial multiplication increases in warm weather. Bacteria need warmth to multiply. In summers, the temperature is high which helps in the conversion of milk to curd.

Snakes, lizards and turtles belong to class Reptilia. Animals of this class are cold-blooded, bear scales and breathe through lungs. Most of them have a three-chambered heart except crocodiles, which have four-chambered heart. They lay eggs with tough coverings.

Notochord (chord – string) is a long flexible rod that provides support to the body. Animals with notochord are called chordates and without notochord are called non-chordates. Reptiles are chordates with a true vertebral column and internal skeleton.

Bill can do it in b hours, so he does 1/b per hour. Tom does it in t hours, so he does 1/t per hour.
Then, working together, they can do 1/b + 1/t = 1/8 per hour (since they took 8 hours working together).
We also know that Tom takes 12 hours longer than Bill, so t = b + 12.
We get:1/b + 1/(b+12) = 1/8 
⇒ 16b + 96 = b² + 12b
⇒ b² - 4b - 96 = 0
(b - 12)(b + 8) = 0
Then, b = 12 and b = - 8. Now, b must be positive, so we'll ignore b = - 8.
Hence, Bill alone takes 12 hours and Tom alone takes 24 hours.

The Average atomic weight of Y = (80.99/100) × 34 + (8.00/100) × 35 + (11.01/100) × 36 = 34.29 u

Law of independent assortment was explained by dihybrid cross involving two traits.

DNA polymerase adds nucleotides to an existing nucleotide strand.

These two nitrogen bases are the purines of DNA.

A normal fetal heart rate (FHR) usually ranges from 120 to 160 beats per minute (bpm) in the in utero period. It is measurable sonographically from around 6 weeks.

The systolic and diastolic pressure of normal human being is 120 mm Hg, 80 mm Hg respectively.