FSc mathematics

Written by Hassan Raza (Mathematics)

GIKI · ریاضی · 32 سوالات

نام: ____________________ تاریخ: ____________

The derivative of sin x is:
- A −cos x
- B −sin x
- C cos x
- D tan x
The integral of cos x with respect to x is:
- A tan x + c
- B sin x + c
- C −sin x + c
- D cos x + c
The sum of the roots of 2x² − 6x + 1 = 0 is:
- A 1/2
- B 3
- C 6
- D −3
The value of (1 + i)² is:
- A −2i
- B 1 + 2i
- C 2i
- D 2
The coefficient of x² in the expansion of (1 + x)⁵ is:
- A 5
- B 15
- C 10
- D 20
The determinant of the matrix with rows (1, 2) and (3, 4) is:
- A −2
- B 10
- C −10
- D 2
The equation of the line with slope 2 that passes through the origin is:
- A y = 2x + 2
- B y = 2x
- C x = 2y
- D y = x + 2
The arithmetic mean between 4 and 16 is:
- A 20
- B 10
- C 12
- D 8
The limit of (1 + 1/x)ˣ as x approaches infinity is:
- A 0
- B ∞
- C e
- D 1
The radius of the circle x² + y² = 49 is:
- A 3.5
- B 14
- C 7
- D 49
The integral of 1/x with respect to x is:
- A −1/x² + c
- B x ln x + c
- C 1/x² + c
- D ln |x| + c
The derivative of tan x with respect to x is:
- A −csc² x
- B cot x
- C sec² x
- D sec x tan x
The limit of (eˣ − 1) ÷ x as x approaches 0 is:
- A e
- B 1
- C ∞
- D 0
The sum of the first 10 odd numbers is:
- A 55
- B 90
- C 100
- D 110
The determinant of the matrix with rows (3, 1) and (2, 5) is:
- A 15
- B −13
- C 17
- D 13
The coefficient of x³ in the expansion of (1 + x)⁶ is:
- A 6
- B 20
- C 15
- D 30
The distance between (1, 2) and (4, 6) is:
- A √7
- B 7
- C 25
- D 5
The slope of the line 3x + 4y = 12 is:
- A 3/4
- B −3/4
- C −4/3
- D 4/3
The equation of the circle with centre (1, 2) and radius 3 is:
- A (x − 1)² + (y − 2)² = 3
- B x² + y² = 9
- C (x + 1)² + (y + 2)² = 9
- D (x − 1)² + (y − 2)² = 9
The value of tan 45° is:
- A 1
- B √3
- C 0
- D 1/2
The product of the roots of x² − 7x + 10 = 0 is:
- A −7
- B 10
- C −10
- D 7
If 2ˣ = 32, then x is:
- A 4
- B 6
- C 16
- D 5
The value of log₂ 8 + log₂ 4 is:
- A 5
- B 6
- C 4
- D 12
The 20th term of the sequence 3, 7, 11, … is:
- A 79
- B 77
- C 83
- D 80
The number of different arrangements of the letters of the word MATH is:
- A 16
- B 12
- C 24
- D 4
A and B are independent events with P(A) = 0.3 and P(B) = 0.5. Then P(A and B) is:
- A 0.8
- B 0.15
- C 0.35
- D 0.2
The dot product of the vectors (2, 1) and (1, 3) is:
- A 5
- B 7
- C 3
- D 6
The area under the line y = x from x = 0 to x = 4 is:
- A 4
- B 8
- C 2
- D 16
If y = x³ − 3x, the value of dy/dx at x = 2 is:
- A 9
- B 3
- C 12
- D 6
The sum (3 + 2i) + (1 − 5i) is:
- A 4 + 7i
- B 4 + 3i
- C 4 − 3i
- D 2 + 7i
The value of sin 90° is:
- A 1
- B √3/2
- C 1/2
- D 0
The set of all real numbers x with x² = 9 is:
- A {3, −3}
- B {3}
- C {−9, 9}
- D {9}

جوابی کلید

1. C, 2. B, 3. B, 4. C, 5. C, 6. A, 7. B, 8. B, 9. C, 10. C, 11. D, 12. C, 13. B, 14. C, 15. D, 16. B, 17. D, 18. B, 19. D, 20. A, 21. B, 22. D, 23. A, 24. A, 25. C, 26. B, 27. A, 28. B, 29. A, 30. C, 31. A, 32. A

This is a standard derivative.
The derivative of sin x is cos x.
The sum of roots is −b ÷ a = 6 ÷ 2 = 3.
(1 + i)² = 1 + 2i + i² = 1 + 2i − 1 = 2i.
The coefficient is 5C2 = 10.
The determinant is 1 × 4 − 2 × 3 = −2.
With zero intercept the line is y = mx.
The mean is (4 + 16) ÷ 2 = 10.
This is the standard limit that defines e.
The right side is r², so r = 7.
This is a standard integral.
This is a standard derivative.
This is a standard limit.
The sum of the first n odd numbers is n².
The determinant is 3 × 5 − 1 × 2 = 13.
The coefficient is 6C3 = 20.
The distance is √(9 + 16) = 5.
Write y = −(3/4)x + 3.
The standard form is (x − h)² + (y − k)² = r².
This is a standard value.
The product is c ÷ a.
2⁵ = 32.
The sum is 3 + 2 = 5.
a + 19d = 3 + 76 = 79.
The number is 4! = 24.
For independent events the probabilities are multiplied.
The product is 2 + 3 = 5.
The area is the integral of x, which is 16 ÷ 2 = 8.
The derivative is 3x² − 3, which is 9 at x = 2.
Add the real and imaginary parts separately.
This is a standard value.
Both 3 and −3 give 9 when squared.