Series-4 (NCERT)

Find sum to n terms of the following series:

5+11+19+29+41……….

(1) (n+1)(2n+1)(3n+2)/6 

(2) n(2n+1)(3n+2)/3  

(3) n(n+2)(2n+3)/3  

(4) n(n+2)(n+4)/3

(5) None of these

Answer follows here:

Series-3 (NCERT)

Find sum to n terms of the following series:

1² + (1²+2²) + (1²+2²+3²) +……….

(1) n(n+1)(n+2)²/12 

(2) n²(n+1)(n+2)/12  

(3) n(n+1)²(n+2)/12  

(4) n(n+1)(2n+1)/6  

(5) n²(n+1)²/4

Answer follows here:

Progressions-4 (NCERT)

Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual installment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him (in Rupees)?

 (1) 18000 * (1.1)¹⁷   (2) 18000 * (1.1)¹⁸   (3) 39100   (4) 37300   (5) None of these

Answer follows here:

Progressions-13 (NCERT)

150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed?

(1)17   (2) 20   (3) 25   (4) 27   (5) 30

Solution follows here:

Statistics-1 (XAT-2011) (5-Marks)

In a list of seven integers, one integer denoted as x is unknown. The other six integers are 20,4,10,4,8 and 4. If the mean, median and mode of these 7 integers are arranged in increasing order, they form an arithmetic progression. The sum of all possible values of x is:

(1)26   (2) 32   (3) 34   (4) 38   (5) 40

For Answer Click on "Read more" below:

Trigonometry-1 (XAT-2011) (3-Marks)

What is the maximum possible value of 21Sinx+72Cosx?

(1)21   (2) 57   (3) 63   (4) 75   (5) None of these

Solution follows here:

Numbers-9 (XAT-2011) (5-Marks)

Let a_n = 111111…1, where 1 occurs n number of times. Then,

(i) a₇₄₁ is not a prime

(ii) a₅₃₄ is not a prime

(iii) a₁₂₃ is not a prime

(iv) a₇₇ is not a prime

(1) (i) is correct

(2) (i) and (ii) correct

(3) (ii) and (iii) correct

(4) All of them are correct

(5) None of them is correct

For Answer Click on "Read more" below:

P & C-6 (XAT-2011)

In a locality there are ten houses in a row. On a particular night a thief planned to steal from three houses of the locality. In how many ways can he plan such that no two of them are next to each other?

(A)56      (B) 73        (C) 80        (D) 120   (E) None of these

For answer click on "Read more" below:

Geometry-11 (CAT-2002)

There is a common chord of two circles with radius 15 and 20.The distance between the two centres is 25.The length of the chord is:
(1)48   (2)24   (3)36   (4)28

For Answer Click on "Read more" below:

Sequence-1 (CAT-2002)

Let S = 2x+5x²+9x³+14x⁴+20x⁵+…    infinity. The coefficient of n^th term is n(n+3)/2. The sum S is:

(1)x(2-x)/(1-x)³  (2) (2-x)/(1-x)³   (3) x(2-x)/(1-x)²   (4)None of these

For Answer Click on "Read more" below:

Algebra-15 (CAT-2002)

For all integers n>0, 7⁶ⁿ-6⁶ⁿ is divisible by:

(1)13  (2)128  (3)549  (4) None of these

For Answer Click on "Read more" below:

Puzzle-14 (XAT-2010)

The chance of India winning a cricket match against Australia is 1/6. What is the minimum number of matches India should play against Australia so that there is a fair chance of winning at least one match?
(A)3      (B) 4        (C) 5        (D) 6   (E) None of these
Solution follows here:

Progressions-5 (XAT-2010)

a,b,c,d and e are integers such that 1 ≤ a < b < c < d < e. If a,b,c,d and e are in geometric progression and lcm(m,n) is the least common multiple of m and n, then the maximum value of 1/lcm(a,b) + 1/lcm(b,c) + 1/lcm(c,d) + 1/lcm(d,e) is:
(A)1      (B) 15/16        (C) 79/81        (D) 7/8   (E) None of these

Answer follows here:

Algebra-14 (XAT-2010)

If x and y are real numbers, then the minimum value of x²+4xy+6y²-4y+4 is:

(A)-4      (B) 0        (C) 2        (D) 4   (E) None of these

Answer follows here:

Numbers-8 (CAT-2001)

If x>5 and y<-1, then which of the following statements is true:

(1)(x+4y) > 1      (2) x > -4y        (3) -4x < 5y        (4) None of these

Solution follows here:

Algebra-13 (CAT-2002)

If f(x) = log((1+x)/(1-x)), then f(x)+f(y)=?

