Is $$a > b $$?
I. $$a^{16} < b^{16}$$
II. $$a^{21} < b^{21}$$
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In the following questions, each question is followed by data in the form of two statements labeled as I and II. You must decide whether the data given in the statements are sufficient to answer the questions. Using the data make an appropriate choice from (a) to (d) as per the following guidelines:
Is $$a > b $$?
I. $$a^{16} < b^{16}$$
II. $$a^{21} < b^{21}$$
If x and y are integers, is $$\sqrt{x^2 + y^2}$$ an integer?
I. $$8x^2 - y^2 = 0$$
II. $$x^2 + y^2$$ is an integer
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What is the value of $$3a + 2b$$ ?
I. $$\frac{a}{b} = \frac{2}{3}$$
II. $$2a - 3b = 10$$
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How many sons does A have ?
I. Bis D’s brother and sonof A.
II. D's father has three children.
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What is the distance between the cities P and Q
I. City A is 60 km from city Q
II. City P is 80 km form city A
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What is the GCD of positive integers a and b?
I. a and b differ by 1.
I. a > b
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What is the value of $$\mid x \mid$$?
I. $$x^4 - 4x^2 + 4 = 0$$
II. $$x$$ is even
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What is the value of the middle term of the sequence of positive integers $$a_1, a_2, ... ... ..., a_{11}$$ if their sum is 1380?
I. The average of first six terms is 100
II. The average of last six terms is 150
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Is $$x > y$$?
I. $$\mid x \mid < 3$$
II. $$\mid y \mid > 3$$
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How many positive integral multiples of 5 are there up to n?
I. 500 is the largest multiple of 10 that is $$\leq$$ n.
II. 1005 is the largest multiple of 5 that is not greater than n.
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What is the LCM of the positive integers m, n?
I. GCD of m, n is 9.
II. m + n = 108
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Is the positive integer n, a prime?
I. n is an odd integer greater than 3
II. m is an even integer greater than 2
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If p, q and rare real numbers: are the roots of the quadratic equation $$px^2 + qx + r = 0$$ real?
I. r - 25p = 0
II. q + 9p = 0
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In how many points do the twocircles intersect?
I. The radii of the circles are 12 em and 5 cm.
II. The distance between their centres is 25 cm.
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In how many days P alone can complete the work:
I. Pand Q together can complete that work in 12 days.
II. Qalone can complete the work in 36 days.
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How many girls are taller than Sarath inhis class?
I. When students in Sarath’s class are ranked in the descending orderof heights. Sarath is $$17^{th}$$ from the top amongall the students and $$12^{th}$$ among boys.
II. Sarath’s rank from the bottom on the basis of height among boys is $$18^{th}$$ and among all the students is $$29^{th}$$.
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If p and q are positive integers. is p multiple of g ?
I. Every prime factor of q is also a prime factor of p.
II. Every factor of q is also a factor of p.
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Paul walks at a constant rate for 80 minutes every day in the same track. How long is the track?
I. Paul began walking at 5.00 a.m yesterday.
II. Paul walked 5km by 5.40 a.m. and 8 km by 6.04 a.m. yesterday.
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p and q are 2 digit numbers that share the samedigits, but in reverse order. Then what is the sum of p and q?
I. p - q = 45
II. The difference between the two digits in each number is 5
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A zebra must get water from either a river or a pond. Which of the two sources of water is closer to the zebra’s current position?
I. Morning at a constant rate, it takes the zebra 2 hours to reach the river fromits current position.
II. Morning at a constant rate, it takes the zebra 2 hours to reach the pond from the river.
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In each of the following questions, a sequence of numbers or letters that follow a definite pattern is given. Each question has a blank space. This has to be filled by the correct answer from the four given options to complete the sequence without breaking the pattern.
7 : 342 :: 11 : ........
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15 : 224 :: 17 : ........
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17 : 306 :: 19 : .........
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7 : 77 :: 13 : .......
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Foot : Inch :: Year : ........
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6, 15, 35, 77, 143, ......
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ABC, BDF, CFI, DHL, .........
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D3B, H7F, L11J, P15N, .......
