If $$N=(\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}})$$, then what is the value of $$\frac{1}{N}$$ ?
Sign in
Please select an account to continue using cracku.in
↓ →
If $$N=(\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}})$$, then what is the value of $$\frac{1}{N}$$ ?
Login to view the detailed solution.
The sum of three consecutive even numbers is always divisible by ____.
Login to view the detailed solution.
How many positive factors of 24 are there?
Login to view the detailed solution.
4/5 part of a tank is filled with oil. After taking out 42 litres of oil the tank is 3/4 part full. What is the capacity (in litres) of the tank?
Login to view the detailed solution.
What is the largest four digit number which is a perfect square?
Login to view the detailed solution.
Two inlet pipes can fill a cistern in 20 and 24 hours respectively and an outlet pipe can empty 160 gallons of water per hour. All the three pipes working together can fill the empty cistern in 40 hours. What is the capacity (in gallons) of the tank?
Login to view the detailed solution.
P alone can complete the work in 5 days, Q alone can do same work in 6 days and R alone can do the same work in 12 days. They jointly complete the work and earn Rs 5400. What is the share of R?
Login to view the detailed solution.
After giving two successive discounts of 20% and 25% a cycle is sold for Rs 4200. What is the marked price (in Rs) of the cycle?
Login to view the detailed solution.
The marked price of an article is 60% more than its cost price. What should be the discount (in %) offered by the shopkeeper so that he earns a profit of 12%?
Login to view the detailed solution.
The ratio of the speed of P, Q and R is 10 : 12 : 15 respectively. What is the ratio of the time taken by P, Q and R respectively to cover the same distance?
Login to view the detailed solution.
Three bottles of equal capacity are containing a mixture of milk and water in ratio 2 : 1, 3 : 7 and 4 : 11 respectively. These three bottles are emptied into a large bottle. What is the ratio of milk and water respectively in this large bottle?
Login to view the detailed solution.
The average of 11 results is 182. If the average of first 6 results is 199 and that of the last 6 results is 161, then what will be the 6th result?
Login to view the detailed solution.
The average of 45 results was calculated as 27 but later it was found that while calculating 39 was taken as 93 by mistake, then what will be the correct average?
Login to view the detailed solution.
A shopkeeper professes to sell his goods at cost price but uses a 960 gm weight instead of 1 kilogram weight. What is the profit percentage of the shopkeeper?
Login to view the detailed solution.
A person sold a book for Rs 21 and got a loss percentage which was numerically equal to the cost price. What is the cost price (in Rs) of the book?
Login to view the detailed solution.
If length of a rectangle is increased by 10% and breadth is increased by 15%, then what will be the percentage increase in the area of rectangle?
Login to view the detailed solution.
If the base of triangle is increased by 10% and height is decreased by 20%, then what will be the percentage change in the area of a triangle?
Login to view the detailed solution.
A bus starts running with some initial speed and its speed increases every hour by 9 km/hr. If it takes 11 hours to cover a distance of 572 km, then what was the initial speed (in km/hr) of the bus?
Login to view the detailed solution.
A boat goes 15 km upstream and 22 km downstream is 5 hours. It goes 20 km upstream and $$\ \frac{55}{2}\ $$km downstream in $$\ \frac{13}{2}\ $$hours. What is the speed (in km/hr) of stream ?
Login to view the detailed solution.
If a certain sum becomes 4 times in 4 years at compound interest, then in how many years, it will become 64 times?
Login to view the detailed solution.
What is the simple interest on Rs 7200 in 7 years at the rate of 14% per annum?
Login to view the detailed solution.
The table give below shows the marks obtained by six students in 5 different subjects.

What are the total marks obtained by student D in all subjects?
Login to view the detailed solution.
What is the average of total marks obtained by all six students in subject R?
Login to view the detailed solution.
What is the aggregate percentage of marks obtained by student C in all the five subjects?
Login to view the detailed solution.
Marks obtained by student B is how much percent more than the marks obtained by A?
Login to view the detailed solution.
The perimeter of base of a right circular cone is 88 cm. If the height of the cone is 48 cm, then what is the total surface area (in cm$$^{2})\ $$of the cone?
Login to view the detailed solution.
What is the length of the longest rod that can be placed in a room which is 3 metres long, 4 metres broad and 5 metres high?
Login to view the detailed solution.
If the area of a square is 48, then what is the diagonal of the square?
Login to view the detailed solution.
A cylindrical well of height 20 metres and radius 14 metres is dug in a field 72 metres long and 44 metres wide. The earth taken out is spread evenly on the field. What is the increase (in metre) in the level of the field?
Login to view the detailed solution.
Radius of hemisphere is thrice than that of a sphere. What is the ratio of total surface area of hemisphere to that of sphere?
Login to view the detailed solution.
If $$x + y = 4$$, then what is the value of $$x^{3} +y^{3} +12xy$$?
Login to view the detailed solution.
If $$x^{4}+\frac{1}{x^{4}}= 198$$ and $$x>0$$, then what is the value of $$x^{2}-\frac{1}{x^{2}}$$?
Login to view the detailed solution.
If $$3x - \frac{1}{3x} = 9$$, then what is the value of $$x^{2} + \frac{x^2}{81}$$?
Login to view the detailed solution.
If $$x^{3} - y^{3} = 112$$ and $$x - y = 4$$, then what is the value of $$x^{2} + y^{2}$$?
Login to view the detailed solution.
If $$x = 5 - \frac{1}{x} $$, then what is the value of $$x^{5} + \frac{1}{x^{5}}$$?
Login to view the detailed solution.
In ΔABC, ∠A : ∠B : ∠C = 3 : 3 : 4. A line parallel to BC is drawn which touches AB and AC at P and Q respectively. What is the value of ∠AQP - ∠APQ?
Login to view the detailed solution.
In the given figure, O is the center of the circle, $$\angle$$CAO = 35$$^\circ$$. What is the value (in degrees) of $$\ \angle$$AOB?
In the given figure, $$\triangle$$PQR is drawn such that PQ is tangent to a circle whose radius is 10 cm and QR passes through centre of the circle. Point R lies on the circle. If QR = 36 cm, then what is the area (in cm$$^{2}\ $$of $$\ \triangle$$PQR?

Login to view the detailed solution.
The side QR of ΔPQR is produced to S. If ∠PRS = 105° and ∠Q = (1/2)∠P, then what is the value of ∠P?
Login to view the detailed solution.
The perimeter of an isosceles triangle is 64 cm and each of the equal sides is 5/6 times the base. What is the area (in cm2) of the triangle?
Login to view the detailed solution.
What is the simplified value of$$\ \sqrt{\frac{sec^{2} \theta+cosec^{2} \theta}{4}}$$?
Login to view the detailed solution.
If$$\ \frac{x-xtan^{2}15^\circ}{1+tan^{2}15^\circ}$$= sin $$60^\circ\ $$+ cos 30$$^\circ\ $$, then what is then what is the value of x?
Login to view the detailed solution.
What is the simplified value of $$\ \frac{2sin^{3}\ \theta\ - sin\theta}{cos\theta\ -\ 2\ cos^{3}\ \theta}$$?
Login to view the detailed solution.
If $$tan(\theta)tan(5\theta)=1$$, then what is the value of $$sin 2\theta$$ ?
Login to view the detailed solution.
The angles of elevation of the top of a building from the top and bottom of a tree are $$30^\circ$$ and $$30^\circ$$ respectively. If the height of the tree is $$50 m$$, then what is the height of the building?
Login to view the detailed solution.
The given pie chart shows the marks obtained (in degrees) by a student in different subjects. The total marks obtained by the student in the examination is 432.

What is the total of marks obtained in Hindi and Maths?
Login to view the detailed solution.
The marks obtained in science is what percentage of the total marks?
Login to view the detailed solution.
The marks obtained in Maths is how much percent more than the marks obtained in Social Science?
Login to view the detailed solution.
In how many subjects marks obtained are more than the average marks per subject?
Login to view the detailed solution.
If the maximum marks per subject is 100, then what is the total marks (in percentage) obtained in English and Hindi together?
Login to view the detailed solution.
In the following question, select the related word from the given alternatives.
Tailor : Needle : : Woodcutter : ?
Login to view the detailed solution.
Scissors : Cloth : : Axe : ?
Login to view the detailed solution.
In the following question, select the related letters from the given alternatives.
PQRS : QSUW : : ABCD : ?
Login to view the detailed solution.
REKM : UHNP : : PKDL : ?
Login to view the detailed solution.
In the following question, select the related number from the given alternatives.
5 : 26 : : 8 : ?
Login to view the detailed solution.
5 : 125 : : 11 : ?
Login to view the detailed solution.
In the following question, select the odd word from the given alternatives.
Login to view the detailed solution.
In the following question, select the odd word pair from the given alternatives.
Login to view the detailed solution.
In the following question, select the odd letters from the given alternatives.
Login to view the detailed solution.
Login to view the detailed solution.
In the following question, select the odd number from the given alternatives.
Login to view the detailed solution.
In the following question, select the odd number pair from the given alternatives.
Login to view the detailed solution.
Arrange the given words in the sequence in which they occur in the dictionary.
1. Brain
2. Brand
3. Beep
4. Boxer
5. Boxed
Login to view the detailed solution.
1. Wrong
2. Write
3. West
4. Wind
5. Walk
Login to view the detailed solution.
A series is given with one term missing. Select the correct alternative from the given ones that will complete the series.
A, D, G, J, ?
Login to view the detailed solution.
AB10, DF101, GJ290, ?
Login to view the detailed solution.
In the following question, select the missing number from the given series.
1, 4, 13, 40, 121, ?
Login to view the detailed solution.
84, 42, 44, 22, 24, 12, ?
Login to view the detailed solution.
Amit's present age is 5/4 of his age at time of his sister's marriage. If his sister's marriage happened 5 years ago and his father's age was twice of Amit's age at that time, then what is his father's present age (in years)?
Login to view the detailed solution.
Six games are kept one on top of the other. Uno is just above Snakes & Ladders. The Monopoly is between Ludo and Chess. Carrom is between Uno and Ludo. Which game is between the Carrom and Monopoly games?
Login to view the detailed solution.
Present age of a father is 3 times that of his son. After 10 years the son’s age will be 5 times of Raman’s present age. If Raman celebrated his third birthday 2 years ago, then what is the present age (in years) of father?
Login to view the detailed solution.
In the following question, select the word which cannot be formed using the letters of the given word.
Precipitation
Login to view the detailed solution.
Imprisonment
Login to view the detailed solution.
In a certain code language, "BALL" is written as "27" and "CANE" is written as "23". How is "YELL" written in that code language?
Login to view the detailed solution.
In a certain code language, "RENTED" is written as "718314" and "SCARF" is written as "92576". How is "CARTED" written in that code language?
Login to view the detailed solution.
In the following question, by using which mathematical operators will the expression become correct?
7 ? 4 ? 5 ? 165 ? 5
Login to view the detailed solution.
In the following question, correct the equation by interchanging two signs.
24 × 8 ÷ 9 + 9 - 10 = 26
Login to view the detailed solution.
If 21 (49) 14 and 159 (169) 146, then what is the value of 'A' in 56 (A) 44?
Login to view the detailed solution.
If $$\ 2^{3}\ $$# $$4^{3}\ $$ @$$\ 3^{3}\ $$= 45 and $$\ 3^{3}\ $$# $$\ 5^{3}\ $$@ $$\ 4^{3}\ $$= 88, then $$\ 4^{3}\ $$# $$\ 2^{3}\ $$@ $$\ 1^{3}\ $$= ?
Login to view the detailed solution.
In the following question, select the number which can be placed at the sign of question mark (?) from the given alternatives.

In the following question, select the number which can be placed at the sign of question mark (?) from the given alternatives.

Login to view the detailed solution.
How many triangles are there in the given figure ?
How many triangles are there in the given figure ?

Login to view the detailed solution.
In each of the following question below are given some statements followed by some conclusions. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. All boys are smart.
II. All smart are thin.
Conclusions:
I. All boys are thin.
II. All smart are boys.
Login to view the detailed solution.
Statements:
I. All cups are pencils.
II. Some pencils are pens.
Conclusions:
I. Some pencils are cups.
II. No pencil are cups.
III. Some cups are pens.
Login to view the detailed solution.
From the given options, which answer figure can be formed by folding the figure given in the question ?

Two position of a cube are shown below. What will come opposite to face containing 'B'?

In the given figure, how many wooden plates are there ?

Login to view the detailed solution.
In the given figure, how many sour fruits are there ?

Login to view the detailed solution.
In the given figure, how many moving cars are not red ?

Login to view the detailed solution.
Which answer figure will complete the pattern in the question figure ?

Login to view the detailed solution.
Which answer figure will complete the pattern in the question figure ?

Login to view the detailed solution.
From the given answer figures, select the one in which the question figure is hidden/embedded.

Login to view the detailed solution.
From the given answer figures, select the one in which the question figure is hidden/embedded.

Login to view the detailed solution.
A piece of paper is folded and punched as shown below in the question figures. From the given answer figures, indicate how it will appear when opened ?

A piece of paper is folded ans punched as shown below in the question figures. From the given answer figures, indicate how it will appear when opened ?

If a mirror is placed on the line AB, then which of the answer figures is the right image of the given figure ?

Login to view the detailed solution.
If a mirror is placed on the line AB, then which of the answer figures is the right image of the given figure ?

Login to view the detailed solution.
A word is represented by only set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as shown in the given two matrices. The column and rows of Matrix-I are numbered from 0 to 4 and that of Matrix-II are numbered from 5 to 9. A letter from these matrices can be represented first by its row next by its column, for example, 'S' can be represented by 00, 24 etc., and 'N' can be represented by 66, 97, etc., Similarly, you have to identify the set for the word "SOIL".

Login to view the detailed solution.
A word is represented by only set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as shown in the given two matrices. The column and rows of Matrix-I are numbered from 0 to 4 and that of Matrix-II are numbered from 5 to 9. A letter from these matrices can be represented first by its row next by its column, for example, 'A' can be represented by 04, 22 etc., and 'O' can be represented by 59, 98, etc., Similarly, you have to identify the set for the word "TRUMP".

Login to view the detailed solution.
Which one of the following is true about mixed economy?
Which among the following is the most appropriate measure of an economic growth of a country?
Green revolution was introduced in which Five Year Plan of India?
Who among the following is the ex-officio chairman of the NITI Aayog in India?
How many Miniratna companies are there in Category - I?
Who is the father of 'Utilitarian School of Thought'?
Which of the following is not a good argument in favour of democracy?
I. Democracy enhances the dignity of citizens
II. Democracies are more prosperous than others
III. Democracies resolve conflicts in a better way
What is a voluntary union of sovereign and independent states called?
What is the minimum age required to become a member of Lok Sabha?
Who declares the National Emergency in India?
Indian Constitution contains how many schedules?
Which of the following articles relates to 'abolition of titles'?
How many members of Lok Sabha are nominated by the President?
Which of the following pair is INCORRECT?
Who among the following started Bengal weekly newspaper ‘Samvad Kaumudi’ in year 1821?
The Vijaynagar ruler Krishna Dev Raya's work 'Amuktamalayada' was written in which language?
Idol of dancing girl (Bronze) is found in which of the following civilzation?
Who is also known as 'Light of Asia'?
What are the imaginary lines touching both the poles of earth called?
On which of the following date, summer solstice is observed in Northern Hemisphere?
Which of the following pair is CORRECT?
Near coastal areas, temperature on land in night time gets reduced due to _____.
Which of the following wind is also known as 'Snow Eater'?
Turmeric is a modified _____.
Which of the following cell organelle is present in both plant and animal cell?
What is the nature of cell membrane?
Which of the following is the longest bone in human body?
What is the main function of white blood cells (WBC's)?
Arrangement of leaves in a plant is called as ______.
Law of Inertia is also known as _____.
Surface water of a lake is about to freeze. What will be the temperature (in 0C) of water at the bottom of the lake?
By the use of photovoltaic cell while converting solar energy which of the following is produced?
Hydraulic brakes used in automatic vehicles is direct virtual application of which law?
Which among the following is/are input devices?
I. Keyboard
II. Scanner
III. Joy-stick
Which among the following is a light sensitive device used for converting images to their digital form?
Which of the following elements are commonly found in most fertilizers?
Which of the following is used as moderator in atomic reactor?
'Oil of vitriol' is the common name of which of the following?
Which among the following acid is also known as 'Muriatic Acid'?
What is a Vermicompost?
Plants which can survive in very less water are called as ______.
Which among the following represents plateau phase in population?
Programme for capacity building of Elected Women Representatives (EWRs) of panchayats has been launched at _____.
Who invented computer?
Which of the following pair is CORRECT?
Match the following.

