Job Solution | Combined Bank (সমন্বিত ব্যাংক)

Combined 7 Banks and 1 Financial Institution || Senior Officer (General) (14-01-2022) || 2022

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Answer the following mathematical problems:
1.

There are two crosswise roads just in the middle of a field of length 50m and breadth 40m. The breadth of each road is 1.5m. Find the area covered by two roads.
Created: 2 months ago | Updated: 3 days ago

Let us depict a picture according to question Here, the area covered by the two roads = (DC × 1.5+BC × 1.5-1.5 × 1.5) m² =(50×1.5+40×1.5-2.25)m2 =(75+60-2.25)m2 =132.75m2

Answer the following mathematical problems:
2.

The angle of elevation of a watch tower at a point on the ground is 60°. If moved back 18m, the angle of elevation becomes 45 degree. What is the height of the watch tower?
Created: 2 months ago | Updated: 6 hours ago

Let us draw the required picture: Here, AB is the height of the watch tower AB=h For △ABC ∴tan 60°=ABBC=hx =3=hx            [∵tan 60°=3] =h=x3 ∴x=h3 For △ABD Again, tan 45°=ABBD=ABDC+BC=h18+x =1=h18+x        [∵tan 45°=1] =h=18+x =h=18+h3 =h-h3=18 =h(1-13)=18 =h(3-1)=183 ∴h=1833-1=42.58m


3.

Among 80 students at a collage, 20 take Mathematics, 30 take English, and 12 take both Mathematics and English. Find the number of the students who take (a) Mathematics or English, (b) neither Mathematics nor English.
Created: 2 months ago | Updated: 6 hours ago

Let us draw a venn-diagram according to question Here,n(U)=80;n(M)=20;n(E)=30;n(M∩E)=12 a) Number of students who take M or E, n(M ∪ E)= n(M) + n(E) -n(M ∩ E) =30+20-12=38 b) Number of students who take neither M nor E Total = n(M) +n(E) - Both + None =80=20+30-12+ None ∴None = 42


4.

Find θ if is an acute angel and 7sin2θ + 3cos2θ=4
Created: 2 months ago | Updated: 3 days ago

Given, 7sin2θ+3cos2θ=4 =7sin2θ+3(1-sin2θ)=4             [∵cos2θ=1-sin2θ] =7sin2θ+3-3sin2θ=4 =4sin2θ=4-3=1 =sin2θ=14 =sinθ=14=12 =sinθ=sin 30° ∴θ=30°


5.

A man agrees to refund the loan of Tk. 7,900 in a few installments. Each installment is Tk. 5 more than the immediate past installment. If the first installment is Tk. 100, in how many installments will the man be able to refund amount?
Created: 2 months ago | Updated: 6 hours ago

Here first installment is Tk. 100 ∴Second installment is Tk. 105 ∴Third installment is Tk. 110 The series := 100 + 105 + 110 + 115 +....... Here, a =100: d = 105 - 100 = 5 If n be the number of installment, we can write n2{2a+(n-1)d}=7,900 =n2{(2×100)+(n-1)5}=7,900

=n2 (200 + 5n - 5) = 7, 900 =n(195 + 5n) = 15, 800 =5n2+195n-15,800=0 =n2+39n-3,160=0 =n2+79n-40n-3,160=0 =n(n + 79) - 40(n + 79) = 0 =(n + 79)(n - 40) = 0 Here, (n + 79) = 0 ∴n=-79 (which is not acceptable) ∴n-40=0 ∴n=40

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