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3)The value of \( \frac{1 – \tan^2 45^\circ}{1 + \tan^2 45^\circ} \) is:
A) 1
B) '0'
C) -1
D) \( \infty \)
View Answer
B) '0'
Explanation:tan 45° = 1
⇒ value = \( \frac{1 – 1}{1 + 1} \)
= 0
4)The value of \( 1 + \sec 19^\circ \sin 71^\circ \) is:
A) 2
B) 1
C) 3
D) 1.5
View Answer
A) 2
Explanation:sin 71° = cos 19°
⇒ sec 19° × sin 71°
= \( \frac{1}{\cos 19°} \) × cos 19° = 1
⇒ total = 1 + 1 = 2
5)The pair of linear equations \( 2x – 3y = 8 \) and \( 4x – 6y = 9 \) represents:
A) The system has a unique solution
B) The system has infinitely many solutions
C) The system has no solution
D) The system represents two parallel lines
View Answer
D) The system represents two parallel lines
Explanation:Multiply first equation by 2
⇒ 4x – 6y = 16
Compare with 4x – 6y = 9
⇒ inconsistent
⇒ parallel lines
6)The solution of system of equations \( \frac{x}{2025} + \frac{y}{2026} = 2 \) and \( \frac{2x}{2025} – \frac{y}{2026} = 1 \) is:
A) x = 4025, y = 2026
B) x = 4040, y = 2025
C) x = 2025, y = 2026
D) x = 4030, y = 2027
View Answer
C) x = 2025, y = 2026
Explanation:Let \( a = \frac{x}{2025} \), \( b = \frac{y}{2026} \)
Then:
a + b = 2
2a – b = 1
Add ⇒ 3a = 3
⇒ a = 1
⇒ x = 2025
b = 1
⇒ y = 2026
7)The roots of quadratic equation \( 2x^2 + x – 4 = 0 \) are:
A) \( \frac{-1 \pm \sqrt{33}}{4} \)
B) \( \frac{-1 \pm \sqrt{33}}{2} \)
C) \( \frac{-1 \pm \sqrt{33}}{2} \)
D) \( \frac{-1 \pm \sqrt{33}}{4} \)
View Answer
A) \( \frac{-1 \pm \sqrt{33}}{4} \)
Explanation:Using quadratic formula:
\( x = \frac{-1 \pm \sqrt{33}}{4} \)
8)The total surface area of a hemisphere solid having radius 7 cm is:
A) 616 cm²
B) 462 cm²
C) 154 cm²
D) 77 cm²
View Answer
B) 462 cm²
Explanation:Total surface area of hemisphere = 3πr²
= 3 × \( \frac{22}{7} \) × 7 × 7
= 462 cm²
9)If \( \frac{5}{x+1} + \frac{1}{y-3} = 2 \) and \( \frac{6}{x+1} – \frac{3}{y-3} = 1 \), then \( x = \dots \):
A) 1
B) 2
C) 3
D) 4
View Answer
B) 2
Explanation:Let \( a = \frac{1}{x+1} \), \( b = \frac{1}{y-3} \)
Then:
5a + b = 2
6a – 3b = 1
Solve ⇒ \( a = \frac{1}{3} \)
⇒ x + 1 = 3
⇒ x = 2
10)Which term of G.P. \( 2, 2\sqrt{2}, 4, \dots \) is 128?
A) 7
B) 8
C) 13
D) 10
View Answer
C) 13
Explanation:a = 2, r = √2
nth term = 2(√2)^(n-1)
= 2 × \( 2^\frac{n-1}{2} = 2^\frac{n+1}{2} \)
Set = 128 = 2⁷
⇒ \( \frac{n+1}{2} \) = 7
⇒ n = 13
