10 second questions

Jai Ganesh · 2009-03-01 18:22:40

#1581. If x is an odd integer such that 26<2x<42 and 51<3x<81, what is the value of x?

#1582. How many 10 digit numbers can be written using the numbers 1 and 2?

#1583. What is the value of x if

?

#1584. What is the coefficient of y in the exapnsion of

?

#1585. Stephen selects six colors at random from a rainbow and inserts them into a computer program designed for mixing and making new colors. A new color is formed by mixing any number of colors, the minimum number of colors mixed being 2 and the maximum being 6. How many new colors would the program give?

#1586. When does the expression

have the maximum value if a. b, and c are greater than zero?

#1587.If

and , what is the ratio between g(f(g(x))) and f(g(f(x))) for x=2?

Jai Ganesh · 2009-03-01 19:04:33

#1588. What is the remainder when the following sum is divided by 5?

#1589. What is xyz equal to if

?

#1590. In a group of sportsmen in a college, 20 are in the basketball team, 24 in the hockey team and 27 in the cricket team. 12 play hockey and basketball, 10 play cricket and basketball, 14 play hockey and cricket, and 7 play all the three games. What is the total number of players in the group?

Jai Ganesh · 2009-03-02 17:27:38

#1591. Richard has enough money to buy 45 eggs. If the eggs cost 10 cents each less, Richard could buy 5 eggs more. Mow much money does Richard have to spend on the eggs?

#1592. Find the digit in the unit's place of

.

#1593. If the remainder obtained on dividing

by is 3, what is the value of p?

Jai Ganesh · 2009-03-03 02:33:33

#1594. When I asked my friend his age, he replied, "the number you get when you subtract 25 times my age from twice the square of my age is thrice the value of your age". If my age is 14 years, what is my friend's age?

#1595. Ronald calculated his average in the last 24 tests and found it to be 76. He finds out that the two digits in the marks of 3 tests were interchanged, by mistake. The actual marks scored in these tests were 87, 79, and 98. What is the approximate percentage difference between his actual average and the average he had calculated earlier?

#1596. The work done by (x-1) people in (x+1) days and the work done by (x+1) people in (x+2) days is in the ratio 5:6. What is the value of x?

#1597. Find the sum of factors of 360, other than itself, which are divisible by 15.

#1598. Three Machine, M, O, and K are used to assemble a unit. M takes 60 hours to assemble a thousand units. O is twice as fast as M. K takes the same amount of time to assemble a thousand units as M and O working together take. How much time would be required to assemble a thousand units if all the three machines work simultaneously?

Jai Ganesh · 2009-03-03 20:51:28

#1599. When two three digit numbers 6r3 and 2s5 are added together, the sum is divisible by 9. What is the maxium possible value of (r+s)?

#1600. What are the last two digits of

?

JaneFairfax · 2009-03-04 05:36:32

Last edited by JaneFairfax (2009-03-04 07:54:19)

Jai Ganesh · 2009-03-04 16:44:51

Answer to #1600:
Correct, JaneFairfax!

Jai Ganesh · 2009-03-05 03:38:24

#1601. The speed of a boat in still water is 15 kilometers/hour and the speed of the cusrrent is 3 kilometers/hour. What is the distance travelled by the boat downstream in 12 minutes?

#1602. The speed of a boat in still water is 20 kilometers/hour. If it can travel 16 kilometers upstream in 1 hour, what time would it take to travel the same dfistance downstream?

#1603. A sum of money invested at compound interest compounded annually amounts to $2,400 in 3 years and $2,520 in 4 years. What is the rate of interest?

#1604. A sum of money becomes

of itself in years at a certain rate of simple interest. What is the rate of interest per annum?

#1605. If the difference between the simple and compound interest compounded annually on a sum of money for 2 years at 4% per annum is $80, what is the sum?

Jai Ganesh · 2009-03-05 04:19:07

#1606. What is the value of x if

?

#1607. If A = {1, 2, 3, 4}, B = {2, 4, 5, 6}, and C = {1, 2, 5, 7, 8}, then what is

?

#1608. What is the value of x if

?

Jai Ganesh · 2009-03-05 17:46:49

#1609. If A is a subset of B, then what is

?

#1610. By what percentage does the volume of a cylinder increase if the radius is doubled and the height remains the same?

