MHT-CET Exam Prep Resources | Soulshift Education

MHT-CET

Chemistry Mathematics Physics

Q. For which value of m does the equation x² + mx + 9 = 0 have roots that are both negative? (2021)

A. -6
B. -4
C. -2
D. 2

Solution

For both roots to be negative, m must be greater than 0 and m² < 36. Thus, m must be in the range (-6, 0). The suitable value is -4.

Correct Answer: B — -4

Learn More →

Q. For which value of m does the equation x² - mx + 9 = 0 have roots 3 and 3? (2023)

A. 6
B. 9
C. 3
D. 0

Solution

The sum of the roots is 3 + 3 = 6, hence m = 6.

Correct Answer: A — 6

Learn More →

Q. For which value of p does the equation x² + px + 4 = 0 have roots 2 and -2? (2022)

A. 0
B. 4
C. -4
D. 2

Solution

Using the sum of roots: 2 + (-2) = -p, hence p = 0.

Correct Answer: C — -4

Learn More →

Q. For which value of p does the equation x² + px + 4 = 0 have roots that are both negative? (2022)

A. -8
B. -6
C. -4
D. -2

Solution

For both roots to be negative, p must be greater than 0 and p² > 16. Thus, p < -4.

Correct Answer: C — -4

Learn More →

Q. For which value of p does the equation x² + px + 9 = 0 have roots that are both negative? (2021)

A. -6
B. -4
C. -3
D. -2

Solution

For both roots to be negative, p must be positive and p² > 4*9. Thus, p > 6, so p = -4 is valid.

Correct Answer: B — -4

Learn More →

Q. For which value of p does the equation x² - px + 9 = 0 have roots 3 and 3? (2021)

A. 6
B. 3
C. 9
D. 0

Solution

The sum of the roots is 3 + 3 = 6, hence p = 6.

Correct Answer: A — 6

Learn More →

Q. How does gravitational potential energy (U) change when the distance from the center of the Earth increases? (2020)

A. It increases
B. It decreases
C. It remains constant
D. It becomes zero

Solution

Gravitational potential energy increases as the distance from the center of the Earth increases.

Correct Answer: A — It increases

Learn More →

Q. How does the gravitational force between two objects change if the mass of one object is halved?

A. It doubles
B. It halves
C. It remains the same
D. It becomes zero

Solution

Gravitational force is directly proportional to the product of the masses. Halving one mass halves the force.

Correct Answer: B — It halves

Learn More →

Q. How many different 4-digit PINs can be formed using the digits 0-9 if digits cannot be repeated?

A. 5040
B. 10000
C. 9000
D. 7200

Solution

The first digit can be any of 10 digits, the second can be any of 9, the third can be any of 8, and the fourth can be any of 7. Total = 10 * 9 * 8 * 7 = 5040.

Correct Answer: A — 5040

Learn More →

Q. How many different 4-digit PINs can be formed using the digits 0-9 if repetition is allowed? (2020)

A. 10000
B. 1000
C. 100
D. 1000

Solution

Each digit can be any of the 10 digits (0-9), so the total number of PINs is 10^4 = 10000.

Correct Answer: A — 10000

Learn More →

Q. How many different 4-digit PINs can be formed using the digits 0-9 without repetition?

A. 5040
B. 9000
C. 10000
D. 1000

Solution

The number of 4-digit PINs is P(10, 4) = 5040.

Correct Answer: A — 5040

Learn More →

Q. How many different ways can 2 out of 5 different fruits be chosen?

A. 10
B. 15
C. 20
D. 25

Solution

The number of ways to choose 2 from 5 is C(5, 2) = 10.

Correct Answer: A — 10

Learn More →

Q. How many different ways can 3 boys and 2 girls be seated in a row?

A. 30
B. 60
C. 120
D. 180

Solution

The number of ways to arrange 5 people is 5! = 120.

Correct Answer: C — 120

Learn More →

Q. How many different ways can 4 different colored balls be arranged in a row? (2020)

A. 12
B. 24
C. 36
D. 48

Solution

The number of arrangements of 4 different colored balls is 4! = 24.

Correct Answer: B — 24

Learn More →

Q. How many different ways can 4 prizes be distributed among 10 students? (2020)

A. 5040
B. 10000
C. 2100
D. 120

Solution

The number of ways to distribute 4 prizes among 10 students is 10P4 = 10! / (10-4)! = 5040.

Correct Answer: A — 5040

Learn More →

Q. How many different ways can 6 people be seated in a row? (2020)

A. 720
B. 600
C. 360
D. 480

Solution

The number of arrangements of 6 people is 6! = 720.

Correct Answer: A — 720

Learn More →

Q. How many different ways can the letters of the word 'BOOK' be arranged? (2014)

A. 12
B. 24
C. 36
D. 48

Solution

The number of arrangements of the letters in 'BOOK' is 4! / 2! = 12.

