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The minute hand of clock is √21 cm long. The area described by a minute hand on the face of the clock between 7 am and 7.05 am is
Given that length of minute hand of clock is √21 cm
Angle described by the minute hand in 60 minutes = 360^{o}
Angle described by the minute hand in 5 minutes = 360/60 x 5 = 30^{o}
We know that Area of sector = θ/360 x πr^{2}
= 30/360 x 22/7 x √21 x √21
= 11/2 = 5.5 cm^{2}
Read the following facts about a family and answer the question that follow them
1. In a family of six persons, R S T X Y Z and F there are two married couples.
2. R is grandmother of X and mother of Y ?
3. Z is wife of Y and mothe of T
4. T is the grand daughter of S
What is Z to X ?
If cos 2A = 1 − 2sin^{2} A, and A = 15^{o } the value of sin 15^{o }=
If 4 x^{4} − 4 x^{3} − 7 x^{2} − 4 x + 4 = 0 ; then x =
Divide throughout by x^{2}
F = m x a = Kg x ms^{2} = N
[1/3 ÷ 5/8 + 1/4 × 3/5 − 2/5 × 5/7], on simplification, gives
In ∆ABC, AD is the median through A and E is the midpoint of AD. BE produced meets AC in F, then AF is equal to
A planet of Solar system has mass four times and diameter twice than those of earth. the value of g on this planet is
ABC is a triangle in which BC is produced to D. In case ∠A:∠B:∠C::3:2:1 and AC⊥CE, the measure of ∠ECD is
If + means ÷, × means , ÷ means × and  means +, then
8 + 6 × 4 ÷ 3  4 = ?
Given expression : 8 ÷ 6  4 × 3 + 4 = 4/3  4 × 3 + 4 = 4/3 12 + 4 =  20/3
The sum of the digits of a twodigit number is 8. The number ontained by reversing the digits is 18 less than the original number. The number is
The original no is greater than the new no by 18
∴ Required number = 11 x 8 + 18/2
= 88 + 18/2 = 106/2 = 53
A pipe of diameter d can drain a certain water tank in 40 minutes. The time taken by a pipe of diameter 2d for doing the same job is
Ratio of volumes
∴ A pipe of radius d/2 can drain a water tank in 40 minutes
⇒ A pipe of radius d can drain the same water tank in 10 minutes
A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount had been offered?
Giving no discount to customer implies selling the product on printed price. Suppose the cost price of the article is Rs. 100
Then, printed price
= Rs. 130.
So the percentage of profit earned = 130  100 = 30
Robert is travelling on his cycle and has calculated to reach point A at 2 P.M., if he travels at 10 kmph; he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?
Let the distance travelled by Robert x km
Then, x/10  x/15 = 2
⇒ 3x  2x = 60
⇒ x = 60 km
Time taken to travel 60 km at 10 km/hr = ( 60/10 )hrs = 6 hrs
So, Robret started 6 hours before 2 P.M. i.e., at 8 A.M.
∴ Required speed = ( 60/5 )kmph. = 12 kmph
A hemispherical bowl is made of steel 0.25 cm thick. The inside radius of the bowl is 5cm. The volume of steel used in making the bowl is nearly (use π = 22/7)
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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