Pre-Test Exam-2022_H. Maths_MCQ_EV_Sample Questions
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Subject Code: 2 6 5
BAF Shaheen College Dhaka
Pre-Test Examination ( Model Question) 2021 Subject : Higher Mathematics (M.C.Q)
Time – 25 minutes Full Marks -25
Darken the circle ( ) of the correct option from the following alternatives.
1. If −1, 0 𝑎𝑛𝑑 2 be three roots of 𝑓(𝑥) = 0, three roots of 𝑓(3𝑥) = 0 be -
a .−3, 0, 6 b. 0, − 1
3, 0, 1
6 c. 0,1
3, −2
3 d. 0, − 1
3,2
3
2. 𝑥2+ 𝑦2+ 2𝑥 − 3𝑦 + 1 = 0 touches the x-axis then point of contact be –
a. (1,0) b. (-1,0) c. (0,1) d. ( 3
2,0) 3. Following figure represent -
a .𝐬𝐢𝐧−𝟏𝒙 b. 𝐜𝐨𝐬−𝟏𝒙 c. 𝐭𝐚𝐧−𝟏𝒙 d. 𝐜𝐨𝐭−𝟏𝒙
4. Middle point of three sides of a triangle are respectively (2, −5), (4, 3) and (3, −4) centroid of the triangle be -
(a) (4, −3) (b) (−3,4) (c) (3, −2) (d) (−3,2) 5. By the straight line 4𝑥 − 5𝑦 − 20 = 0 -
(i)Length of intercept part from 𝑥 – axis = 5 unit (ii) Slope of the straight line = 4
5
(iii) Area of the triangle with both axes = 10 square unit.
Which one of following is true?
(a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii
6. For which condition, sum of two roots of the equation 𝑥3− 𝑝𝑥2+ 𝑞𝑥 − 𝑟 = 0 be zero?
a. 𝑝 + 𝑞 + 𝑟 = 0 b. 𝑝𝑞 − 𝑟 = 0 c . 𝑝𝑟 − 𝑞 = 0 d. 𝑞𝑟 − 𝑝 = 0
7. For which value of 𝑘, the expression 4𝑥2+ 12𝑥 + 𝑘 will perfect square?
a.3 b. 4 c. 6 d. 9
8. For which value of 𝑘, two root of the equation 𝑥2 + (𝑘2 − 4)𝑥 + 2𝑘 − 6 = 0 be reciprocal and opposite sign each other?
a. ±√3 b. ±√5 c. 5
2 d.− 5
2
9. Graph of 𝑥 + 𝑦 = 0 be –
a. b. c. d.
10. If the three roots of the equation 𝑝𝑥3+ 𝑞𝑥 + 1 = 0 are 𝑎, 𝑏, 𝑐 then what is the value of 𝑎𝑏 + 𝑏𝑐 + 𝑐𝑎 ?
a. −𝑞
𝑝 b. 𝑞
𝑝 c. −1
𝑝 d. 0
Pre-Test Exam-2022_H. Maths_MCQ_EV_Sample Questions
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11. Length of the latus rectum of the parabola 𝑥2− 4𝑥 + 12𝑦 − 40 = 0 be in unit -
a.2 b. 11
3 c. 12 d. 48
12. If the line 𝑦 = 3𝑥 + 1 touches the parabola 𝑦2 = 4𝑎𝑥 then length of the latus rectum of the parabola be
a. 1
3 b. 3
4 c. 12 d. 16
On the basis of following information answer the question no. 14 & 15
In a parabola vertex (4,-3), length of latus rectum 4 units and axis is parallel to x- axis.
13. Equation of parabola is –
a. (𝑦 + 3)2 = 16(𝑥 − 4) b. (𝑦 + 3)2 = 4(𝑥 − 4) c. (𝑦 − 3)2 = 16(𝑥 + 4) d. (𝑦 − 4)2 = 4(𝑥 − 3) 14. . Equation of the axis of the parabola is
a. 𝑦 + 3 = 0 b. 𝑦 − 3 = 0 c. 𝑥 − 4 = 0 d. 𝑥 − 4 = 0 15. sin(2 sin−1𝑥) =?
a. √(1 − 𝑥2) b.2𝑥√(1 − 𝑥2) c. 2𝑥 d. 𝑥
16. If 2 tan−1𝑥 = sin−1𝑝 then value of p be – a. 2𝑥
1+𝑥2 b. 2𝑥
1−𝑥2 c.2𝑥 d. 𝑥
17. i) cosec−1 1
𝑥+ sin−1√1 − 𝑥2 =𝜋
2
ii) 2 cot−1𝑥 = cot−1(𝑥2−1
2𝑥 ) iii) sin−1𝑥 = cot−1( 𝑥
√1−𝑥2)
On the basis of above information which one of following is true?
a. i and ii b. i and iii c. ii and iii d. i, ii and iii
18. lim
𝑥→0 1
𝑥𝑙𝑛(1 + 𝑥) = ?
(a) 1 (b) 1
2 (c) e (d) 0 19. 𝑓(𝑥) = 𝑥3− 6𝑥2+ 9𝑥 + 5
(i)In the interval 𝑥 < 1 the function be increased.
(ii) In the interval 𝟏 < 𝒙 < 𝟑 the function be decreased.
(iii) In the interval 𝟑 < 𝐱 the function be increased.
Which one of following is true?
(a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii 20. In which interval the function 𝑓(𝑥) = 𝑥3 − 3𝑥 + 5 is increasing?
a. (−1,1) b. (−∞. −1) ∪ (1, ∞)
c. (−2,3) d. (−∞, −1] ∪ [1, ∞)
21. lim
𝑥→0 sin 7𝑥 tan 9𝑥=?
a. 9
7 b. 49
81 c. 7
9 d. 1
22. Derivative of sec−1(1+𝑥2
1−𝑥2) with respect to sin−1( 2𝑥
1+𝑥2) be –
a. −1 b. 0 c. 1 d. 1
1+𝑥2
23. Which equation of followings is not circle?
a. 𝑥2 + 𝑦2− 2𝑥 − 2𝑦 − 1 = 0 b. 𝑥2+ 𝑦2− 2𝑥 − 2𝑦 − 1 = 0 c. 𝑥2 + 𝑦2+ 4𝑥 + 2𝑦 = 0 d. 𝑥2+ 𝑦2+ 2𝑥 − 2𝑦 + 9 =0 24. 𝐭𝐚𝐧 𝒙 𝐭𝐚𝐧 𝟐𝒙 = 𝟏 , 𝒇𝒐𝒓 𝒏 ∈ 𝒁 , 𝒙 =?
a. 𝒏𝝅 ±𝝅
𝟔 b. 𝒏𝝅 +𝝅
𝟑
c. 𝒏𝝅 −𝝅
𝟒 d. 𝟐𝒏𝝅 ±𝝅
𝟔
25. On the basis of straight line 𝟒𝒙 + 𝟑𝒚 − 𝟕 = 𝟎 distance of image from the point (𝟐, 𝟑) be - (a) 2 (b) 3 (c) 4 (d) 6
