General MCQs

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Q701.The derivative of sin(x) with respect to x is?

Medium
A cos(x)
B -cos(x)
C -sin(x)
D 1
Other PPSC

Correct Answer: A

By standard calculus limits, d/dx[sin(x)] = cos(x).

Q702.In which quadrants is the cosine (cos) function positive?

Medium
A I and III
B II and IV
C I and II
D I and IV
Other PPSC

Correct Answer: D

By standard trigonometric quadrant definitions, cosine is positive in the 1st quadrant (where all are positive) and 4th quadrant (where x is positive).

Q703.What is the value of sin(30°)?

Medium
A 1/2
B 3.2
C 1
D 0
Other PPSC

Correct Answer: A

In trigonometry, the sine of 30 degrees is exactly 1/2 or 0.5.

Q704.Find the determinant of the 2x2 matrix with row 1 as [1, 3] and row 2 as [2, 4].

Medium
A 4
B 2
C -2
D 6
Other PPSC

Correct Answer: C

Determinant = ad - bc = (1 × 4) - (3 × 2) = 4 - 6 = -2.

Q705.Evaluate: log 3 + log 6 - log 5 =?

Medium
A log(18/5)
B log(9/5)
C log(6)
D log(15/2)
Other PPSC

Correct Answer: A

Using log properties: log 3 + log 6 = log(18). Then log(18) - log 5 = log(18 / 5).

Q706.Evaluate: 1397 × 1397

Medium
A 1951609
B 19516
C 19671609
D
Other PPSC

Correct Answer: A

1397² = 1,951,609.

Q707.What is tan(45°) equal to?

Medium
A 1
B 0.5
C -1
D None of these
Other PPSC

Correct Answer: A

By standard trigonometric unit values, the tangent of 45 degrees is exactly 1.

Q708.If 9 eggs cost Rs. 60, what is the price of 3 eggs?

Medium
A Rs. 15
B Rs. 18
C Rs. 20
D Rs. 25
Other PPSC

Correct Answer: C

Since 3 eggs is exactly 1/3 of 9 eggs, the cost will also be 1/3 of Rs. 60, which is: 60 / 3 = Rs. 20.

Q709.A pencil costs 50 paise. How many pencils can you buy with 5 rupees?

Medium
A 5
B 8
C 10
D 12
Other PPSC

Correct Answer: C

5 Rupees = 500 paise. Pencils that can be bought = 500 / 50 = 10.

Q710.Simplify: 20 ÷ (5 - 3) × 2

Medium
A 4
B 5
C 8
D 20
Other PPSC

Correct Answer: D

20 ÷ (5 - 3) * 2 = 20 ÷ 2 * 2 = 10 * 2 = 20.

Q711.Transpose of the product of matrices AB is equal to?

Medium
A Transpose of A multiplied by Transpose of B
B Transpose of B multiplied by Transpose of A
C AB itself
D Inverse of AB
Other PPSC

Correct Answer: B

According to matrix algebra, the transpose of a product of two matrices is the product of their transposes in reverse order: (AB)^T = B^T * A^T.

Q712.When Transpose of matrix B is equal to B, then it is called?

Medium
A Diagonal
B Identity
C Inverse
D Symmetric
Other PPSC

Correct Answer: D

A square matrix B is symmetric if it is equal to its transpose, i.e., B^T = B.

Q713.Matrices do not obey which of the following laws?

Medium
A Associative Law
B Distributive Law
C Inverse Law
D Commutative Law (under multiplication)
Other PPSC

Correct Answer: D

Matrix multiplication is generally non-commutative, meaning that for two matrices A and B, AB is usually not equal to BA.

Q714.cos 60° = sin:

Medium
A 60°
B 45°
C 30°
D 90°
Other PPSC

Correct Answer: C

By trigonometric co-function identities: cos(theta) = sin(90° - theta). For theta = 60°: cos 60° = sin 30° = 1/2.

Q715.Cos (90° − ∅) = sin:

Medium
A 90°
B ∅
C (90° − ∅)
D 0
Other PPSC

Correct Answer: B

According to standard trigonometric co-function identities, cos(90° - theta) is exactly equal to sin(theta).

Q716.sin² 60° + ___ = 1

Medium
A cos² 60°
B sec² 60°
C cot² 60°
D tan² 60°
Other PPSC

Correct Answer: A

By the Pythagorean trigonometric identity: sin^2(theta) + cos^2(theta) = 1. For theta = 60°, we have: sin^2 60° + cos^2 60° = 1.

Q717.If the price of 1 dozen eggs is 12 rupees, then the price of 2 and a half dozen eggs is?

Medium
A 30 rupees
B 24 rupees
C 36 rupees
D 18 rupees
Other PPSC

Correct Answer: A

Price of 1 dozen = Rs. 12. Price of 2.5 dozen = 2.5 * 12 = Rs. 30.

Q718.sin²θ + cos²θ is equal to ________?

Medium
A 2
B 1
C 4
D 5
Other PPSC

Correct Answer: B

The core Pythagorean trigonometric identity states that sin²θ + cos²θ = 1.

Q719.Tanθ can also be written as?

Medium
A cosθ / sinθ
B sinθ / cosθ
C 1/sinθ
D 1/cosθ
Other PPSC

Correct Answer: B

In trigonometry, tangent is the ratio of sine to cosine: tanθ = sinθ / cosθ.

Q720.Cosecθ is equal to?

Medium
A 1/tanθ
B 1/sinθ
C 1/cosθ
D 1/secθ
Other PPSC

Correct Answer: B

Cosecθ is defined as the reciprocal of sinθ, which is written as 1/sinθ.