10 second questions

Jai Ganesh · 2009-03-18 04:44:49

#1723. In a Geometric Progression with first term a and common ratio r, what is the Arithmetic Mean of the first five terms?

#1724. What is the sum of the integers from 1 to 100 that are divisible by 2 or 5?

#1725. What is the value of
(1)[sub]2[/sub] + (11)[sub]2[/sub] + (111)[sub]2[/sub] + (1111)[sub]2[/sub] + (11111)[sub]2[/sub]?

Jai Ganesh · 2009-03-18 06:40:03

#1726.Eighteen football teams take part in a tournament and every team meets every other team twice. How many matches are played in the tournament?

#1727. Out of 40 children, 30 can swim, 27 can play chess and only 5 can do neither. How many children can swim only?

#1728. What is the value of

?

#1729. If m and n are the roots of the equation 4x[sup]2[/sup] - 4x - 1 = 0, then what is the value of m[sup]3[/sup] + n[sup]3[/sup]?

Jai Ganesh · 2009-03-18 08:17:48

#1730. What is the number of 2 digit even numbers that can be formed from the digits 1, 2, 3, 4, and 5, repetition not being allowed?

#1731. The first and eighth terms of a Geometric Progression are x[sup]-4[/sup] and x[sup]52[/sup] respectively. What is the second term?

#1732. What is the value of

?

Jai Ganesh · 2009-03-18 19:31:40

#1733. What is the value of

?

#1734. What is the value of

?

#1735. What is the value of

?

Jai Ganesh · 2009-03-18 22:24:41

#1736. Find the 10[sup]th[/sup] term of an Arithmetic Progression whose first term is 12 and the common difference is 5.

#1737. Find the sum

.

#1738. If A = {a, b, c, d, e}, B = {b, d, f, g}, and C = {b, e, f, h}, find

.

#1739. If the straight line 7x - 5y = k passes through the point (1,1), find the value of k.

#1740. In a Geometric Progression, the fourth term is 27 and the seventh term is 729. Find the fourth term.

Jai Ganesh · 2009-03-19 04:05:11

#1741. Find the value of 104 x 96.

#1742. If x = 2 + √3, find the value of

.

#1743. In a right angled triangle,

.
Find the value of tan A x cosec A.

#1744. Find the point of intersection of the straight line 2x-3y = 6 with the y-axis.

#1745. Three solid spheres of radii 3 cm, 4cm, and 5 cm are melted and a bigger spher is formed. Find the radius of the bigger sphere.

Jai Ganesh · 2009-03-19 06:56:14

#1746. Solve for x and y:

.

#1747. Find the value of k for which the following system of equations has infinite solutions:
kx + 3y = 3
12x + ky = 6.

Jai Ganesh · 2009-03-19 17:18:25

#1748. What is th sum of the Geometric Progression
1, 3, 9, 27, .... to 9 terms?

#1749. What is the remainder when x[sup]3[/sup] + x[sup]2[/sup] + 5 is divided by (x-1)?

#1750. What is the square root of 36a[sup]16[/sup]?

#1751. What is the equation of the straight line passing through
(2, -3) an parallel to the x-axis?

#1752. What is the square root of 9x[sup]2[/sup]+30x+25?

#1753. In a cyclic quadrilateral ABCD, the measure of angle A is 5x degrees and measure of angle C is 3x degrees. What is the value of x in degrees?

#1754. The center of a circle is (-6,4). A diameter of the circle has its one end at the origin. What are the coordinates of the other end?

#1755. Find the Least Common Multiple of

.

Jai Ganesh · 2009-03-20 05:05:41

#1756. The sum of a number and its reciprocal is

.
Find the number.

#1757. Which term of the Arithmetic Progression 21, 42, 63, .... is 420?

#1758. A cone has radius 7 cm and slant height 25 cm. Find the curved surface area of the cone.

#1759. Find m if 5x[sup]5[/sup] - 9x[sup]3[/sup] + 3x + m leaves a remainder 7 when divided by
(x + 1).

#1760. Solve:- x[sup]2[/sup] - x - 12 = 0.

Last edited by Jai Ganesh (2009-03-20 05:07:05)

JohnnyReinB · 2009-03-21 03:57:16

Is it just me or are most of the questions getting just a little bit easier?

Jai Ganesh · 2009-03-21 05:12:00

Answers to #1723, #1727, #1736, #1738, #1739, #1740, #1742, #1744, #1745, #1747, #1750, #1751, #1752, #1754, #1755, #1756, and #1757:-

All the answers are correct, JohnnyReinB, other than #1723, #1739, and #1755.

