Maths and Logical Reasoning Test- 2 - CAT MCQ

Let the highest marks obtained by the student be x

Then, second-highest marks x = 2

Sum of marks of these 2 subjects = (87 x 8) - (85 x 6)

Hence, the correct option is (C).

Given:

Hence, the correct option is (C).

Given: Their steps measure 80 cm, 85 cm, and 90 cm.

We have to find the L.C.M. of the measures of their steps to calculate the required distance each should walk.

L.C.M. of 80 cm, 85 cm, and 90 cm.

80=2⁴×5

85=17×5

90=2×3²×5

L.C.M 80,85,90=2⁴×3²×5×17 =12240 cm

So, the minimum distance each should walk so that all can cover the same distance in complete steps are 122.40 m.

Hence, the correct option is (A).

Let's take cost Price =100

Then, Selling Price =100+10% of 100=100+10=110

Since we get 1 kg amount with fair weights.

⇒ With unfair weights, we will get 20% less

=1000-20% of 1000=800 g =0.8 kg

Now, For 0.8 kg ⇒S.P.=110 Rs.

1 kg ⇒S.P.=110/0.8=137.5 Rs.

Net profit =137.5-100=37.5 Rs.

Net Profit %=(37.5/100) x 100=37.5%

Hence, the correct option is (D).

The pattern is-

8 × 3 = 24

24 ÷ 2 = 12

12 × 3 = 36

36 ÷ 2 = 18

18 × 3 = 54

54 ÷ 2 = 27

Hence, the correct option is (A).

Dividing by sinθ in the numerator and denominator,

⇒ 2 - cot θ = 1 + cot θ

⇒ 2 cot θ = 1

⇒ cot θ = ½

Hence, the correct option is (A).

Given expression:

42 + 36 – 6 ÷ 15 x 8 ÷ 20 + 20 – 5 = ?

After changing the symbols:

42 – 36 ÷ 6 × 15 + 8 x 20 – 20 ÷ 5

= 42 – 6 x 15 + 160 – 4

= 42 – 90 + 160 – 4

= 108

Hence, the correct option is (B).

The pattern follows here is:-

Hence, the correct option is (A).

The pattern followed here is:

The addition is two numbers is a multiple of 10.

Option (A) → 23 - 18 → 23 + 18 = 41, Not divisible by 10.

Option (B) → 30 - 20 → 30 + 20 = 50 → 10 x 5 = 50

Option (C) → 62 - 8 → 62 + 8 = 70 → 10 x 7 = 70

Option (D) → 21 - 9 → 21 + 9 = 30 → 10 x 3 = 30

All except, '23 - 18' follow the same pattern.

Hence, the correct option is (A).

The given figure can be drawn as,

Let O be the centre of the circle, AB be the chord and P is the centre point of chord AB, such that OP is the distance of the chord from the centre of the circle

Now, OA = OB = radius of circle = 25 cm

Length of chord = AB = 48 cm

⇒ PB = AB/2 = 48/2 = 24 cm

Applying Pythagoras theorem in ΔOPB,

⇒ OB² = OP² + PB²

⇒ 25² = OP² + 24²

⇒ OP² = 625 - 576 = 49

⇒ OP = √49 = 7 cm

∴ Distance of chord from centre of circle = 7 cm

Hence, the correct option is (A).

The least possible Venn diagram is given below,

Conclusions:

I. Some cats are monkeys → True (Some cats are dogs and all dogs are monkeys, so some cats are monkeys.)

II. No pig is cat → False (Some cats are dogs, all dogs are monkeys and all monkeys are pigs, so some cats are pigs.)

III. All dogs are pigs → True (All dogs are monkeys and all monkeys are pigs, so all dogs are pigs.)

So, only conclusion I and III follow.

Hence, the correct option is (A).

Pitch is the place where cricket is played.

Similarly, arena is the place where Wrestling is done.

Hence, the correct option is (C).

Given: tan⁴θ + tan²θ = 1

⇒tan²θ (tan²θ + 1)

⇒ tan²θ. sec²θ = 1 {∵ sec²θ = 1 + tan²θ}

⇒ 1– cos²θ = cos⁴ θ {∵ sin² θ = 1 – cos²θ}

⇒ cos⁴ θ + cos² θ = 1

Hence, the correct option is (C).

OA = OB = OC = Circum-radius

In ΔABC, we know that

∠ABC + ∠BCA + ∠BAC = 180°

∠BAC = 180° – 70° – 40° = 70°

We know that, The angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.

∴ ∠BOC = 2 x ∠BAC

= 2 x 70° = 140°

Hence, the correct option is (D).

Given

Squaring both sides,

⇒ 16 + y = 49

⇒ y = 49 – 16 = 33

∴ 5y – 15 = 5 x (33) – 15

= 165 – 15 = 150

Hence, the correct option is (C).