726 soldiers were divided in two groups for arranging each group in a solid square. It was found that there were some excess soldiers in the second group. Number of rows in the first group was 32. So the minimum number of soldiers in excess in the second group is :
(a) 32
(b) 41
(c) 100
(d) 102
02. In N is the smallest perfect square which is exactly divisible by 10, 12 and 25, then the quotient obtained when N is divided by 25 is
(a) 16
(b) 25
(c) 36
(d) 64
03. When a heap of pebbles is arranged into groups of 32 each 10 pebbles are left over. When they are arranged in heaps of 40 each, 18 pebbles are left over and when in groups of 72 each, 50 are left over. The least number of pebbles in the heap is
(a) 1450
(b) 1440
(c) 1418
(d) 1412
04. A man buys three houses, the second one at twice the price of the first and the third one at twice the price of the second. He manages to sell the first and the second both at a profit of 20% but incurs a loss of 10% over selling the third. Overall, he has
(a) Got a profit less than 3%
(b) Incurred a loss of 3%
(c) Got a profit more than 3%
(d) Incurred loss less than 3%
05. On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs. 7. Ifhe sells the pen at 5% gain and the book at 10% gain, then he gains Rs. 13. The actual price of the book is :
(a) Rs. 80
(b) Rs. 90
(c) Rs. 100
(d) Rs. 120
06. ABC is right angled triangle, B being the right angle. Mid-points of BC and AC are respectively B’ and A’. The ratio of the area of the quadrilateral AA’ B’B to the area of the triangles ABC is
(a) 1 : 2
(b) 2 : 3
(c) 3 : 4
(d) None of the above
07. If D, E and F are respectively the mid-points of sides BC, AC and AB of a ABC. If EF = 3 cm, FD = 4 cm and AB =10 cm, then DE, BC and CA respectively will be equal to:
(a) 6, 8 and 20cm
(b) 10/3, 9 and 12 cm
(c) 4, 6 and 8 cm
(d) 5, 6 and 8cm
08. The area of a circle whose radius is 8 cm is trisected by two concentric circles. The ratio of radii of the concentric circles in ascending order is :
(a) 1 : 2 : 3
(b) 3 : 3 : 5
(c) 1 : √2 : √3
(d) √2 ∶√3 ∶√5
09. The volume of a solid right circular cylinder is V, the whole surface area is S, height is h and radius of base is r. Then the ratio V(1/h+1/r) ∶ S equals
(a) 1 : 4
(b) 1 : 3
(c) 1 : 2
(d) 1 : 1
10. If area of a parallelogram with sides p and q is R and that of a rectangle with sides p and q is S, then:
(a) R>S
(b) R<S
(c) R=S
(d) None of these
Answers....
01.(4)Number of soldiers in the first group = 32 x 32 = 1024
(a) 32
(b) 41
(c) 100
(d) 102
02. In N is the smallest perfect square which is exactly divisible by 10, 12 and 25, then the quotient obtained when N is divided by 25 is
(a) 16
(b) 25
(c) 36
(d) 64
03. When a heap of pebbles is arranged into groups of 32 each 10 pebbles are left over. When they are arranged in heaps of 40 each, 18 pebbles are left over and when in groups of 72 each, 50 are left over. The least number of pebbles in the heap is
(a) 1450
(b) 1440
(c) 1418
(d) 1412
04. A man buys three houses, the second one at twice the price of the first and the third one at twice the price of the second. He manages to sell the first and the second both at a profit of 20% but incurs a loss of 10% over selling the third. Overall, he has
(a) Got a profit less than 3%
(b) Incurred a loss of 3%
(c) Got a profit more than 3%
(d) Incurred loss less than 3%
05. On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs. 7. Ifhe sells the pen at 5% gain and the book at 10% gain, then he gains Rs. 13. The actual price of the book is :
(a) Rs. 80
(b) Rs. 90
(c) Rs. 100
(d) Rs. 120
06. ABC is right angled triangle, B being the right angle. Mid-points of BC and AC are respectively B’ and A’. The ratio of the area of the quadrilateral AA’ B’B to the area of the triangles ABC is
(a) 1 : 2
(b) 2 : 3
(c) 3 : 4
(d) None of the above
07. If D, E and F are respectively the mid-points of sides BC, AC and AB of a ABC. If EF = 3 cm, FD = 4 cm and AB =10 cm, then DE, BC and CA respectively will be equal to:
(a) 6, 8 and 20cm
(b) 10/3, 9 and 12 cm
(c) 4, 6 and 8 cm
(d) 5, 6 and 8cm
08. The area of a circle whose radius is 8 cm is trisected by two concentric circles. The ratio of radii of the concentric circles in ascending order is :
(a) 1 : 2 : 3
(b) 3 : 3 : 5
(c) 1 : √2 : √3
(d) √2 ∶√3 ∶√5
09. The volume of a solid right circular cylinder is V, the whole surface area is S, height is h and radius of base is r. Then the ratio V(1/h+1/r) ∶ S equals
(a) 1 : 4
(b) 1 : 3
(c) 1 : 2
(d) 1 : 1
10. If area of a parallelogram with sides p and q is R and that of a rectangle with sides p and q is S, then:
(a) R>S
(b) R<S
(c) R=S
(d) None of these
Answers....
01.(4)Number of soldiers in the first group = 32 x 32 = 1024
Remaining soldiers = 4726 – 1024 = 3702
Now, 60 x 60 = 3600
∴ Minimum number of soldiers in excess = 3702 – 3600 = 102
02.(3) LCM of 10, 12 and 25 = 300
Now,
300 = 3 x 2 x 2 x 5 x 5
= 3 x 22 x 52
∴ N = 3 x 300 = 900
Now, 900 ÷25=36
03.(3)Here, 32-10=22
40-18=22
72-50=22
∴ Required number of pebbles = (LCM of 32, 40 and 72) – 22
= 1440-22=1418
04.(1) Let the CP of first, second and third houses be Rs. 100,Rs.200 and Rs. 400 respectively.
Gain = 20+40-40=Rs.20
∴ Gain % = 20/700×100=20/7=2 6/7%
05.(1) Let the CP of a pen = Rs.x and that of a book = Rs. y.
∴ 15y-5x=700
⇒ 3y-x=140 ……….(i)
And 2y+x=260
From equations (i) and (ii),
5y=400
⇒ y= 400/5=80
∴ CP of a book = Rs.80
06.(3)
07.(4)As the line joining the mid-points of any two sides of a triangle is parallel to the third side and is half of the third side.
∴ DE = 1/2 AB=1/2×10=5 cm.
EF = 1/2 BC ⇒ BC = 2EF
= 2 × 3 = 6 cm.
DF = 1/2 AC ⇒ AC = 2×DF
=2 ×4=8cm.
08.(4)
09.(3) V=πr^2 h
S = 2πrh+2πr^2
∴V(1/h+1/r) ∶ S
⇒ πr^2 h (1/h+1/r) : 2πrh+2πr^2
⇒ πr^2+ πrh : 2πrh+2πr^2
⇒ 1 : 2
10.(2)Let h be the height of the parallelogram. Then, clearly, h<q
So, R = P x h < p x q = S
So, R < S
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