JohnnyReinB · 2009-03-21 05:33:24

ay, LCM, haha

curious, what's the answer to 1739?

Jai Ganesh · 2009-03-21 05:43:34

Answer to #1755:
Correct, JohnnyReinB!

JohnnyReinB · 2009-03-21 20:27:26

ahh, yes.
Oh my, I keep on forgetting 7-5=2
For some weird reason, my brain insists it's 3, as my answer suggests, haha.

Jai Ganesh · 2009-03-22 02:00:22

#1761. A can do a work in 80 days. He works for 10 days and then leaves. B alone finishes the remaning work in 42 days. In how many days would both A and B finsih the work, working together?

#1762. X and Y undertake to finish a job for $600. X alone can do it in 6 days and Y alone can do it in 8 days. With the help of Z, they finish the job in 3 days. How many Dollars does each of them get?

#1763. P and Q working separately can finish a work in 9 days and 12 days respectively. If they work for alternate days, starting with P, in how many days would the work be completed?

#1764. 45 men can complete a work in 16 days. Six days after starting the work, 30 more men join them. How many days would they now take to complete the remaining work?

#1765. 2 men and 3 boys can do a work in 10 days while 3 men and 2 boys can do the same work in 8 days.In how many days can 2 men and 1 boy do the work?

Jai Ganesh · 2009-03-22 02:26:47

#1766. The sum of squares of three consecutive numbers is 2030. What is the middle number?

#1767. The product of three consecutive even numbers, when divided by 8 is 720. What is the product of their squares?

#1768. The product of three consecutive even numbers, when divided by 8 is 720. What is the product of their square roots?

#1769. The sum of two numbers is 40 and their product is 375. What is the sum of their reciprocals?

#1770. If the sum and difference of two numbers are 20 and 8 respectively, then what is the difference of their squares is?

Jai Ganesh · 2009-03-23 23:41:57

#1771. What is the value of

?

#1772. What is the value of e[sup]2.3026[/sup] approximately?

#1773. What is the value of

?

Jai Ganesh · 2009-03-24 05:00:10

#1774. If L = {x:x is a factor of 45}, M = {x:x is a factor of 63}, and N = {x:x is a factor of 120}, then what is

?

#1775. How many common solutions do the equationsx + y = 2, 3x + 4y = 7, and x - y = 3 have?

#1776. Let p, q, and r be non-zero integers such that (p,r) = 1 and (q, r) = 1 where (p,q) denotes the Greatest Common Divisor of p and q. Then, what is the value of (p,q,r)?

#1777. What is the value of the remainder when f(x) = 2x³ - 5x² - x + 10 is divided by (x-2)?

#1778. What is

equal to?

Jai Ganesh · 2009-03-24 19:09:18

#1779. What is the value of

?

#1780. What is the value of the expression

?

#1781. What is the logarithm of 0.0001 to the base 0.001?

#1782. What is the value of x if

?

#1783. What is the value of x if

?

Jai Ganesh · 2009-03-25 05:29:22

#1784. Albert invested an amount of $8000 in a fixed deposit scheme for 2 years at 5% per annum inteterest compounded annually. How much would Albert receive on maturity of the fixed deposit afer 2 years?

#1785. What would be the compound interest on a sum of $25,000 after 3 years at the rate of 12% per annum compound interest compounded annually?

#1786. Sam invested $15,000 at the rate of 10% per annum for one year. If the interest is compounded half-yearly, what amount would Sam receive at the end of one year?

#1787. A bank offers 5% compound interest calculated half-yearly. A customer deposits $1600 each on January 1st and July 1st of the year. At the end of the year, what is the amount of interest he would get?

#1788. What is the difference between the simple interest and compound interest on $1200 for one year at the interest rate of 10% per annum compounded half-yearly?

Jai Ganesh · 2009-03-26 08:24:52

#1789. What is the value of (x + y + z) if

?

#1790. If we multiply a fraction by itself and divide the product by the reciprocal of the original fraction,

is obtained. What is the original fraction?

#1791. What is the smallest rational number that should be subtracted from the sum of

to make the sum a whole number?

#1792. How many

?

#1793. When the capacity of a bucket is 13.5 liters, 12 buckets of water are required to fill a tank. How many buckets of capacity 9 liters each would be required to fill the same tank?

Jai Ganesh · 2009-03-27 08:12:11

#1794.

.

#1795. Find the square root of

.

#1796. Find the point of intersection of the straight lines 2x + 3y = 8 and 2x - 3y = 4.

#1797. Find the common ratio of the geometric Progression 0.2, 0.06, 0.018, 0.0054, ....

