1000+ CAT Aptitude Questions and Answers 2023 - 2024 Pdf - 1
Question: 1
A rectangular field has dimensions 25 m by 15 m. Two mutually perpendicular passages, 2 m wide have been left in its central part and grass has been grown in rest of the field. The area (in sq. metres) under the grass is
(A) 295
(B) 296
(C) 299
(D) 301
Ans: C
Area of the field = (25 × 15) m2 = 375 m2.
Area of the passages = (25 × 2 + 15 × 2 - 2 × 2)m2
Area under grass = (375 - 76) m2 = 299 m2.
Question: 2
What will be the length of the diagonal of that square plot whose area is equal to the area of a rectangular plot of length 45 metres and breadth 40 metres?
(A) 42.5 metres
(B) 50 metres
(C) 60 metres
(D) 75 metres
Ans: C
Area = (45 × 40) m2
⇒ $${1}/{2}$$ × (diagonal)2.
= 1800 ⇒ diagonal = 60 m.
Question: 3
If the area of a square with side a is equal to the area of a triangle with base a, then the altitude of the triangle is
(A) a
(B) 2a
(C) 4a
(D) $${a}/{2}$$
Ans: B
Area of a square with side a = a2 sq. units.
Area of a triangle with base
= a = $$({1}/{2} × a × h)$$ sq.units
∴ a2 = $${1}/{2}$$ × a × ⇔ h = 2a.
Question: 4
In a circle of radius 28 cm, an arc subtends an angle of 72° at the centre. Find the length of the arc and the area of the sector so formed.
(A) 490.8 cm2
(B) 491.8 cm2
(C) 492.8 cm2
(D) 494.8 cm2
Ans: C
r = 28 cm, Θ = 72°
∴ Length of arc = $$(2 × {22/7} × 28 × {72/360})$$ cm = 35.2 cm.
Area of the sector = $$({22/7} × 28 × 28 × {72/360})$$cm2 = 492.8 cm2.
Question: 5
Find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of Rs.12.40 per square metre.
(A) Rs.1934.40
(B) Rs.1935.40
(C) Rs.1936.40
(D) Rs.1937.40
Ans: A
<Area of the carpet = Area of the room = (13 × 9) m2 = 117 mm2.
Length of the carpet = $$({Area} / {Width})$$ = $$(117 × {4}/{3})$$ m = 156 m.
∴ Cost of carpeting = Rs. (156 × 12.40) = Rs.1934.40.
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