(1) f(x+y)   (2) f(1+xy)   (3)(x+y) f(1+xy)   (4)f((x+y)/(1+xy))

Solution follows here:

Geometry-10 (CAT-2002)

In the following figure, the area of isosceles right triangle ABE is 7 sq.cm. If EC=3BE, then the area of
rectangle ABCD is (in sq.cm):

(1)64   (2)82   (3)26   (4)56

Solution follows here:

Numbers-7 (CAT-2002)

Number S is equal to the square of the sum of digits of a 2 digit number D. if the difference between S and D is 27, then D is:

(1)32   (2)64   (3)54   (4)52

Solution follows here:

Algebra-12 (CAT-2002)

If x²+5y²+z²=2y(2x+z), then which of the following statements are necessarily true?

I. x=2y  II. x=2z  III. 2x=z

(1)only I   (2)only II   (3)only III   (4)both I and II

Solution follows here:

Geometry-9 (CAT-2001)

A square, whose side is 2 meters, has its corners cut away so as to form an octagon with all sides equal. Then the length of each side of octagon, in meters is:
(1)√2/√2+1      (2) 2/√2+1        (3) 2/√2-1        (4) √2/√2-1
Solution follows here:

Progressions-4 (CAT-2000)

Consider a sequence of seven consecutive integers. The average of first five integers is n. the average of all seven integers is:

(1)n      (2) n+1        (3) K*n, where K is a function of n        (4) n+(2/7)

Solution follows here:

Algebra-11 (CAT-2000)

What is the value of the following expression:

(1/(2²-1))+ (1/(4²-1))+ (1/(6²-1))+……….. (1/(20²-1))

(1)9/19      (2) 10/19        (3) 10/21        (4) 11/21

Solution follows here:

Numbers-6 (CAT-2000)

If a₁ = 1 and a_n+1 = 2a_n+5, n=1,2,… then a₁₀₀ is equal to

(1)(5*2⁹⁹ - 6)      (2) (5*2⁹⁹ + 6)        (3) (6*2⁹⁹ + 5)        (4)(6*2⁹⁹ - 5)

Solution follows here:

Numbers-5 (CAT-2007)

Consider four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?

(1)   3

(2)   2

(3)   4

(4)   0

(5)   1

Solution follows here:

Geometry-8 (CAT-2007)

Two circle with centres P and Q cut each other at two distinct points A and B. the circles have the same radii and neither P nor Q falls with in the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees?

(1)   Between 0 and 90

(2)   Between 0 and 30

(3)   Between 0 and 60

(4)   Between 0 and 75

(5)   Between 0 and 45

Solution follows here:

Stocks-2 (SNAP-2008)

Which investment gives a better return, assuming the face value of the shares to be Rs. 10?

A.    5% stock at 75, subject to 30% income tax

B.     4% stock at 90, tax free

a.     B

b.     A

c.      Both A and B

d.     None of these

Solution follows here:

Arithmetic-13 (XAT-2009)

Rajesh walks to and fro to a shopping mall. He spends 30 minutes in shopping. If he walks at a speed of 10 km an hour, he returns to home at 19.00 hours. If he walks at 15 km an hour, he returns to home at 18.30 hours. How fast must he walk in order to return home at 18.15 hours? 

A.     17 km/hour

B.      17.5 km/hour

C.      18 km/hour

D.     19 km/hour

            E.    None of these

Solution follows here:

Puzzle-13

How many 3 digit numbers have the sum of their digits as an odd number?

(A)540            (B)450             (C)500             (D)125            (E) None of these

Solution follows here:

Algebra-10 (CAT-2008)

A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?