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$$\frac{6}{5}, \frac{35}{12}, \frac{143}{24}, \frac{323}{36}, \frac{667}{52}, ............$$
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MILK : 54 :: CURD : ........
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In the Following questions pick the odd thing out.
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The following question followg definite pattern. Observe the same and fill in the blanks with suitable answers.
BZE, DYH, HWN, ........
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7, 10, 16, 28, ......... 100
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4T, 16W, 52U, ..... 484V
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E3V. I4R, G12T, K45P, ........
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3, 4, 12, 39, 103, .........
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6, 24, 60, 120, ........
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75, 79, 72, 80, 69, 81, ........
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1, 2, 6, 22, 86, ........
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0, 6, 24, 60, .......... 210
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$$\frac{1}{2}, \frac{4}{3}, \frac{13}{5}, ..........., 11$$
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The following table gives the number of elected members of parties X, Y, Z, A, and B to the state assembly. Study it carefully and answer the following questions.

What percentage of seats did party y get in 1990?
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what percentage of growth did the party A gain 1995 overthe previous election?
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Howm any more seats did the party A get overthe party B inall elections put together?
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The following pie chart shows the expenditure of a person’s monthly income on different heads A, B, C, D, E and F. Basing on the information given in the pie chart, answer the following questions.

If the amount spent on the head D is Rs. 43,320, then the amount in rupees that he has spent on the head E is
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The percentage of his monthly income spent on the head D corrected to two decimals, is
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If the income of the person in that month is Rs.93,240, then the amountin rupees that he spent on the head B in that month is
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If the amount spent on the heads A and C together in that month is Rs 60,450 then the amount he spent on the head B in that month in rupees is
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If the person spent on the head E is Rs. 11,520 in a month. then the amount spent on the head C in that month in rupees is
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60 students of a class were asked which TV programmes among A, B and C they had watched on a particular Sunday. 30 had watched programme A, 38 programme B, 25 programme C, 18 watched both A and B, 12 both B and C, 10 both A and C while 4 watchedall the three. Based on this information answer the following questions.
How many watched only one programme?
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How many watched exactly two programmes?
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In a certain code $$n^{th}$$ letter of the English alphabet is coded as $$(n + 10)^{th}$$ letter cyclically. The reverse process is used for decoding. with this information answerthe following questions.
what is the code for the word ‘ATTACK’
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The code for ‘APICET” is
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“SYSTEM” is coded as
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‘USVV" is decoded as
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"BKREV" is decoded as
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If ‘BEAT’ is coded as ‘EHDW’, the code for ‘ROAD’ is
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If ‘SAFE’ is coded as ‘“OWBA’. then whatis the code for ‘CROW’?
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In a certain code language if the word ‘TOKEN’ is coded as ‘YTPJS’ . then in the same code language the word ‘CLOSED’ is coded as
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In a certain code ‘BEST’ and ‘PORT’ are coded as 51 and 84 respectively. then in the same code ‘WORD’ is coded as
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In a certain code the word ‘RAMBO’ and ‘ BRING * are coded as 114 and 109 respectively, then in the same code ‘BLIND’ is coded as
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The number of leap years in between the years 2018 and 2126 is
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The angel between hour hand and the minute hand of a clock when the time is 5.40 is
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If two hands of a clock coincide (are together) every 64 minutes. the time gained, in minutes, by that clock in a day is
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If P is the wife of the grandsonof the father of father of Mr R and R’s father is the only child of his father, then P is related to R as
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A bus for Tirupati leaves every two hours from Bangalore bus station. An announcement was made at the Bangalore bus station that the bus for Tirupati had left 40 minutes ago and the next bus will leave at 4.00 pm. At what time the announcement was made?
