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A trapezium based prism with two parallel sides 8 cm and 14 cm respectively and distance between two parallel sides is 8 cm. Find the height of the prism if the volume of the prism is 1056 ?
Volume of prism = (Base area) × height.
Base Area = Area of trapezium
= 1/2(8 + 14) × 8 = 88
∴ 1056 = 88 × height
The base of a right prism is an equilateral triangle. If its height is onefourth and each side of the base is tripled, then the ratio of the volumes of the old to the new prism is
y = 24 sin x + 7 cos x
dy/dx = 24 cos x  7 sin x = 0
7 sin x = 24 cos x, or
sin x / cos x = 24/7
tan x = 24/7
Or sin x = 24/(24^2+7*2)^0.5 = 24/(576+49)^0.5 = 24/25 and cos = 7/25.
Thus the max value of y = 24*24/25 + 7*7/25
= (576+49)/25
= 625/25
= 25. Answer.
A sum of money triples itself in 15 years 6 months. In how many years would it double itself?
A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:
A money lender finds that due to a fall in the annual rate of interest from 8% to 7^{3/4}%, his yearly income has diminished by Rs 61.50. What is his capital amount?
Let Capital invested is X
X(8%7.75%)= 61.50
X = 61.50/.0025= Rs. 24,600/
Income when interest rate is 8%
24600* 8%= 1968
Interest when interest reduced to 7.75%
24600 * 7.75% = 1906.5
Difference Amount Rs. 61.5
Therefore Capital Amount is Rs. 24,600/
A train X starts from Meerut at 4 p.m. and reaches Ghaziabad at 5 p.m. while another train Y starts from Ghaziabad at 4 p.m. and reaches Meerut at 5.30 p.m. The two trains will cross each other at:
Suppose, the distance between Meerut and Ghaziabad is x km.
Time taken by X to cover x km = 1 hour.
Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
Let the length of the train be x metres and its speed by y m/sec.
At what price should a shopkeeper mark a radio that costs him Rs. 1200 in order that he may offer a discount of 20% on the marked price and still make a profit of 25%?
Two shopkeepers announce the same price of Rs. 700 for a sewing machine. The first offers successive discounts of 30% and 6% while the second offers successive discounts of 20% and 16%. The shopkeeper that offers better discount, charges ………… less than the other shopkeeper.
In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?
Which of the following can’t be the ratio of the sides of a triangle.
We know that sum of the two side are always greater than third side.
Now, if we consider option (b)
The ratio of the sides of a triangle , 1 : 3 : 6 side of a triangle x, 3x, & 6x but here x + 3x < 6x
So, 1 : 3 : 6 can’t be the ratio of side of a triangle.
The marked price of an article is 20% more than its cost price. A discount of 20% is given on the marked price. In this kind of sale, the seller bears
% gain or loss = 2020+(20 (20))/100 = 4% loss
A shopkeeper fixed a price of an article 25% more of its cost price and then allowed 10% discount. The actual profit percent is
Profit percent = 2510+(25 (10))/100 = 12.5%
After allowing a discount of 16%, there was still a gain of 5%. Then the percentage of marked price over the cost price is
If C.P. is Rs. 100 then S.P. = Rs.105 So, marked price 84/100 = 105 So, marked price = (105*100)/84 =125 So, marked price is 25% over the cost price
A man invests half of his capital at the rate of 10% per annum, onethird at 9% and the rest at 12% per annum. The average rate of interest per annum, which he gets is :
Rs. 800 becomes Rs. 956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what amount will Rs. 800 become in 3 years ?
A contractor undertakes to build a wall in 40 days. He employs 50 people for the same. However, after 20 days he finds that only 40% of the work is completed. How many more man need to be employed to complete the work in time?