(1)2 ≤ x ≤ 6 (2)5 ≤ x ≤ 8 (3)9 ≤ x ≤ 12 (4)11 ≤ x ≤ 14 (5) 13 ≤ x ≤ 18

Solution follows here:

Algebra-9 (CAT-2008)

Three consecutive positive integers are raised to the first, second and third powers respectively and then added. The sum so obtained is a perfect square whose square root equals to the total of the three original integers. Which of the following best describes the minimum, say m of these three numbers?

(1)1 ≤ m ≤ 3 (2)4 ≤ m ≤ 6 (3)7 ≤ m ≤ 9 (4)10 ≤ m ≤ 12 (5) 13 ≤ m ≤ 15
Solution follows here:

Algebra-8 (CAT-2008)

If the roots of the equation x³-ax²+bx-c=0 are three consecutive integers, then what is the smallest possible value of b?

(A)-1/√3        (B)-1       (C)0      (4)1      (5)1/√3

Solution follows here:

Stocks-1 (FMS-2009)

BSNL offers its share at a premium of Rs 40, where as its par value is Rs 160. Parul Mehra invested Rs 50,000 in this stock. After one year BSNL declared a dividend of 19%. What rate of interest did Ms Mehra receive on her investment?
(A)15.2%        (B)16.2%         (C)19%            (D)19.2%

For answer click on "Read more" below:

Geometry-7 (CAT-2008)

Consider obtuse angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer, then how many such triangles exist?
(1)5      (2)21         (3)10           (4) 15          (5) 14
Solution follows here:

Arithmetic-12 (XAT-2010)

There are two types of employees in sun Metals, general graduates and engineers. 40% of the employees in Sun Metals are general graduates, and 75% engineers earn more than Rs 5 lakh/year. If 50% of of the organization’s employees earn more than Rs 5 lakh/year what proportion of the general graduates employed by the organization earn Rs 5 lakh or less?

A. 3/5

B. 3/4

C. 1/2

D. 2/5

E. None of the above

For answer click on "Read more" below:

Arithmetic-11 (XAT-2010)

A manufacturer has 200 litres of acid solution which has 15% acid content. How many litres of acid solution with 30% acid content may be added so that acid content in the resulting mixture will be more than 20% but less than 25% ?

A. More than 100 litres but less than 300 litres

B. More than 120 litres but less than 400 litres

C. More than 100 litres but less than 400 litres

D. More than 120 litres but less than 300 litres

E. None of the above
Answer follows here:

Geometry-6 (XAT-2010)

Two poles of height 2 meters and 3 meters are 5 meters apart. The height of the point of intersection of the lines joining the top of each pole to the foot of the opposite pole is,

A. 1.2 meters

B. 1.0 meters

C. 5.0 meters

D. 3.0 meters

E. None of the above

Answer follows here:

Geometry-5 (XAT-2010)

ABCD is a parallelogram with ÐABC = 60⁰. If the longer diagonal is of length 7 cm and area of parallelogram ABCD is 15√3/2, then the perimeter of parallelogram in cm is---

A. 15

B. 15√3

C. 16

D. 16√3

E. None of the above
To enter your answer, click on "comments" below:

Geometry-4 (XAT-2010)

In an equilateral triangle ABC, whose length of each side is 3cm, D is a point on BC such thatBD = ½ CD. What is the length of AD?

A. √5cm

B. √6cm

C. √7cm

D. √8cm

E. None of the above
Answer follows here:

Geometry-3 (XAT-2010) (Data Sufficiency)

The question is followed by two statements labeled as I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:

A. Statement I alone is sufficient to answer the question.

B. Statement II alone is sufficient to answer the question.

C. Statement I and statement II together are sufficient, but neither of the two alone is sufficient to answer the question.

D. Either statement I or statement II alone is sufficient to answer the question.

E. Both statement I and statement II are insufficient to answer the question.

(Q)In a trapezoid PQRS, PS is parallel to QR. PQ and SR are extended to meet at A. What is the value of ÐPAS ?

I. PQ = 3, RS = 4 and ÐQPS = 60⁰

II. PS = 10, QR = 5
To enter your answer, click on "comments" below:

P&C-5 (CAT-2008)

How many integers greater than 999 but not greater than 4000, can be formed with the digits 0,1,2,3 and 4, if repetition on digits is allowed?