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A person came to his office 40 minutes late at 10.55 a.m on Friday. Next day he started early and reached his office 25 minutes before the scheduled time. Then the time of his arrival at office on Saturday is
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5 persons A, B, C. D and E are sitting around a circle facing its center. B sits between A and E. C is sitting on immediate right side of the E. Then the person on the immediate left of D is
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If $$\triangle$$ denotes multiplication, * denotes subtraction, $$\triangledown$$ denotes addition and $$\oplus$$ denotes
division then $$10 \triangledown 8 \oplus 2 * 5 \triangle 3 = ?$$
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If $$x * y = \frac{1}{x} + \frac{1}{y}$$ for all $$x, y \epsilon R - \left\{0\right\}$$ then $$(4 * 5) * (3 * 2) =$$
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For $$m, n \epsilon R$$, define $$m * n = m + n - 2$$ and $$m \oplus n = \frac{mn}{2}$$ then $$(3 * 5) \oplus (9 * 7) = ?$$
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$$(3^{2x + 4} \times 9^{4x + 2}) \div (9^{x + 4} \times 3^{2x + 2}) = 9^5 \Rightarrow x = ?$$
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If $$x = \sqrt{7} - \sqrt{6}$$ then $$x^4 + \frac{1}{x^4} =$$
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$$5(x^2 + y^2 + z^2) = 4(xy + yz + zx)$$ then $$x : y : z$$
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$$yz : zx : xy = 1 : 2 : 3 \Rightarrow \frac{x}{yz} : \frac{y}{zx} =$$
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$$\sqrt{4 + \sqrt{4 + \sqrt{4 + \sqrt{4 + ........ \infty}}}} = $$
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$$\sqrt{8 + 2\sqrt{15}} =$$
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If 11 divides 29x03 then x =
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How many integers are there from 200 to 400 which are multiples of 7?
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The smallest positive integer which when divided by 6, 9, 12 and 15 leaves 5 as remainder in each case is
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A trader has three kinds ofoils. the first kind 462 liters, the second kind 286 liters and the third kind 187 liters. What is the least numberof tins of equal volume required to fill them completely and store these oils without mixing?
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$$\left(1 - \frac{1}{7}\right)\left(1 - \frac{1}{8}\right)\left(1 - \frac{1}{9}\right)\left(1 - \frac{1}{10}\right) .................. \left(1 - \frac{1}{51}\right) =$$
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$$0.2\overline{34} =$$
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The increasing order of $$a = \sqrt{7} - \sqrt{6}, b = \sqrt{3} - \sqrt{2}, c = \sqrt{6} - \sqrt{5}, d = \sqrt{2} - 1$$ is
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The smallest among $$\frac{9}{1}, \frac{8}{9}, \frac{5}{6}$$ and $$\frac{7}{8}$$ is
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A person gave 12%of his moneyto charities. After spending 80% of the remainder, he is still left with Rs.264. The amount of money he hadat the beginning. in Rupees, is
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When 40% of a number is added to 84. if the resultant is the number itself. then that number is
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A man purchased 11 booksfor Rs. 100 and sold at the rate of 10 books for Rs. 110. How much percentage of profit or loss he made on a book?
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To successive profits of 8% and 10% are equal to a single profit of
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P and Q enter into a partnership with capitals in the ratio 9:7. At the end of 8 months Q withdrewhis capital from the business. If they received profits in the ratio 9:4, the time (in months) P’s capital remained, is
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In a partnership. P, Q and R shared profit in the ratio 1:4:5. If the total profit is Rs. 55,000, then the difference of profit between the shares of P and Q (in Rs.) is
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A pipe can fill a tank in 9 hours. Due to a leak in the bottom,it is filled in 10 hours. If the tank is full. then the time (in hours) that the leak takes to empty that tank is
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Two taps P and Q can separately fill a cistern in 36 minutes and 45 minutes respectively. After both the taps are opened simultaneously by what time (in minutes) the pipe Q should be closed so that the cistern is completely filled in 27 minutes?
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Car A starts at 8 am from the place P, with a speed of 65 kmph. AnothercarB starts at 9 am from the same place P. and follows the car A with a speed of 70 kmph. Then the meeting time of the cars A and B is
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A bus covers a total distance of 400 km forits to and fro journey, in 8 hours. If the average speed of the bus in the onward journey is 25% more than that in the return journey, then the speed of the bus in the onward journey (in km/hr) is
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P alone can do a work in 15 days and Q alone cando it in 20 days. With the help of R they finish the work in 5 days. How many days R alone will take to finish the work?
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5 men can prepare 10 toys in 6 days working 6 hours per day. In how many days can 12 men prepare 16 toys working 8 hours per day?