According to the given information, 50 men completed 0.4 work in 20 days and (M + 50) men should complete the remaining 1 – 0.4 = 0.6 work in remaining time i.e. 40 – 20 = 20
Anita and Bindu can finish a work in 10 days while Bindu and Chitra can do it in 18 days. Anita started the work, worked for 5 days, then Bindu worked for 10 days and the remaining work was finished by Chitra in 15 days. In how many days could Chitra alone have finished the whole work?
Let Chitra alone can finish a work in Days. !lso !’s 5 days work + B’s 10 days work + C’s 15 days’ work equals the total work.
⇒ (! + B)’s 5 days work + (B + C)
A man is twice as fast as a woman. Together the man and the woman do the piece of work in 60 days. In how many days each will do the work if engaged alone?
Let one women is one unit then man will be 2 units and 3 units finished the work in 60 days hence one units will finish the work in 180 days therefore woman will take 180 days and man will take 90 days being twice efficient as compared to woman.
The cost price of 10 articles is equal to the selling price of 9 articles. Find the profit percent.
If a man estimates his loss as 20% of the selling price, then his loss percent is
A dishonest milkman sells milk at cost price but he mixes water and earns 16 % profit. Find the ratio of mixture to milk in the mixture?
Let C.P. of 1 litre milk = 10/
bought milk = x litre then C.P. = 10x
Let water mixed in milk = y litre
then quality = (x + y) litre
Mixture is sold on C.P.
then S.P. = 10 (x + y)
= 10x + 10y
profit = S.P. – C.P. = (10x + 10y) – (10x)= 10y
What is the LCM of (6x^{3} + 60x^{2} + 150x) and (3x^{4} + 12x^{3} – 15x^{2})?
If HCF of (x^{2} + x – 12) and (2x^{2} – kx – 9) is (x – k), then value of k is
∵ x – k is a factor of 2x^{2} – kx – 9
∴ 2k^{2} – k^{2} – 9 = 0
∴ k = ± 3
But factor of (x^{2} +x  12) are (x+4),(x3) Hence value of k is 3.
If (3x^{3} – 2x^{2}y – 13xy^{2} + 10y^{3}) is divided by (x – 2y), then what is the remainder?
Required remainder = 3(2y)^{3} – 2 (2y)^{2} y – 13 (2y) y^{2} + 10y^{3} (using factor theorem) = 24y^{3} – 8y^{3} – 26y^{3} + 10y^{3} = 34y^{3} – 34y^{3} = 0
Two numbers are such that the sum of twice the first number and thrice the second number is 36 and sum of thrice the first number and twice the second number is 39. Which is the smaller number?
Let the numbers be x and y
2x + 3y = 36
3x + 2y = 39
4x + 6y = 72
If the sum and difference of two numbers are 20 and 8 respectively, then the difference of their square is:
A 4digit number is formed by repeating a 2digit number such as 2525, 3232, etc. Any number of this form is always exactly divisible by:
By 101 which is the smallest 3digit prime number.
A number divided by 68 gives the quotient 269 and remainder zero. If the same number is divided by 67, then the remainder is:
The number is 68 × 269 = 18292. 18292, when divided by 67, leaves a remainder of 1.
What is the mode of the following numbers? 1, 2, 4, 6, 4, 3, 5, 4
Find the median of the following data. 27, 39, 49, 20, 21, 28, 38
Series =20, 21,27,28, 38,39,49
Total number in the series=7 Median=7+1/2=4th number=28
Bronze statue of dancing girl has been excavated at:
A proclamation of emergency must be placed before the Parliament for its approval
The permanent president of Constituent Assembly was
Which one of the following rights has been described by Dr. !mbedkar as ‘The heart and soul of the Constitution’?
Which of the following is not provided for by the Constitution of India?
Which one of the following is the largest committee of the Parliament?
The Speaker of the Lok Sabha can resign his office by addressing his resignation to
Which of the following is definitely a major indication of the state of the economy of a country?
In which year ‘Bombay plan’ was launched by some industrialists?
Which sector is the backbone of Indian economy?