#1611. If f(x) = 3x - 9 and g(x) = 7x - 10, what is gof?

#1612. What is the number of terms in the Arithmetic Progression 7, 13, 19, ....97?

#1613. If (x-1) is a factor of 3x² - 2x - p, what is the value of p?

#1614. What are the roots of the equation 2x² - 3x - 5 = 0?

#1615. What is the value of k for which the equation 9x² - 12x + k = 0 has equal roots?

Jai Ganesh · 2009-03-06 03:19:05

#1616. The total of three consecutive even numbers is 36 more than the average of the three numbers. Which is the middle number?

#1617. The average age of a team of 10 people remains the same as it was 3 years ago, when a young person replaces one of the members. How much younger was the young person than the person he replaced?

#1618. The marks scored by david in an examination atre 62 out of 100 in Mathematics, 34 out of 50 in English and 66 out of 75 in Physics. What are the average marks scored by him in the three subjects taken together?

#1619. What is the value of x if

?

#1620. What is the value of a if

?

#1621. What is the value of b if

?

#1622. If log(k² - 4k + 5) = 0, what is the value of k?

Jai Ganesh · 2009-03-06 20:30:50

#1623. A number when divided by 119 leaves remainder of 19. What would the remainder by when the number is divided by 17?

#1624. When n is divided by 4, the remainder is 3. What is the remainder when 2n is divided by 4?

#1625. What is the least value of * such that 63576*2 is divisible by 8?

#1626. How many prime factors does the following product contain?

?

#1627. What is the least number that has to be subtracted from 3000 to get a number divisible by 19?

#1628. Which is the number by which the difference between the squares of two consecutive odd numbers is always divisible by?

#1629. The sum of three prime numbers is 100. If one of the prime numbers is greater than another by 36, which is the greatest prime number?

#1630. What is the number of digits of the smallest number, which when multiplied by 7, gives a result containing entirely of nines?

Jai Ganesh · 2009-03-07 03:24:29

#1631. What is the value of

if
?

#1632. What is the remainder when

is divided by (x - 3)?

#1633. The sum and product of the roots of a quadratic equation are 5 and 20 respectively. What is the equation?

#1634. The sum of the squares of three consecutive positive odd numbers is 251. What are the numbers?

#1635. What is the solution for the following pair of equations?

.

Jai Ganesh · 2009-03-07 03:50:28

#1636. The Greatest Common Divisor of two terms p and q is 1. What is their Least Common Multiple?

#1637. Express

as a rational number.

#1638. What is the value of

if ?

#1639. What is the smallest integral value of x such that 5(x+63)+469 is divisible by 7?

#1640. If n is an odd number and n>1, then by what greatest number is n(n²-1) certainly divisible by?

Jai Ganesh · 2009-03-07 17:36:47

#1641. If 5 tan θ = 4, then what is the value of

?

#1642. What is

equal to?

#1643. If (sin θ) + (cos θ) = 1, what is the value of (sin θ) x (cos θ)?

#1644. If 2cos²θ - 2sin²θ =1, then what is θ equal to?

#1645. A person is standing on a tower of height 15(√3 + 1) meters and observing a car coming towards the tower. He observes that the angle of depression changes from 30° to 45° in 3 seconds. What is the speed of the car in kilometers per hour?

#1646. If

lies between 0° and 90° and
,
then what is the value of ?

#1647. What is the following expression equal to?

?

#1648. The perimeter of a right-angled triangle is 30 centimeters. Its hypotenuse is 13 centimeters in length. What is the lenght of the samlles side of the right-angled triangle?

#1649. What is the measure of angle

if it is an acute angle and
?

#1650. What is the value of x if

?

Jai Ganesh · 2009-03-09 02:31:36

#1651.In a school, there are three sections in class X, viz. A, B, and C. The ratio of the number of student sin sections A and B is 3:5 and that in B and C is 4:7. If the total number of students in the three sections together are 134, then how many students are there in section A?

#1652. Of the three numbers, the ratio of the first to the second is 8:9 and that of the second to the third is 3:4. If the product of the first and the third is 2400, what is the second number?

#1653. The ratio of the present ages of Adam and Patrick is 2:3. After 3 years, the ratio of their ages would be 3:4. What is the present age of Patrick?

