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A student obtained 87 average marks in 8 subjects. If the students highest gaining subject is 2 marks more than the secondranked subject. If these two subjects are eliminated then the average of the remaining subjects will become 85. The highest marked subject is:
Let the highest marks obtained by the student be x
Then, secondhighest 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).
Three persons walking together in the morning. The distance of their one footstep is 80 cm, 85 cm, and 90 cm respectively. How much minimum distance they cover so that distance can be measured with the complete number (integer number) of their footsteps completely?
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=2^{4}×5
85=17×5
90=2×3^{2}×5
L.C.M 80,85,90=2^{4}×3^{2}×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).
A shopkeeper sells rice on 10% profit and also uses 20% less weight, his total percent of profit is:
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
=100020% 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 =137.5100=37.5 Rs.
Net Profit %=(37.5/100) x 100=37.5%
Hence, the correct option is (D).
Direction: What will come in place of the question mark (?) in the following number series?
8,24,12,36,18,54,?
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).
In a certain code language, '×' represents '+', '÷' represents '×', '' represents '÷' and '+' represents ''. Find out the answer to the following question.
42 + 36 – 6 ÷ 15 × 8 ÷ 20 + 20 – 5 = ?
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).
A series is given with one term missing. Select the correct alternative from the given ones that will complete the series.
EJK, DIJ, BGH, ?
The pattern follows here is:
Hence, the correct option is (A).
Four pairs of number have been given, out of which three are alike in some manner, while one is different. Choose out the odd one.
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).
Calculate the distance (in cm) of the chord from the centre of the circle, if the chord of length 48 cm is drawn in the circle of radius 25 cm.
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,
⇒ OB^{2} = OP^{2} + PB^{2}
⇒ 25^{2} = OP^{2} + 24^{2}
⇒ OP^{2} = 625  576 = 49
⇒ OP = √49 = 7 cm
∴ Distance of chord from centre of circle = 7 cm
Hence, the correct option is (A).
Direction: In the question below there are three statements followed by three conclusions I, II and III. You have to take the three given statements to be true even if they seem to be at variance from commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements:
I. Some cats are dogs.
II. All dogs are monkeys.
III. All monkeys are pigs.
Conclusions:
I. Some cats are monkeys.
II. No pig is cat.
III. All dogs are pigs.
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).
Select the option that is related to the third term in the same way as the second term is related to the first term.
Pitch : Cricket :: Arena : ?
Pitch is the place where cricket is played.
Similarly, arena is the place where Wrestling is done.
Hence, the correct option is (C).
If tan^{4}θ + tan^{2}θ = 1, then the value of cos^{4}θ + cos^{2}θ is:
Given: tan^{4}θ + tan^{2}θ = 1
⇒tan^{2}θ (tan^{2}θ + 1)
⇒ tan^{2}θ. sec^{2}θ = 1 {∵ sec^{2}θ = 1 + tan^{2}θ}
⇒ 1– cos^{2}θ = cos^{4} θ {∵ sin^{2} θ = 1 – cos^{2}θ}
⇒ cos^{4} θ + cos^{2} θ = 1
Hence, the correct option is (C).
In ΔABC, ∠ABC = 70°, ∠BCA = 40°. O is the point of intersection of the perpendicular bisectors of the sides, then the angle ∠BOC is
OA = OB = OC = Circumradius
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).
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