#1798.The radius and height of a cone are 7 cm and 15 cm respectively. Find the volume of the cone.

#1799. Find the sum to infinity of the series

.

#1800. Find the product:-

.

Jai Ganesh · 2009-03-28 03:37:08

#1801. What is the length of the longest pole that can be kept in a room 5 meters long, 4 meters broad and 6 meters high?

#1802. A rectangular water reservoir contains 42000 liters of water. If the length of the reservoir is 6 meters and its breadth is 3.5 meters, what is its depth?

#1803. The area of the base of a rectangular tank is 6500 cm² and the volume of the water contained in it is 2.6 cubic meters. What is the depth of the water in the tank?

#1804. A rectangular water tank is open at the top. Its capacity is 24 m³. Its length and breadth are 4 meters and 3 meters respectively. Ignoring the thickness of the material used for building the tank, what is the total cost of painting the inner and outer surfaces at the rate of $10 per m²?

#1805. The water in a rectangular reservoir having a base of 80 meters length and 60 meters breadth is 6.5 meters deep. In what time can the water be emptied by a pipe which has cross-section area in the shape of a square of side 20 centimeters, if the water flows through it at the rate of 15 kilometers per hour?

#1806. A rectangular tankis 225 meters long and 162 meters wide at the base. With what speed must water flow into it through an aperture 60 centimeters in length and 45 centimeters in breadth so that the level may be raised 20 centimeters in 5 hours?

#1807. A cuboidal tank of capacity 216 liters has depth one-third of its length and the breadth is half of one-third of the difference between the length and the breadth. What is the length of the tank?

#1808. A swimming pool is 24 meters long and 15 meters broad. When a number of men dive into the pool,the height of the water rises by 1 centimeter. If the averagevolume of water displaced by each man is 0.1 m³, how many men dived into the swimming pool?

#1809. What part of a ditch 48 meters long, 16.5 meters broad, and 4 meters deep can be filled by the earth got by digging a cylindrical tunnel of diameter 4 meters and length 56 meters?

#1810. If the areas of the three adjacent faces of a cuboid are x, y, and z respectively, what is the volume of the cuboid?

Jai Ganesh · 2009-03-29 03:22:46

#1811. Which term of the Arithmetic Progression 5, 13, 21, ...... is 181?

#1812. Determine k so that

are the three consecutive terms of an Arithmetic Progression.

#1813. Determine k so that k+2, 4k - 6, and 3k - 2 are three consecutive terms of an Arithmetic Progression.

#1814. Detrmine the 25[sup]th[/sup] term of an Arithmetic Progression whose 9[sup]th[/sup] term is -6 and common difference is

.

#1815. Which term of the Geometric progression

?

#1816. Which term of the Geometric progression

?

#1817. The third term of a Geometric Progression is the square of the first erm. If the seond term is 8, determine the 6[sup]th[/sup] term.

#1818. If the 4[sup]th[/sup] term and 8[sup]th[/sup] term of a Geometric Progression are 24 and 384 respectively, then find out the first term and the common ratio.

#1819. The sum of a series in Arithmetic progression is 525. Its first term is 3 and last term is 39. Find the common difference.

#1820. The fifth term of a Geomeric Progression is 2. Find the product of the first 9 terms of the Geometric progression.

Jai Ganesh · 2009-03-30 05:17:18

#1821. The ratio of the altitudes of two similar triangles is 4:5. What is the ratio of their areas?

#1822. What is the slope of the line which is parallel to the joining the points (0,0) and (-5,5)?

#1823. What is the value of p given that the line

passes through the point (-4,4)?

#1824. In Δ ABC, A(-, -2), B(-6,-2), and C(-2,1) are the vertices.What are the coordfinates of the centroid of the triangle?

#1825. If x - y = 3 and x + 2y = 6 are the diamters of a circle, what are the coordinates of the center of the circle?

#1826. What is the equation of a straight line which has the y-intercept -5 and slope 2?

#1827. What is the value of

?

#1828. If x = a secθ and y = b tanθ, what is the value of x² - y²?

#1829. What is the value of sinθ if

?

#1830. The Standard Deviation of 5 values is 5√2. What is the value of the new Standard Deviation if each value is increased by 4?

#1831.The line joining A(-1, -2) and B(5,6) is perpendicular to the line joining C(4,2) and D(0,y). Find y.

#1832. Find the equation of the line cutting off intercepts

on the x-axis and the y-axis respectively.

#1833. Find the equation of a line parallel to 3x-4y-5 = 0 and passing therough the point (2,3).

#1834. Find the value of

?

#1835. Solve: 2cos3θ = 1 where 0° ≤ θ ≤ 90° .

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