Numerical Ability
 From a circular sheet of paper of radius 30 cm, a sector of 10% area is removed. If the remaining part is used to make a conical surface, then the ratio of the radius and height of the cone is __

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90% of area of sheet = Cross sectional area of cone
⇒ 0.9 × π × 30 × 30 = π × r_{1} × 30
⇒ 27 cm = r_{1}
∴ height of the cone =√30^{2}  27^{2}= 13.08 cmCorrect Option: C
90% of area of sheet = Cross sectional area of cone
⇒ 0.9 × π × 30 × 30 = π × r_{1} × 30
⇒ 27 cm = r_{1}
∴ height of the cone =√30^{2}  27^{2}= 13.08 cm
 A coin is tossed thrice. Let X be the event that head occurs in each of the first two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occurs in three tosses. Based on the above information, which one of the following statements is TRUE?

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x = {HHT, HHH}
y depends on x
z = {TTH, TTT}
∴ ‘d’ is the correct choice.Correct Option: B
x = {HHT, HHH}
y depends on x
z = {TTH, TTT}
∴ ‘d’ is the correct choice.
 Right triangle PQR is to be constructed in the xy– plane so that the right angle is at P and line PR is parallel to theaxis. The x and y coordinates of P, Q, and R are to be integers that satisfy the inequalities: 4 <, x < 5 and 6 < y < 16. How many different triangles could be constructed with these properties?

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We have the rectangle with dimensions 10 ×11 (10 horizontal dots and 11 vertical). PQ is parallel to yaxis and PR is parallel to xaxis.
Choose the (x, y) coordinates for vertex P (right angle): ^{10}C_{1} × ^{11}C_{1}
Choose the x coordinate for vertex R (as y coordinate is fixed by A): ^{9}C_{1}, (10 – 1 = 9 as 1 horizontal dot is already occupied by A)
Choose the y coordinate for vertex Q (as x coordinate is fixed by A): ^{10}C_{1}, (11 – 1 = 10 as 1 vertical dot is already occupied by A).
Hence, required number of triangles will be ^{10}C_{1} × ^{11}C_{1} × ^{9}C_{1} × ^{10}C_{1} = 9900.Correct Option: C
We have the rectangle with dimensions 10 ×11 (10 horizontal dots and 11 vertical). PQ is parallel to yaxis and PR is parallel to xaxis.
Choose the (x, y) coordinates for vertex P (right angle): ^{10}C_{1} × ^{11}C_{1}
Choose the x coordinate for vertex R (as y coordinate is fixed by A): ^{9}C_{1}, (10 – 1 = 9 as 1 horizontal dot is already occupied by A)
Choose the y coordinate for vertex Q (as x coordinate is fixed by A): ^{10}C_{1}, (11 – 1 = 10 as 1 vertical dot is already occupied by A).
Hence, required number of triangles will be ^{10}C_{1} × ^{11}C_{1} × ^{9}C_{1} × ^{10}C_{1} = 9900.
 Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in km) at which I live from Arun's place?

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I = I live
AH = Ahmed lives
M = Michel lives
S = Susan lives
A = Arun livesCorrect Option: C
I = I live
AH = Ahmed lives
M = Michel lives
S = Susan lives
A = Arun lives
 The binary operation – is defined as a– b = ab + (a + b), where a and b are any two real numbers. The value of the identity element of this operation, defined as the numberx such that a– x = a, for any a, is ______.

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The binary operation – is defined
⇒ a – b = ab + (a + b)
a – x = a
∴ From the equation ‘b’ is the variable
Option A: x = 0
a – o = a × 0 + (a + 0) = 0 + a = a
Option B: x = 1
a – 1 = a × 1 + (a + 1) = a + a + 1 = 2a + 1
Option C: x = 2
a – 2 ⇒ a × 2 + (a + 2) = 2a + a + 2 = 3a+ 2
Option D: x = 10
a – 10 ⇒ a × 10 + (a + 10) = 10a + a + 10 = 11a + 10
∴ Option ‘A’ only True.Correct Option: A
The binary operation – is defined
⇒ a – b = ab + (a + b)
a – x = a
∴ From the equation ‘b’ is the variable
Option A: x = 0
a – o = a × 0 + (a + 0) = 0 + a = a
Option B: x = 1
a – 1 = a × 1 + (a + 1) = a + a + 1 = 2a + 1
Option C: x = 2
a – 2 ⇒ a × 2 + (a + 2) = 2a + a + 2 = 3a+ 2
Option D: x = 10
a – 10 ⇒ a × 10 + (a + 10) = 10a + a + 10 = 11a + 10
∴ Option ‘A’ only True.