(1) 499         (2)500                (3)375       (4)376       (5)501

Solution follows here:

Algebra-7 (CAT-2008)

What is the number of distinct terms in the expansion of (a+b+c)²⁰?    

(1)231              (2)253    (3)242   (4)210          (5) 228

Solution follows here:

Geometry-2 (FMS-2009)

Let each side of a square is 20 cm. Four equal circles, each of radius 10 cm are drawn about the four corners of the square so that each touches two of the others. Find the area enclosed between the circumferences of the circles?

(1)86 sq.cm  (2)314 sq.cm    (3)78 sq.cm        (4)none of these

For answer click on "Read more" below:

Algebra-6 (FMS-2009)

If log₇log₅ (√(x+5) + √x) = 0, what is the value of x?               

(1)2                (2)3                (3)4               (4)5

For answer click on "Read more" below:

Algebra-5 (CAT-2008)

Let f(x) be a function satisfying f(x)f(y) = f(xy) for all real x,y. If f(2) = 4, then what is the value of f(1/2)?

(1)0   (2)1/4   (3) ½   (4) 1   (5) cannot be determined
Solution follows here:

Arithmetic-10 (XAT-2009)

Let X be a four digit number with exactly three consecutive digits being same and is a multiple of 9. How many such X’s are possible?

(A) 12

(B) 16

(C) 19 

(D) 21

(E) None of the above

Answer follows here:

Arithmetic-9 (XAT-2010)

Let X be a four digit positive integer such that the unit digit of X is prime and the product of all digits of X is also prime. How many such integers are possible?

(A) 4

(B) 8

(C) 12  

(D) 24

      (E) None of the above

Solution follows here:

Arithmetic-8 (CAT-2008)

What are the last two digits of 7²⁰⁰⁸
(1) 21      (2) 61          (3) 01           (4) 41             (5) 81
Solution follows here:

Arithmetic-7 (Placement Q's) (GMAT/GRE word problem)

Potatoes are made up of 99% water and 1% "potato matter." Jack bought 100 pounds of potatoes and left them outside in the sun for a while. When he returned, he discovered that the potatoes had dehydrated and were now only made up of 98% water. How much did the potatoes now weigh?

(A) 98 pounds

(B) 99 pounds

(C) 90 pounds

(D) 50 pounds 

Solution follows here:

Algebra-4

You own a pet store. If you put in one canary per cage, you have one canary too many. If you put in two canaries per cage, you have one cage too many. How many canaries and cages do you have?
      (A) five canaries and four cages

(B)four canaries and five cages

(C)three canaries and four cages

(D)four canaries and three cages

(E) none of the above

Solution follows here:

Algebra-3 (Placement Q's)(GRE/GMAT Word problems)

A group of friends went for a dinner and got a bill of Rs 2400. They have decided to contribute equally for the bill. But two of them could not contribute and to compensate that, rest all contributed Rs 100 more. How many are there in the group?

(A) 6       (B)10        (C) 8        (D) 12

Solution follows here:

Puzzle-12 (Numbers-4)

A transporter receives the same number of orders each day. Currently he has some pending orders to be shipped. If he uses 7 trucks then at the end of 4th day, he can clear all the orders. Alternatively If he uses only 3 trucks, then all the orders are cleared at the end of 10th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 5th day?

(A)  4               (B)  5               (C)  6               (D) 7

To enter your answer, click on "comments" below:

Arithmetic-6 (Profit & Loss)(SNAP2008)

A merchant wants to make profit by selling food grains. Which of the following would maximize his profit?

I.  Sell product at 30% profit

II. Increase the price by 15% over the cost price and reduce weight by 15%

III. Use 700gm of weight instead of 1 kg

IV. Mix 30% impurities in grains and sell it at cost price

(A) III

(B)  II and I

(C)  II

(D) All give same profit

Solution follows here:

Puzzle-11 (P&C) (IIFT-2008)

The number of ways in which a mixed double tennis game can be arranged amongst 9 married couples if no husband and wife play in the same game is: 

(A)  1514

(B)  1512

(C)  3024

(D) None of the above

Solution:

It involves selection of 2 men and 2 women first and then arrangements in between the pairs.