#1654. Two numbers are in the ratio 2:3. If 3 be added to both of them, then their ratio becomes 3:4. Find the sum of the numbers.

#1655. The ratio of incomes of A and B is 5:6. If A gets $1,100 less than B, what is the total income of A and B?

Jai Ganesh · 2009-03-10 17:59:57

#1656. If 2x + y = 5 and 3x - 4y = 2, then what is the value of 2xy?

#1657. What is the value of

?

#1658. If the quadratic equation 2x[sup]2[/sup] + 3x + p = 0 has equal roots, then what is the value p?

#1659. What is the value of x[sup]3[/sup] if

?

#1660. In which quadrant does the complex number

lie?

Jai Ganesh · 2009-03-11 01:00:41

#1661. Factorize:- (x+y)[sup]3[/sup] - (x-y)[sup]3[/sup].

#1662. If a, b, c are three consecutive integers, then what is log(ac+1) equal to?

#1663. What is the value of x for which
2[sup]x+4[/sup]-2[sup]x+2[/sup] = 3?

#1664. What are the factors of x[sup]2[/sup] - 7x + 12?

#1665. What is the quotient when

is divided by
?

Jai Ganesh · 2009-03-11 02:03:24

#1666. The sides of a traingle are in the ratio

.
If he perimeter of the riangle is 52 centimeters, what is the length of the smallest side?

#1667. The area of a triangle is 216 cm[sup]2[/sup] and the length of the sides of the triangle are in the ratio 3:4:5.What is the perimeter of he triangle?

#1668. The sides of a traingle are 3 centimeters, 4 centimeters, and 5 centimeters in length. What is the area in cm[sup]2[/sup] of the triangle formed by joining the midpoints of the sides of this triangle?

#1669. If the perimeter of an isosceles right triangle is (6 + 3√2) meters, then what is the area of the triangle?

#1670. The perimeter of a triangle is 30 centimeters and its area is 30 cm[sup]2[/sup]. If the largest side measures 13 centimeters, what is the length of the smallest ide of the triangle?

Jai Ganesh · 2009-03-11 03:18:47

#1671. A sector of angle 120° is cut from a circle, and it has area of

cm[sup]2[/sup]. Find the radius of the circle.

#1672. A cube of edge 15 centimeters is completely immersed in a rectangular vessel containing water. What is the rise in the water level of the container ifthe base of the vessel are 20 centimeters long and 15 cetimeters wide.

#1673. How many iron rods of length 7 meters and diameter 2 centimeters can be made out of 0.88 cubic meter of iron?

#1674. How many spherical bullets, each of 1.5 centimeter diameter, can be made out of a lead cylinder 28 centimeters long and with base radius 6 centimeters?

#1675. Find the value of

.

Jai Ganesh · 2009-03-11 17:28:44

#1676. If cos²30° + cos²60° = sin x, what is the value of x?

#1677. What is the value of θ if

?

#1678.If

,
then what is the value of
?

#1679. Given sin 40° = 0.6428, what is the value of

?

#1680. What is the following expression equal to?

?

Jai Ganesh · 2009-03-12 05:51:45

#1681. By what number the following product must be multiplied to make it aperfect square?

.

#1682. Which of the following is the smallest in value?
1.

2.
3.
4.

#1683. Find the number in the unit's place in

?

#1684.What would be the number in the unit's place of

?

#1685. What is the remainder when the following is divided by 5?

?

Jai Ganesh · 2009-03-12 06:35:25

#1686. If

,
then what is equal to?

#1687. What is the value of

?

#1688. If log 2 = x, log 3 = y and log 7 = z, what is the value (in terms of x, y, and z) of

?

#1689. If log[sub]10[/sub]2 = 0.3010 and log[sub]10[/sub]7 = 0.8451, what is the value of log[sub]10[/sub]2.8?

#1690. If log[sub]10[/sub]2 = 0.30103, how many digits does
2[sup]64[/sup] contain?

Jai Ganesh · 2009-03-12 09:57:13

#1691. what is the value of

?

#1692.What is the value of

?

#1693. What is the value of

?

#1694. What is the value of

?

#1695. What is the value of

?

Jai Ganesh · 2009-03-13 02:22:09

#1696. What is the value of sec θ if

?

#1697. What is the value of

?

Math Is Fun Forum

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