Correct Answer: B — 24

Learn More →

Q. How many different ways can the letters of the word 'MATH' be arranged?

A. 12
B. 24
C. 36
D. 48

Solution

The number of arrangements of the letters in 'MATH' is 4! = 24.

Correct Answer: B — 24

Learn More →

Q. How many grams are in 0.5 moles of glucose (C6H12O6)? (2023)

A. 90 g
B. 180 g
C. 45 g
D. 60 g

Solution

Molar mass of C6H12O6 = 6*12 + 12*1 + 6*16 = 180 g/mol. Mass = 0.5 moles x 180 g/mol = 90 g.

Correct Answer: A — 90 g

Learn More →

Q. How many grams are in 4 moles of potassium chloride (KCl)? (2022)

A. 74 g
B. 148 g
C. 296 g
D. 37 g

Solution

Molar mass of KCl = 39 + 35.5 = 74.5 g/mol. Mass = 4 moles x 74.5 g/mol = 298 g.

Correct Answer: C — 296 g

Learn More →

Q. How many grams are in 4 moles of sulfuric acid (H2SO4)? (2023)

A. 196 g
B. 98 g
C. 392 g
D. 294 g

Solution

Molar mass of H2SO4 = 2*1 + 32 + 4*16 = 98 g/mol. Mass = 4 moles x 98 g/mol = 392 g.

Correct Answer: C — 392 g

Learn More →

Q. How many grams of KCl are needed to prepare 0.5 M solution in 500 mL of water? (2023)

A. 14.9 g
B. 7.45 g
C. 29.8 g
D. 3.73 g

Solution

Molarity = moles/volume(L). Moles = 0.5 mol/L * 0.5 L = 0.25 mol. Mass = moles * molar mass = 0.25 mol * 74.5 g/mol = 18.625 g.

Correct Answer: B — 7.45 g

Learn More →

Q. How many grams of KCl are needed to prepare 250 mL of a 0.5 M solution? (2023) 2023

A. 7.45 g
B. 12.5 g
C. 9.25 g
D. 5.25 g

Solution

Molar mass of KCl = 74.55 g/mol. Grams = Molarity * Volume (L) * Molar mass = 0.5 M * 0.25 L * 74.55 g/mol = 9.31 g.

Correct Answer: A — 7.45 g

Learn More →

Q. How many grams of KCl are needed to prepare 250 mL of a 2 M solution? (2023)

A. 37.25 g
B. 50 g
C. 75 g
D. 25 g

Solution

Molar mass of KCl = 74.55 g/mol. Grams = moles × molar mass = 0.5 moles × 74.55 g/mol = 37.25 g.

Correct Answer: A — 37.25 g

Learn More →

Q. How many grams of KCl are needed to prepare 250 mL of a 2 M solution? (Molar mass of KCl = 74.5 g/mol) (2023)

A. 37.25 g
B. 74.5 g
C. 18.625 g
D. 9.25 g

Solution

Grams = moles × molar mass = (2 moles/L × 0.25 L) × 74.5 g/mol = 37.25 g.

Correct Answer: A — 37.25 g

Learn More →

Q. How many liters of a 0.5 M NaOH solution are needed to obtain 1 mole of NaOH? (2023)

A. 1 L
B. 2 L
C. 0.5 L
D. 0.25 L

Solution

Volume = moles / molarity = 1 mole / 0.5 M = 2 L.

Correct Answer: A — 1 L

Learn More →

Q. How many liters of a 0.5 M solution contain 2 moles of solute? (2023)

A. 2 L
B. 4 L
C. 1 L
D. 0.5 L

Solution

Volume = moles / molarity = 2 moles / 0.5 M = 4 L

Correct Answer: B — 4 L

Learn More →

Q. How many liters of a 3 M solution can be made from 6 moles of solute? (2023)

A. 1 L
B. 2 L
C. 3 L
D. 4 L

Solution

Volume = moles / molarity = 6 moles / 3 M = 2 L.

Correct Answer: B — 2 L

Learn More →

Q. How many molecules are in 0.1 moles of oxygen gas (O2)? (2021)

A. 6.022 x 10^22
B. 6.022 x 10^23
C. 1.2044 x 10^23
D. 3.011 x 10^23

Solution

Number of molecules = moles x Avogadro's number = 0.1 moles x 6.022 x 10^23 molecules/mole = 6.022 x 10^22 molecules.

Correct Answer: A — 6.022 x 10^22

Learn More →

Q. How many molecules are in 0.25 moles of oxygen gas (O2)? (2022)

A. 3.011 x 10^23
B. 6.022 x 10^22
C. 1.2044 x 10^23
D. 1.5055 x 10^23

Solution

Number of molecules = moles x Avogadro's number = 0.25 moles x 6.022 x 10^23 molecules/mole = 1.5055 x 10^23 molecules.

Correct Answer: B — 6.022 x 10^22

Learn More →

Showing 691 to 720 of 2530 (85 Pages)

MHT-CET

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?