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If the area of an equilateral triangle is $$4\sqrt3$$ sq.cm.. then its perimeter, in centimetres, is
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The length and breadth of a rectangle are in the ratio 7:5 andits area is 3500 sq.cm. What is the perimeter of the rectangle. in cm?
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If the surface area of a cube is 726 sq.cm., then its volume. in cubic centimeters, is
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A solid sphere of radius 10 cm is melt and moulded into 8 solid spherical balls of equal radius. The surface area of eachball. in sq. cm. is
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The breadth of a rectangular plot is 75% of its length and the perimeter of the plot is 1050 m. Thenthe area. in square meters, of the plot is
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The base of a triangular shape field is 3 times its height. If the cost of cultivating the field at Rs.73.44 per hector is Rs. 991.44, then the height of triangular field (in meters) is
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The breadth of a cuboid is $$\frac{2}{3}$$ of its length and its height is $$\frac{3}{4}$$ of its breadth. If its volume is 72 cu.mts, then its surface area. in sq.mts, is
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$$1212_{(7)} = x_{(10)} \Rightarrow x =$$
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$$101_{(2)} + 110_{(2)} =$$
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$$P \rightarrow (Q \rightarrow P) \Rightarrow $$
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The negation of the statement $$p \vee (\sim p \wedge q)$$ is
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If $$A = \left\{(x, y) \epsilon z \times z \mid x^2 + y^2 \leq 16 \right\}$$, then the number of reflexive relations defined on A is
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If n(A) = 5, then the number of relations on A which are not symmetric is
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Let $$f$$ be defined on $$[0, 7]$$ and $$g(x) = \mid 2x + 1 \mid$$. Then the domain of $$(fog)(x)$$ is
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The equation of the straight line passing through (-5, 4) and which makes an intercept of $$\frac{2}{\sqrt{5}}$$ units between the lines $$x + 2y + 1 = 0$$ and $$x + 2y - 1 = 0$$, is
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The equation of the straight line passing through the point (-2, 3) and which makes intercepts in the ratio 1 : 3 on the coordinate axes, is
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$$\tan 480^\circ + \sec 510^\circ + \cosec 750^\circ + \cot 765^\circ =$$
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$$\frac{\sin 150^\circ - 5 \cos 300^\circ + 7 \tan 225^\circ}{\tan 135^\circ + 3 \sin 210^\circ} =$$
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If $$\sec \theta + \tan \theta = \frac{2}{3}$$, then $$\sin \theta =$$
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The height of the pillar when it is found that on walking towards it 60 meters in a horizontal line through the base. the angle of elevation of its top changes from $$30^\circ$$ to $$60^\circ$$. its height (in meters) is
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The smallest value of x for which $$\left(\frac{12}{x} + 36\right)(4 - x^2) = 0$$ is
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If $$\alpha$$ and $$\beta$$ are the roots of the equation $$8x^2 - 3x - 27 = 0$$, then the value of $$\left(\frac{\alpha^2}{\beta}\right)^{\frac{1}{3}} + \left(\frac{\beta^2}{\alpha}\right)^{\frac{1}{3}} =$$
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If the number obtained after subtracting x from 2035 leaves the same remainder 5 when it is divided by 9, 10 and 15, then the smallest possible x is
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If the remainder obtained whena certain integer x is divided by 5 is 2, then which one of the following is never an integer?