India is an agrarian area. Fundamentally, the Indian economy is agrarian. Agriculture is the core of the Indian economy, given rapid growth and industrialisation. As Mahatma Gandhi claimed, "India exists in villages and the soul of the Indian economy is agriculture"
Agriculture is the backbone of the Indian economy, as 75% of the population of India depends on agriculture. It has now become apparent that India's economic growth does not live up to expectations, as agricultural growth lags behind.
In which form of the market structure is the degree of control over the price of its product by a firm very large?
Which among the following statements with regard to Raja Rammohan Roy are correct?
1. He started the Atmiya Sabha
2. He wrote the Gift of Monotheist
3. He published the Precepts of Jesus
4. He founded the Brahma Sabha
Select the correct answer from the codes given below:
Codes:
The person who returned his token of honour to Government of India on May 30, 1919 was
The Muslim League demanded separate Pakistan for the first time in the year
Which music instrument belongs to Hari Prasad Chaurasia?
The image of Nataraja (the lord of dance) is a superb masterpiece of the period of
Chakan GaanNgai, a postharvest festival is celebrated in ___________.
Sports coaches receive which of the following awards?
Under which article of Indian Constitution, a High Court can issue writs to protect the fundamental rights?
Which provision relating to the fundamental rights is directly related to the exploitation of children?
The article of Indian Constitution related to abolition of untouchability is
The ‘Cannes !ward’ is given for excellence in which field?
The Constitution of India does not contain any provision for the impeachment of
Which one of the following is not a method of measurement of National Income?
Labour intensive technique would get choosen in a
Who said, “Economics is the Science of Wealth”?
Supply creates its own demand. This statement is related to
Coconut and mango grouped under which kind of fruit?
Which of the following gland disappear during old age?
Estimation of age of woody plant by counting annual ring is—
The aqueous solution of which acids is called Vinegar ?
Medicines are more effective, if they are used in—
Cooking oil can be converted into vegetable ghee by the process of
Force of attraction between the molecules of different substances is called
Stars which appear single to the naked eye but are double when seen through a telescope are
Which of the following is an electromagnetic wave?
Which of the following show photoelectric effect?
Which of the following instrument is used to measure the strength of winds
Sound wave cannot pass through above which of the following?
A plane mirror reflects a beam of light to form a real image. The incident beam is
We have : (101 + 15) – (35 + 43) = 38.
So, missing number = (48 + 184) – (56 + 34) = (232 – 90) = 142.
Read the following information carefully and answer the questions given below it:
(i) A, B, C, D and E are five friends.
(ii) B is elder to E, but not as tall as C.
(iii) C is younger to A, and is taller to D and E.
(iv) A is taller to D, but younger than E.
(v) D is elder to A but is shortest in the group.
Q. Who among the following is the eldest?
In terms of age, we have : E < B, C < A, A < E, A < D. So we have : C < A < E < B, A < D.
In terms of height, we have : B < C, D < C, E< C, D < A.
(i) A, B, C, D and E are five friends.
(ii) B is elder to E, but not as tall as C.
(iii) C is younger to A, and is taller to D and E.
(iv) A is taller to D, but younger than E.
(v) D is elder to A but is shortest in the group.
Q. Which of the following pairs of students is elder to D?
In terms of age, we have : E < B, C < A, A < E, A < D. So we have : C < A < E < B, A < D.
In terms of height, we have : B < C, D < C, E< C, D < A.
It cannot be determined for sure.
A man is facing West and turns 45° clockwise, again 180° clockwise and then turns 270° anticlockwise. Which direction is he facing now?
As shown in figure, the man initially faces in the directions OA. On moving clockwise, the man faces in the direction OB. On further moving clockwise, he faces in the direction OC. Finally, on moving anticlockwise, he faces in the direction OD, which is Southwest.
In All other groups, the numbers are in the ratio 1 : 2 : 4 : 3.
What is the product of all the numbers in the dial of a telephone?
Since one of the numbers on the dial of a telephone is zero, so the product of all the numbers on it is 0.
In a certain code language ‘123’ means ‘hot filtered coffee,’‘356’ means ‘very hot day’ and ‘589’ means ‘day and night’. Which digit stands for ‘very’?
In the first and the second statements, the common code digit is ‘3’ and the common word is ‘hot’. So, ‘3’ means ‘hot’.
In the second and third statements, the common code digit is ‘5’ and the common word is ‘day’. So, ‘5’ means ‘day’.
Thus, in the second statement ‘6’ means ‘very’
Which of the following will complete the series?
2Z5, 7Y7, 14X9, 23W11, 34V13, ?
In this question, arrange the given words in a meaningful sequence and then choose the most appropriate sequence from amongst the alternatives?
1. Puberty
2. Adulthood
3. Childhood
4. Infancy
5. Senescence
6. Adolescence
In this questions, one term in the number series is wrong. Find out the wrong term.
3, 7, 15, 39, 63, 127, 255, 511
The correct pattern is × 2 + 1.
So, 39 is wrong and must be replaced by (15 × 2 + 1) i.e. 31.
In the following list of numerals, how many 2s are there each of which is followed by 1 but not preceded by 4?
4 2 1 2 1 4 2 1 1 2 4 4 4 1 2 2 1 2 1 4 4 2 1 4 2 1 2 1 2 4 1 4 2 1 2 4 1 4 6
Cyclone is related to Anticyclone in the same way as Flood is related to?
The words in pair represent opposite conditions.
Number of letters skipped in between adjacent letters in the series decreases by three.
In the Venn diagram given below, circle represents sportspersons, square represents unmarried persons, triangle represents women and rectangle represents educated persons. Each section is numbered. Study this diagram to answer the following question.
Which sections are represented by the region numbered 11?
Clearly, 11 lies inside all the four figures. So, 11 represents unmarried educated sportswomen.
Which of the following word cannot be formed by using the letters of the given word? LIBERATIONIST
LIBER!TIONIST does not contain two ‘L’ letters.
Which of the following number is wrong in the given series?
3601, 3602, 1803, 604, 154, 36, 12
Among P, Q, R, S and T each reaching school at a different time, R reaches before S and P and only after Q. T is not the last to reach school. Who among them reached school last?
The sequence is Q > R > T, S, P
In a row of forty boys facing North, R is twelfth from the left end and T is eighteenth from the right end. How many boys are between R and T in the row?
R = 12th from left
T = 18th from right
No. of boys between R and T = 40  (12+18) = 10
In this question, which answer figure will complete the question figure?
In this question a number series is given. Below the series one number is given followed by (1), (2), (3), (4) and (5). You have to complete this series following the same logic as in the original series and answer the question that follow.
15, 9, 8, 12, 36, 170
19, (1), (2), (3), (4), (5)
What will come in place of (2)?
If × stands for addition, < for subtraction, + stands for division, > stands for multiplication, – stands for equal to, ÷ stands for greater than, and = stands for less than, state which of the following is true?
Select the correct combination of mathematical signs to replace * sings and to balance the given equation.
15 * 24 * 3 * 6 * 17
In this question below are given two statements followed by two conclusions numbered I and II. You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusion and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts.
Q.
Statements: A
ll men are married.
Some men are educated
Conclusions:
I. All men are educated.
II. Some educated are married.
From the Venn diagram we can infer that conclusion I is definitely false. And as all men are married and some men are educated we can say that some educated are married is true.
How many triangles are there in the figure given below?
In the figure, there are 16 triangles.
In this question, find the missing number/letters, from the given responses.
25 – K – 8, 23 – I – 11, 21 – G – 14, 19 – E – 17, ?
P, T, V, R, M, D, K and W are sitting around a circular table facing the center. V is second to the left of T. T is fourth to right of M. D and P are not sitting next to T. D is third to the right of P. W is not sitting next to P. P is sitting next left of K. Then who is second to the left of K?
How many 9s are followed by 6s as well as preceded by 6s in the following set of figures?
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