The sides of a triangle are in the ratio 13:14:15 and its perimeter is 168cm. The length of the altitude corresponding to the longest side is
Ratio of sides = 13 : 14 : 15
Perimeter of triangle = 168 cm
Let the sides are 13x, 14x, and 15x
∴ 13x + 14x + 15x = 168
⇒ 42x = 168
⇒ x = 4
∴ sides are 13 x 4 = 52 cm
14 x 4 = 56 cm
15 x 4 = 60 cm
s = sum of sides/2 = 168/2 = 84
Let BL be altitude on the largest side AC of ABC
Area of Δ ABC = 1344 cm^{2}
⇒ 1/2 x base x altitude = 1344 cm^{2}
⇒ 1/2 x AC x BL = 1344 cm^{2}
⇒ 30 BL = 1344
⇒ BL = 1344/30 = 44.8 cm
. Now square both sides
Again squaring both sides
x^{2} − 6 x + 9 = 9 x − 2
x^{2} − 6 x + 9 = 9 x − 18
x^{2} − 15 x + 27 = 0
D = 25^{2} − 4 x 1 x 27 = 225 − 108 = 17 D is not a perfect square: root cannot be rational
As options (a), (b) and (c) are rational, therefore none of them can be true.
The value of the expression sec^{2}33^{0} − cot^{2} 57^{0} , is
The value of the expression
AB∥CD and AC∥BD. CD is produced to E. If ∠CAD=37^{o} and ∠BDE=68^{o}, then ∠ABD is :
A body of mass 25 kg has a momentum of 125 kg. m/s. What is the velocity of the body?
Given: m = 25 kg
p = 125 kg. m/s
v = ?
we know momentum = mass (m) x velocity(v)
p = mv
125 = 25 x v
v = 125/25
v = 5 m/s
If Δ denotes =, + denotes > ,  denotes >, □ denotes ≠, x denotes > and ÷ denotes < then a + b c denotes :
10^{o}C temperature is equal to
Choose the correct alternative from the given ones that will complete the series.
2, 5, 9, 19, 37, ___
x^{2} + 1, x^{2 } 1,x^{2} + 1,x^{2}  1 and so on
∴ Missing number = (37 x 2) + 1 i.e. 75
A cisten has a leak which would empty it in 8 hrs. If a tap is turned on, which admits 6 litres of water in a minute into the cistern which is now emptied in 12 hrs, then the capacity of the cistern is
Let X = 8 hrs
Y = 6 x 60 = 360
Z = 12
The eapacity of the tank is
= ( XYZ/Z  X ) litres
A house worth Rs 150000 is sold by X at 5% profit to Y. Y sells the house back to X at a 2% loss. Then, in the entire transaction
CP = Rs 150000
Overall gain percentage
= 5  2  10 100 = 2.9%
⇒ 150000 x 29/1000 = Rs 4350 gain
1080 ÷ 12 ÷10 = ?
, then the value of x is
The Ambanies were recently on vacation and bought each of their four children (one of who is Madhuri) a stuffed animal as a souvenir. Hoping to avoid confusion and squabbles, they bought four animals which were clearly different types (one was hippo) and different colours (one was yellow). Using the following clues, can you find each child’s are (no two children are the same age and the ages are all one year apart, expressed in whole number of years) and the type and colour of the stuffed animal which each Ambani Child received?
1. Karim was so excited by her present that the ripped off the wrapping from her package first, followed by the threeyearold. Next the bunny unwrapped and finally the blue toy was uncovered.
2. The eldest child (who was not Ravikant) received an orange animal as a gift.
3. Sandeep, who did not received the teddy bear, is a year younger than the child who received the lamb (which was not blue).
4. The twoyearold’s toy was soon forgotten when a bright red toy was unwrapped immediately after it.
Q. What was the colour of the animal that the youngest Ambani got is gift?
The Ambanies were recently on vacation and bought each of their four children (one of who is Madhuri) a stuffed animal as a souvenir. Hoping to avoid confusion and squabbles, they bought four animals which were clearly different types (one was hippo) and different colours (one was yellow). Using the following clues, can you find each child’s are (no two children are the same age and the ages are all one year apart, expressed in whole number of years) and the type and colour of the stuffed animal which each Ambani Child received?
1. Karim was so excited by her present that the ripped off the wrapping from her package first, followed by the threeyearold. Next the bunny unwrapped and finally the blue toy was uncovered.
2. The eldest child (who was not Ravikant) received an orange animal as a gift.
3. Sandeep, who did not received the teddy bear, is a year younger than the child who received the lamb (which was not blue).
4. The twoyearold’s toy was soon forgotten when a bright red toy was unwrapped immediately after it.
Q. Which of the following statements is not correct?
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