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Rahim is 6 years older than David and David is 8 years older than Amar. After 8 years, if Rahim will be twice as old as Amar. then 4 years ago, David’s age was
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Set X contains 10 consecutive integers. Sum of the 5 least numbers of the set is 265. The sum of the four greatest numbers of that set is
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If the sum of three consecutive numbers in a geometric progression is 26 and the sum of their squares is 364, then the product of those numbers is
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The sum of all the natural numbers between 100 and 1000 which are multiples of 5 is
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The middle term in the expansion of $$\left(x^2 - \frac{1}{2x}\right)^{10}$$ is
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The numerically greatest term in the expansion of $$(2 + 3x)^5$$ when $$x = \frac{5}{4}$$ is
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If $$A = \begin{bmatrix}3 & -4 \\1 & -1 \end{bmatrix}$$ then $$A^4 - A^3 + A^2 - A =$$
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The value of x for which the matrix $$\begin{bmatrix}x-2 & 2x-3 & 3x-4 \\x-4 & 2x-9 & 3x-16 \\x-8 & 2x-27 & 3x-64 \end{bmatrix}$$ does not possess inverse, is
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$$\lim_{x \rightarrow 0}\frac{e^x - 1}{\sqrt{1 + x} - 1} =$$
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$$\lim_{x \rightarrow 3}\frac{x^4 - 81}{2x^2 - 5x - 3} =$$
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In the adjoining figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If $$\angle DBC = 55^\circ$$ and $$\angle BAC = 45^\circ$$, then $$\angle BCD =$$

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A and B are the end points of the longest line drawn in the circle with centre x. If C is a point on the circle such that AC = Ax = 3. Then the perimeter of $$\triangle ABC$$ is
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A, B and C are three points on the circumference of a circle with centre O. If in $$\triangle ABC \angle B = 60^\circ$$ and $$\angle C = 70^\circ$$ then $$\angle BOC = $$
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If A(3, 10), B (-3, 4) and C (5, 8) are the vertices of a $$\triangle ABC$$ and AD and CF are its medians. then the ratio of the length of AD to the length of CF is
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If (-2, -1), (1, 0) and (4, 3) are three consecutive vertices of a parallelogram, then the sum of the lengths of the diagonals of that parallelogram is
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The arithmetic mean of 28, 32, 34, 24, 42, 46, 38, 36 is
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The median of 18, 16, 18, 12, 10, 14, 16 is
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The mode of the following frequency distribution is

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The standard deviation of 6, 7, 8, 9, 10 is
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The standard deviation of any three consecutive integers is
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If $$d_i$$ stands for the difference of ranks and if $$\sum_{i = 1}^n d_i^2 = \frac{(n - 1)n(n + 1)}{8}$$, then the value of the
coefficient of rank correlation is
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A problem in Mathematics is given to three students A, B and C whose chances of solving it are $$\frac{1}{3}, \frac{1}{4}$$ and $$\frac{1}{2}$$ respectively. What is the probability that the problem will be solved by at least one of them?
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If a card is drawn at random form a well shuffled pack of 52 cards, then the probability that it is a spade or a king is
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The probability that a non-leap year has 53 Mondays is
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A and B are two sets such that n(A) = 3 and n(B) = 2. If a relation from A to B is selected at random, then the probability that the relation will be a function is
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Choose the correct meaning of the word given:
Angst
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Exotic
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Aberration
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Gratuitous
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Deferential
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Subservience
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Fill in the blank choosing the correct word:
Money lenders are often accused of ............., as they are habituated to recovering by force or threats
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Once committed to their goals, people work with a missionary ............
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When the going gets tough. the tough get ..........
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The seven year old boyis the legal .......... of the huge property.
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Choose the correct answer:
A technique in computer graphics that makes an image to look smooth froma distance is called
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Balance sheet means ............
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Company AGMs are meetings of
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Whatis the name of the device that connects two computers by means of a telephone line?
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Maslow’s hierarchy conceptis a theory of
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A terminal that can function only whenit is lined to a computeris called a
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The term ‘golden handshake’ refers to the payment made to
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Withdrawal of money in excess of the credit balance on a bank accountis called
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The term ‘cybersquatting’ refers to
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Obtaining information or opinions from a large group of people via the internetis called
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The officer told his visitors that there was no room for discussion on the subject they broached. Here ‘no room’ means
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Identify the correct statement:
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Low paying jobs are a dime a dozen.
The underlined phrase means
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A : Did your husband consult youbefore taking up the newventure?
B : No. He is on his own.
B meansthat her husband
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Don’t worry. Everything will happen as a matter of course.
The underlined phrase means
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Fill in the blank with the appropriate phrase/verb/preposition:
He does not hanker .......... sensual pleasures.
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Hetried his best to ........... his point.
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She has been looking forward ............... her parents
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By mistake, I took him ............. a thief.
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‘Procrastination’ means ‘to .............’