Who among the following is not a recipient of Nobel Prize 2016 in the field of Chemistry?
'Life on my terms: from the grassroots to the corridors of power' is an autobiography of _____.
The 'One belt, One road' summit was held in which of the following cities?
Maitree Express' is an international train between India and ______.
In the following question, some part of the sentence may have errors. Find out which part of the sentence has an error and select the appropriate option. If a sentence is free from error, select 'No Error'.
The CEO has decided to visit all the (a:/ departments of the office tomorrow (b:/ evening to review of the situation. (c:/ No Error (d:
Neha is a very good fashion (a:/ designer but her designs are not (b:/ easily accessible with the public. (c:/ No Error (d:
Dr. APJ Abdul Kalam's life was a (a:/ sage of dedication in the (b:/ cause of educational reforms in India. (c:/ No Error (d:
Ashish was listening (a:/ to a radio when (b:/ Sunita arrived. (c:/ No Error (d:
When the professors are on strike (a:/ and a notice of this effect is pasted on the university gate (b:/ there is no sense to go there. (c:/ No Error
(d:
In the following question, the sentence given with blank to be filled in with an appropriate word. Select the correct alternative out of the four and indicate it by selecting the appropriate option.
_____ of the five persons will appear in the court.
_____ the child saw his parents, he became happy.
Ruhika was married _____ Akshay.
Neha's pay is _____ of her work.
Rahul can _____ the four candles in one breath.
In the following question, out of the four alternatives, select the word similar in meaning to the word given.
Imbecility
Somnolent
Invidious
Haughty
Lethal
In the following question, out of the four alternatives, select the word opposite in meaning to the word given.
Festal
Slender
Tardy
Attenuate
Extant
In the following question, out of the four alternatives, select the alternative which best expresses the meaning of the idiom/phrase.
Lion's mouth
A stiff-necked person
Cross out
Make away with
To put one out of countenance
Improve the bracketed part of the sentence.
Practically (every part) of the papaya tree is used by man.
Kanika shall be grateful to you if you (are of help) her now.
Shweta unnecessarily (picked up) a quarrel with Kanishk and left the party hurriedly.
Not a word (she spoke) to the unfortunate mother about it.
Shrey has got many friends because he has got (much money).
In the following question, out of the four alternatives, select the alternative which is best substitute of the phrase.
A state of mental weariness from lack of occupation
A dabbler in the art and literature
Being able to pay one's debt
One who is subject to failure or to committing mistakes
A short stay in a place
In the following question, four words are given out of which one word is incorrectly spelt. Select the incorrectly spelt word.
In the following passage some of the words have been left out. Read the passage carefully and select the correct answer for the given blank out of the four alternatives.
Science is both a blessing and a _____. While it has given us many things which have made life better and _____, it has also given terrible instruments of _____. Science has discovered and invented many things to _____ pain and cure terrible diseases. These discoveries have enabled man to live a longer and _____ life.
Science is both a blessing and a _____.
Many things which have made life better and _____,
It has also given terrible instruments of _____.
Discovered and invented many things to _____ pain and cure
Enabled man to live a longer and _____ life.
A passage is given with five questions following it. Read the passage carefully and select the best answer to each question out of the given four alternatives.
Corruption is not a new phenomenon in India. It has been prevalent in society since ancient times. History reveals that it was present even in the Mauryan period. Great scholar, Kautilya, mentions the pressure of forty types of corruption in his contemporary society. It was practised even in Mughal and Sultanate period. When the East India Company took control of the country, corruption reached new height. Corruption in India has become so common that people now are averse to thinking of public life with it. Corruption has been defined variously by scholars. But the simple meaning of it is that corruption implies perversion of morality, integrity, character or duty out of mercenary motives, i.e. bribery, without any regard to honour, right and justice. In other words, undue favour for any one for some monetary or other gains is corruption. Simultaneously, depriving the genuinely deserving from their right or privilege is also a corrupt practice. Shrinking from one's duty or dereliction of duty are also forms of corruption. Besides, thefts, wastage of public property constitute varieties of corruption. Dishonesty, exploitation, malpractices, scams and scandals are various manifestations of corruption.
According to the passage, corruption is _____ .
Kautilya mentions the pressure of how many types of corruption in his contemporary society?
Perversion of what is not mentioned in the passage?
According to the passage, what all are the manifestation of corruption?
What people are averse of due to corruption in India?
Educational materials for CAT preparation