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JEE Main MCQ questions — Mathematics, Physics, Chemistry for engineering entrance.

158 Q 3 Subjects 12th (PCM)
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Difficulty: All Easy Medium Hard 11–20 of 158
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Q.11 Easy Mathematics
sin 30° = ?
A 1
B 0.5
C √3/2
D 1/√2
Correct Answer:  B. 0.5
EXPLANATION

This question tests your knowledge of standard trigonometric ratios for common angles.

Step 1: Recall the standard trigonometric ratios table for common angles (0°, 30°, 45°, 60°, 90°).
Step 2: Locate the value of sin 30° from the standard table:
\[\sin 30° = \frac{1}{2} = 0.5\]
Step 3: Verify using the unit circle or right triangle approach — in a 30-60-90 triangle, the side opposite to 30° is half the hypotenuse, giving us \(\sin 30° = \frac{1}{2}\).
Step 4: Convert the fraction to decimal form:
\[\frac{1}{2} = 0.5\]

Therefore, sin 30° = 0.5

Answer: B) 0.5

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Q.12 Easy Mathematics
In triangle ABC, point D lies on BC such that AD is the angle bisector. If AB = 6 cm, AC = 9 cm, and BD = 4 cm, what is the length of DC?
A 5 cm
B 6 cm
C 7 cm
D 8 cm
Correct Answer:  B. 6 cm
EXPLANATION

By the Angle Bisector Theorem, the angle bisector divides the opposite side in the ratio of the adjacent sides.

Therefore, BD/DC = AB/AC, which gives 4/DC = 6/9.

Solving: DC = (4 × 9)/6 = 36/6 = 6 cm.

This theorem is essential for solving numerous geometry problems in competitive exams.

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Q.13 Easy Mathematics
In a right-angled triangle, the altitude drawn to the hypotenuse divides it into segments of lengths 9 cm and 16 cm. What is the length of the altitude?
A 12 cm
B 15 cm
C 18 cm
D 20 cm
Correct Answer:  A. 12 cm
EXPLANATION

By the geometric mean altitude theorem, when an altitude is drawn to the hypotenuse of a right triangle, the altitude is the geometric mean of the two segments of the hypotenuse.

Therefore, altitude = √(9 × 16) = √144 = 12 cm.

This is a fundamental property used frequently in competitive exams.

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Q.14 Easy Mathematics
If p and q are roots of x² - 5x + 6 = 0, then the value of (1/p + 1/q) is:
A 5/6
B 6/5
C 1/2
D 2
Correct Answer:  A. 5/6
EXPLANATION

Using Vieta's formulas: p + q = 5 and pq = 6.

We need 1/p + 1/q = (p+q)/pq = 5/6.

This approach avoids finding individual roots and uses the relationship between roots directly.

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Q.15 Easy Mathematics
If x, y, z are in arithmetic progression and x + y + z = 15, then the middle term is:
A 3
B 5
C 7
D 9
Correct Answer:  B. 5
EXPLANATION

When three numbers are in arithmetic progression, they can be written as (a-d), a, (a+d) where a is the middle term.

Their sum is (a-d) + a + (a+d) = 3a = 15, giving a = 5.

Therefore, the middle term y = 5.

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Q.16 Easy JEE Chemistry Chemical Kinetics
Which factor does NOT affect the rate constant k of a reaction?
A Temperature
B Concentration of reactants
C Nature of reactants
D Presence of catalyst
Correct Answer:  B. Concentration of reactants
EXPLANATION

Rate constant k is independent of reactant concentration; it depends on T, nature of reactants, and catalyst

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Q.17 Easy JEE Chemistry Chemical Kinetics
Consider the mechanism: (1) A + B ⇌ C (fast equilibrium), (2) C + D → E + F (slow). Which is the rate-determining step?
A Step 1
B Step 2
C Both steps
D Cannot be determined
Correct Answer:  B. Step 2
EXPLANATION

The slowest step in a mechanism is the rate-determining step (RDS), which is step 2

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Q.18 Easy JEE Chemistry Chemical Kinetics
For a zero-order reaction, the integrated rate law is [A] = [A]₀ - kt. If [A]₀ = 0.5 M and k = 0.02 M·s⁻¹, find time when [A] = 0
A 15 s
B 20 s
C 25 s
D 30 s
Correct Answer:  C. 25 s
EXPLANATION

0 = 0.5 - 0.02t; t = 0.5/0.02 = 25 s

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Q.19 Easy JEE Chemistry Chemical Kinetics
Which of the following statements about collision theory is INCORRECT?
A Molecules must collide with proper orientation
B All collisions lead to reaction
C Collision frequency increases with temperature
D Only collisions with energy ≥ Eₐ are effective
Correct Answer:  B. All collisions lead to reaction
EXPLANATION

Not all collisions are effective; only those with proper orientation and sufficient energy lead to reaction

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Q.20 Easy JEE Chemistry Chemical Kinetics
Half-life of a first-order reaction is 30 minutes. What fraction of reactant remains after 90 minutes?
A 1/2
B 1/4
C 1/8
D 1/16
Correct Answer:  C. 1/8
EXPLANATION

After 90 min = 3 half-lives, remaining = (1/2)³ = 1/8

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