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He had no hopeleft. as all his plans were .............
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The expression. “to go at it hammer and tongs” means, ...............
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The answer given by the film star to the question by the press reporters is wide off the mark. The underlined phrase means
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The patriot ............... his life for his country.
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Never ............. such an amusing show.
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Read the following passage and answer questions
The comradeship of the young both sustains them in their own image of themselves and gives them the emotional sustenance they need for the independence of their lives. They live apart from us. they hold themselves back, and from the untouchable center of their personal lives they look distantly at our existence and our knowledge as items possessed by beings on a different planet. They are not what they seem to the professor who merely looks at the faces before him. He cannot be certain even of their attention, since they have learned howto occupy a classroom and look attentive while they take their minds elsewhere. He cannot be sure of their respect. since they have learned how to be quiet and howto act respectfully. The silence of the present generation has been many ways deceptive, and it is false to assume that the silence has meant either consent or lack of creative and critical thought.
The students must be asked to determine for themselves which books are great, which ideas are viable, which values are compelling. To do otherwise is to use the familiar brand name approachas a formofintellectual propaganda. It is to take the young through an educational tour of the museumsofliterature. to inspire a dutiful pious attitude to authors other than anattitude of expectancy and involvement.
Friendship among youngsters confers upon them
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Students in a classroom
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The silence of the students is a mark of
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Students must
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Which word means ‘feasible’?
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Read the passage below and answer questions.
Some years ago when executives and managers talked about the type of employees they wanted to contract for their businesses they spoke of skills and qualifications. These wordsare still used but have been overshadowed by the term competencies. Competencies are a concept taken on board by Human Resource departments to measure a person’s appropriateness fora particularjob.
In simple terms a competencyis a tool that an individual can use in order to demonstrate a high standard of performance. Competencies are characteristics that we use to achieve success. These characteristics or traits can include things like knowledge, aspects of leadership, self-esteem, skills or relationship building. There are a lot of competencies but they are usually divided into groups. Most organizations recognize two main groups and they have numerous sub groups which competencies can be further divided into.
Competencies can be divided into twodistinct types: technical competencies (sometimes referred to as functional) and personal competencies. As the name suggests. technical competencies are those whichare related to the skills and knowledge that are essential in order for a person to do a particular job appropriately. An example of a technical competency for a secretary might be: “Word processing: able to word process a text at a
rate of 80 words per minute with no mistakes.” Personal competencies are not linked to any particular function. They include characteristics that we use together with our technical competencies in order to do our work well. An example of a personal competency is: “interpersonal sensitivity: Demonstrates respect for the opinions ofothers, even when not in agreement.”
Competencies are probably here to stay so it is worth thinking about your own competencies and trying to categories them: first into the two sub-categories mentioned above and then into a more detailed list.
Which qualities have been found necessary for selecting employees by the managers and executives. until recently?
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For achieving success. which of the following is NOT mentioned as necessary in the passage?
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Into what categories have competencies been divided?
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Personal competency results in ................
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According to the passage. infuture. the identified competencies are going to be .............
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Read the following passage and answerquestions.
A writer creates a world of characters and situations and philosophy that have a life of their own and may have no relation to him. After writing ten novels and a number of short stories. I find that I have created good men, bad men.idiots and saints. Once they have served their purpose. they pass clean out of my memory. I have no time to think of them again, although for months everyone of those characters could have occupied my thoughts obsessively while the story was in progress. Once the last line is written and “The End” is inscribed with a happy flourish. out goes the character. But this is a solution that the readeris not likely to take into account.
A readeris attracted or repelled by a character and expects the writer to offer various explanations and interpretations of the particular character and his or her philosophy. The reader will also have the advantage having gone through the book recently and possibly more than once. But the writeris likely to have forgotten the whole subject, especially if he has had to write a great deal else since then. When people expect
him to say wise or significant things about his own book, they may find him tongue-tied and disappointing. In my viewto find the author less than the book is an excellent situation.
Identify the correct statement:
According to the author. a writer
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The speaker of the passage is a ...........
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After writing a book, the writer .............. every character in the novel
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According to the passage, the writer
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Identify the correct statement based onthe last line of the passage
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