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Rahul is younger than Radha by 10 yrs. If 5 yrs back their ages were in the ratio 1:2, how old is Radha?
Let Rahul age = x years
⇒ Radha's age = (x + 10)years
⇒ x  5/x + 105 = 1/2
⇒ 2x  10 = x + 5
⇒ x = 15 years
Hence, Radha's age = (15 + 10)years = 25 years
Roots of the equation 21x^{2} − 41 x + 10 = 0 are
Solve by splitting the middle term
If 1 + cos^{2} θ = 3 sin θ cos θ, then the integral value of cost θ is (0 < θ < π/2 )
[Divide by sin^{2}θ both sides]
1/sin^{2} θ + cot^{2} θ = 3 cot θ , cosec^{2}θ + cot^{2}θ = 3 cot θ
(1 + cot^{2}θ) + cot^{2}θ = 3 cot θ , 1 + 2 cot^{2}θ = 3 cot θ
2 cot^{2}θ − 3 cot θ + 1 = 0
⇒ 2 cot^{2}θ − 2 cot θ − cot θ + 1 = 0
⇒ 2 cot θ cot θ − 1 − 1 cot θ − 1 = 0
⇒ 2 cot θ − 1 cot θ − 1 = 0
If 2 cot θ − 1 = 0
∴ cot θ = 1/2
If cot θ − 1 = 0
∴ cot θ = 1
A typist uses,lengthwise,a sheet of paper 9 cm x 12 cm. She leaves a margin of 1 cm on each side and 1 1/2 cm at the top and at the bottom. What fractional part of the paper is used for typing?
ABCDE is a regular pentagon. The measure of angle x is
Let ABCD be a rectangle such that AB=2 BC. If O is any point on AB such that ∠BOC=∠COD. Then the value of ∠ODC is :
The greatest integer that divides 358,376 and 232 leaving the same remainder in each case is
Let each number is divided by n, leaving remainder r
So we can write
232 = q_{1}n + r
358 = q_{2}n + r
376 = q_{3}n + r
Where q_{1}, q_{2} and q_{3} are unequal integers
Subtracting the first equation from second, and the second equation from third, we get
126 = (q_{2}  q_{1}) n
18 = (q_{3}  q_{2}) n
Thus n must be a divisor of 126 and 18
we want n to be the greatest common divisor of 126 and 18
Since, 126 = 7 x 18
So the greatest common divisor is 18
∴ 18 is the greatest integer that can divide each of the number 358, 376 and 232 to leave the same remainder
Study the following diagram :
The value of 'x' is
3 x 4 = 12
12 x 5 = 60
3 x 5 = 15 = x
In questions below, equations have become wrong due to wrong orders of signs. Choose the correct order of signs from the alternative given.
5×6÷312=136
A bus increases its speed from 36 km/h to 72 km/h in 10 seconds. Its acceleration is
Here u = 36 km/h = 10 m/s
v = 72 km/h = 20 m/s
t = 10s
a = ?
We know v = u + at
20 = 10 + a x 10
10 a = 10
a = 10/10
a = 1 m/s^{2}.
If (x + y):(x  y),then (x^{2} + y^{2}) : (x^{2}  y^{2}) is equal to
x + y/ x  y
= 7/3
⇒ 3x + 3y = 7x  7y
⇒ 3x  7x + 3y + 7y = 0
⇒ 10y  4x = 0
⇒ 10y = 4x
⇒ x/y = 10/4 = 5/2
⇒ x = 5
y = 2
x^{2} + y^{2}/ 2 x^{2} − y^{2} = 25 + 4/25  4 = 29/21
On a 20 km tunnel connecting two cities A and B, there are three gutters. The distance between gutters 1 and 2 is half the distance between gutters 2 and 3. The distance from city A to its nearest gutter, gutter 1 is equal to the distance of city B from gutter 3. On a particular day the hospital in city A receives information that an accident has happened at the third gutter. The victim can be saved only if an operation is started within 40 minutes. An ambulance started from city A at 30 km/hr and crossed the first gutter after 5 minutes. If the driver had doubled the speed after that, what is the maximum amount of time the doctor would get to attend the patient at the hospital. Assume 1 minute is elapsed for taking the patient into and out of the ambulance.
Distance AG_{1} = BG_{3} = 30 x 5/60 = 2.5 km.
∴ Distance G_{1}G_{3} = (20  2.5  2.5) = 15 km.
Given, G_{1}G_{2} : G_{2}G_{3} = 1 : 2
∴ G_{1}G_{2} = 5 km. and G_{2}G_{3} = 10 km.
Now time taken from reaching A to G_{3} and back to A
Form A to G_{1} = 5 min (given)
From G_{1} to G_{3} = 15/60 x 60 = 15 min
From G_{3} to A 17.5/60 x 60 = 17.5 min
and time elasped for taking the patient into and out of the ambulance = 1 min.
Total time taken = (5 + 15 + 17.5 + 1) = 38.5
Remaining time = (40  38.5) = 1.5 min
A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 3 cm to form a cone. The volume of the cone so formed is :
Volume of the cone formed
= 1/3 x π x (3)^{2} x 4 = 12 π cm^{3}
The angle of elevation of a cloud is 30^{o}. A thunder is heard 4 second after the lightning is observed. What is the vertical height of the clound?(Speed of sound is 330 m/s)
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Four people of different nationalities live on the same side of a street in four houses each of different colour. Each person has a different favourite drink. The following addition information is also known :
A. The Englishman lives in the red house.
B. The Italian drinks tea.
C. The Norwegian lives in the first house on the left.
D. In the second house from the right they drink milk.
E. The Norweigan lives adjacent to the blue house.
F. The Spaniard drinks fruit juice.
G. Tea is drunk in the blue house.
H. The white house is to the right of the red house.
I. Coca is drunk in the yellow house.
Q. Milk is drunk by :
Four people of different nationalities live on the same side of a street in four houses each of different colour. Each person has a different favourite drink. The following addition information is also known :
A. The Englishman lives in the red house.
B. The Italian drinks tea.
C. The Norwegian lives in the first house on the left.
D. In the second house from the right they drink milk.
E. The Norweigan lives adjacent to the blue house.
F. The Spaniard drinks fruit juice.
G. Tea is drunk in the blue house.
H. The white house is to the right of the red house.
I. Coca is drunk in the yellow house.
Q. The Norwegian drinks :
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