To select 2 men from the given 9 men      ------ 9C2 ways

To select 2 women from the given 9 women excluding the two, who are wives of already selected 2 men              ------ 7C2 ways

After selecting M₁, M₂, W₁ and W₂, the set of pairs may be

{(M₁,W₁) and (M₂,W₂)} Or

{(M₁,W₂) and (M₂,W₁)}          ----2 possibilities

Hence the total number of arrangements = 9C2 * 7C2 * 2

= (9*8/2) * (7*6/2) * 2 = 1512

Answer (B)

Geometry -1 (IIFT-2008)

If D is the mid point of side BC of a triangle ABC and AD is the perpendicular to AC then:

(A)  3AC² = BC²-AB²

(B)  3BC² = AC²-3AB²

(C)  BC²+ AC² = 5AB²

(D) None of the above
To enter your answer, click on "comments" below:

Puzzle-8 (SNAP-2008)

In a row at a bus stop, A is 7th from the left and B is 9th from the right. They both interchange their positions. A becomes 11th from the left. How many people are there in the row?
(A)  18        (B)  19           (C)  20        (D) 21
Solution follows here:

Arithmetic -5 (SNAP-2008)

A cyclist drove one kilometer with the wind in his back, in three minutes and drove the same way back against the wind in four minutes. If we assume that the cyclist always puts constant force on the pedals, how much time would it take him to drive one kilometer without wind?

(A)  7/3    (B)  24/7    (C)  17/7    (D) 43/12

Solution follows here:

Arithmetic -4 (CSAT-2011)

Three friends R,S and T shared toffees from a bowl. R took 1/3rd of the toffees, but returned 4 to the bowl. S took 1/4th of what was left but returned 3 toffees to the bowl. T took 2/3rd of what was left but returned 7 toffees to the bowl. If the bowl had 17 toffees left, how many toffees were originally there in the bowl?
(A) 38

(B) 31

(C) 48

(D) 41
Solution follows here:

Arithmetic-3 (GATE-2011)

There are two candidates P and Q in an election.During the campaign, 40% of the voters promised to vote for P, and rest for Q. However on the day of election 15% of the voters went back on their promise to vote for P and instead voted for Q. 25% of the voters went back on their promise to vote for Q and instead voted for P. Suppose P lost by 2 votes, then what was the total number of voters?

(A) 100

(B) 110

(C) 90

(D) 95
Solution follows here:

Progressions-3 (CSAT-2011)

A contract on construction job specifies a penalty for delay in completion of work beyond a certain date is as follows:

Rs 200 for the first day, Rs 250 for the second day, Rs 300 for the third day etc..,. The penalty for each succeeding day is Rs 50 more than the preceding day. How much penalty should the contractor pay if he delays the work by 10 days?

(A) Rs 4950

(B) Rs 4250

(C) Rs 3600

(D) Rs 650
Solution follows here:

Arithmetic -2 (GATE-2010)

5 skilled workers can build a wall in 20days; 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30 days; If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?

(A) 20 days

(B) 18 days

(C) 16 days

(D) 15 days
Solution follows here:

P & C -4 (CSAT-2011)

There are four routes to travel from city A to city B and six routes from city B to city C. How many routes are possible to travel from city A to city C?

(A) 24

(B) 12

(C) 10

(D) 8
Solution follows here:

Algebra-2 (Sets) (GATE-2010)

25 persons are in a room. 15 of them play hockey,17 of them play football and 10 of them play both hockey and football.Then the number of persons playing neither hockey nor football is:

(A) 2

(B) 17

(C) 13

(D) 3
Solution follows here:

Puzzle-7 (APPSC-2011)

How many letters of the English alphabet (Capitals)appear same when looked at in a mirror:

(A) 9

(B) 10

(C) 11

(D)12
Solution follows here:

Progressions - 2 (IIFT-2008)

The interior angles of a polygon are in A.P. If the smallest angle is 120⁰ and common difference is 5⁰, then the number of sides in the polygon is:

(A) 7    (B) 8    (C) 9    (D)None of the above

Solution follows here:

Progressions - 1 (IIFT-2008)

If the positive real numbers a, b and c are in Arithmetic Progression, such that abc = 4, then minimum possible value of b is:

(A)  2^3/2

(B)   2^2/3

(C)   2^1/3

(D)None of the above
Solution follows here: