What is the $$100^{th}$$ term of a sequence ?
I. The sequence is an Arithmetic Progression.
II. The first term of the sequence is 5.
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In the following questions a question is followed by data in the form of two statements labelled as I and Il. 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 :
What is the $$100^{th}$$ term of a sequence ?
I. The sequence is an Arithmetic Progression.
II. The first term of the sequence is 5.
Can we find the quadratic equation $$ax^2 + bx + c = 0$$?
I. The sum of the roots is given.
II. The difference of the roots is given.
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Do the two circles with their centres at A and B and having radii $$r_1$$, and $$r_2$$, intersect ?
I. Distance between A and B is ‘a’ units.
II. $$\mid r_1 - r_2 \mid < a < r_1 + r_2$$
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Are two triangles similar ?
I. They are equilateral.
II. Their areas are equal.
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What is the area of a regular hexagon ?
I. A circle of radius ‘a’ units is inscribed in the hexagon.
II. Each side of the hexagon subtends an angle of $$60^\circ$$ at the centre ofthe circle.
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What is the value of $$\log_{10}x$$?
I. x > 3
II. $$\log_{10}x + \log_{10}(x - 3) = 1$$
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Is ABCD a cyclic quadrilateral ?
I. The lengths of the diagonals are given.
II. A circle with mid point of a diagonal as centre passes through the vertices.
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What is the angle subtended by the chord AB of a circle at a point P onthe circumference ?
I. The radius of the circle is 5 cm.
II. The length of the chord AB is 5 cm.
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What is the value of 119x + 247y ?
I. 118x + 246y = 482
II. x is greater than y by 2
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What is the percentage of profit on the sale of 50 books ?
I. The cost price of each bookis ₹ 100.
II. The sale price of each bookis ₹ 125.
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What is the value of n ?
I. $$1^3 + 2^3 + 3^3 + ..... + n^3 = 225$$
II. n is positive integer
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What is the day of $$31^{st}$$ December of an year ?
I. In that year the first of March was Monday.
II. That year was a leap year.
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What is the Arithmetic Mean of the numbers x, y, z and t ?
I. x + 2y - z - 3t = K
II. 2x + y + 4z + 6t = L
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What is the equation of a straight line ?
I. The line is parallel to 2x + 3y = 5.
II. The line does not pass through the origin.
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What is the value of $$8a^3 + b^3 - 27c^3$$ ?
I. abc = k
II. 2a + b = 3c
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What is the distance between two ships ?
I. Seen from the top of a mountain their angles of depression are $$60^\circ$$ and $$30^\circ$$.
II. Height of the mountain is 60 metres.
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Is (x - a) a factor of the polynomial f(x) ?
I. f(a) ≠ 0
II. The sum of the coefficients of f(x) is constant.
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What is the simple interest eamed yearly on a deposit in a bank ?
I. The amount deposited is ₹ 10,000.
II. The rate of interest is 8%.
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What is the surface area of a sphere ?
I. The sphere is made of iron.
II. The radius of the sphere is given.
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What is the value of $$x^4 + y^4$$, if $$xy = 1$$?
I. x + y = 5
II. x > O, y > 0
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In the following Questions a sequence of numbers and letters that follow a definite pattern is given. Each question has a blank space. This blank space is to be filled by the correct answer from one of the four given options to complete the sequence without breaking the pattern.
122 : 145 :: 257 : ...........
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1001 : 1332 :: ........ : 2198
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ABCD : ZYXW :: ....... : VTUS
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Tiger : Goat :: ........ : Herbivore
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Quadrilateral : Square :: Triangle : .........
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Wood : Chair :: .......... : Ornament
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Ice : Water :: ....... : Ghee
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$$\frac{n(n + 1)}{2} : \sum n :: ....... : \sum n^2$$
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ABCDEFG : STUVXYZ :: GECA : .......
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Volume of a cylinder : Area of curved surface of the cylinder :: $$\pi r^2 h$$ : .........
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In the following questions pick the odd thing out :
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Each of the questions follows definite pattern. Observe the same and fill in the blanks with suitable answers.
$$\frac{1}{5}, \frac{5}{10}, \frac{10}{17}, \frac{17}{26}, ..........., \frac{37}{50}$$
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6, 12, 20, 30, ......, 56
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$$\frac{1}{2}, \frac{8}{5}, \frac{27}{10}, ...... \frac{125}{26}, \frac{37}{50}$$
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4, 1, 9, 3, 16, 6, 25, 10, 36, ............
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1, 4, 27, 256, .........
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$$1, \frac{1}{2}, \frac{1}{6}, \frac{1}{24}, .........., \frac{1}{720}, \frac{1}{5040}$$
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4, 7, 12, 19, 28, ......., 52
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1 x 8, 3 v 6, 5 t 4, .........
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1, 2, 3, 5, 8, 13, 21, ..........
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5, 6, 10, 19, 35, 60, ........
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The following table gives the details of the 5 commodities A, B, C, D, E required, with their costs, for a family in a month.
Study the table and answer the questions.

The total amount(in ₹) spent on all the 5 commodities by the family in 1990 is
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The percentage of increase(per kg) in the rate of the commodity E from 1990 to 1995 is
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The amount (in ₹) spent extra on commodities B and C in the year 1995 than in the year 1990 is
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The amounts spent by a person under various heads in a month is given in the following Pie Chart. Based on this information answer the following questions.

If the monthly incomeof the person is ₹ 54,000, then the difference between the amounts spent on travel and food per month (in ₹) is
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If the amounts spent on savings and children education put together is ₹ 22,000, then the monthly incomeof the person(in ₹) is
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The amount spent on children education is equal to the amounts spent on which of the following two heads ?
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If the amount spent on house rent in a month is ₹ 5,000 more than the amount spent on travel and savings put together, then the monthly income(in ₹) of the person is
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Monthly savings percentage is
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In a group of 75 students 28 students study Mathematics (M), 32 study Physics (P), 30 study Chemistry (C) and 15 students study none of these; 13 study both M and P, 12 study P and C and 10 study C and M. Based on this information answer the questions.
The number of students who study only Chemistry is
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The number of students who study Physics alone is
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The letters of English alphabet are arranged cyclically. Then the letters are coded as follows : (i) a vowel is to be coded as the second vowel after it in the clockwise direction. and (ii) a consonant is to be coded as the second consonant after it in the clockwise direction. For decoding, the inverse process is to be followed. Based on this coding and decoding system answer the questions.
Code word for HAND is
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The word that is coded as RIUT is
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The word that is coded as RNIVO is
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The code word for LEAVE is
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The word that is coded as QUEUE is
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If the word COMPUTER is coded as RFUVQNPC, the code word for MEDICINE is
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If the word DWUKPGUU is coded as BUSINESS, the word MANAGEMENT is coded as
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If the word CENTRAL is coded as LARTNEC then the code word for SEMINAR is
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If the word FLUTE is coded as EJRPZ, then the code word of PLANE is
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If the code word for VICTORY is XKEVQTA then the code word for SUCCESS is
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If the first day of March in a year happens to be Friday, then the day on which Indian Independenceday falls in that year is
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If a clock shows 15 minutes past 3 O’clock then the angle between the hours and minutes hands is
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If the minutes hand of a clock is facing South, then the direction of the minutes hand after 210 minutes is
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A is the mother of B and C. D is the husband of C. Then A is related to D as
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Four buses $$B_1, B_2, B_3, B_4,$$ depart from the station $$S_1$$, and arrive the stations $$S_2$$, and $$S_3$$,. The bus numbers and the order in which they depart or arrive is not the same. The first bus to leave $$S_1$$, is the second to reach $$S_3$$, and the third to reach $$S_2$$. The first bus to reach $$S_3$$, is the second bus to leave $$S_1$$, and the last bus to reach $$S_2$$.
Based on this information answerthe following questions.
The first bus to reach the station $$S_1$$ is
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The second bus to reach the station $$S_2$$ is
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In a queue, Anitha is the $$10^{th}$$ from the front while Meena is $$25^{th}$$ from the last and Mohan is just in the middle of the two. If there are 50 persons in the queue, the position of Mohan from the front is
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If $$a * b = a + b + ab$$ for $$a, b \epsilon Q$$ then the value of $$x$$ satisfying $$(1 * 2) * x = -13$$ is
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$$a * b = \frac{1}{ab} + 1 \Rightarrow \sum_{n = 1}^{2013} n * (n + 1) =$$
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If $$a * b = a + b - \frac{ab}{2}\forall a, b \epsilon R$$ and if c is a non-zero real number, then the value of x satisfying x * c = x is
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If $$\frac{8^3. (27)^4. 6^5}{(36)^2.9^4.(18)^2} = 2^{\alpha}.3^{\beta}$$ then $$\alpha + \beta =$$
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The smallest number among
$$\sqrt[3]{4}, \sqrt[5]{7}, \sqrt[4]{5}, \sqrt{3}$$ is
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If (a + b) : (b + c) : (c + a) = 2 : 3 : 4 and a + b + c = 9,then the value of c =
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A circle and a square have the same area. Then the ratio of the side of the square to the radius of the circle is
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$$\sqrt{6 + 2\sqrt{2} + 2\sqrt{3} + 2\sqrt{6}}$$ =
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$$\left(\frac{\sqrt{5} + \sqrt{7}}{\sqrt{5} - \sqrt{7}} + \frac{\sqrt{5} - \sqrt{7}}{\sqrt{5} + \sqrt{7}}\right)^2$$ =
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The number that is exactly divisible by 11 among the following is
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The remainder when 73 x 79 x 81 is divided by 11 is
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The greatest 4-digited number which is exactly divisible by each of the numbers 18, 24 and 36 is
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If the l.c.m. of the positive integers a and b is 60 and $$a^2 . b^2 = 32400$$, then the g.c.d. of a and b is
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If $$\mid x - 6 \mid = 5$$ and $$\mid 3y - 12 \mid = 6$$ then the maximum value of $$\frac{x}{y} =$$
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If 3 is added to the denominator of a rational number then that number becomes $$\frac{1}{3}$$ and if 4 is added to numerator of the same rational number, then it becomes $$\frac{3}{4}$$ then that rational number is
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The difference between the biggest and smallest fractions among $$\frac{1}{2}, \frac{5}{6}, \frac{7}{9}, \frac{4}{5}$$ is
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The ascending order of the rational numbers $$\frac{13}{14}, \frac{11}{12}, \frac{15}{16}, \frac{8}{11}$$ is
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If 7% of 5% of 8% of x is 105, then x =
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If the length and breadth of a rectangle are increased vy 20% each, then the area of the rectangle increases by x%, then x =
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An article when sold at a gain of 5% yields rupees 15 more than when it is sold at a loss of 5%. Then the cost price of that article in rupees is
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By selling 15 items, a seller recovers the cost price of 20 items. Then his profit percent is
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A, B, C entered into a business with a total capital of ₹ 50,000/-. A invested ₹ 4,000/- more than B and B invested ₹ 5,000/- more than C. If there is a total profit of ₹ 35,000/- then A’s share in the profit, in rupees is
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A, B and C are running a business by investing the capitals in the ratio 2 : 4 : 5. If C’s sharein the profit is ₹ 2,200/-, then A’s share in the profit, in rupees, is
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Two pipes A and B can fill a tank independently in 20 and 30 minutes respectively. Both the pipes are opened simultaneously and after 6 minutes tap B is closed. Then the total time taken, in minutes,to fill the tank, is (assume that the tank is emptyinitially)
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Tap A can fill an empty tank in one hour, while a drain pipe B can empty that full tank in 6 hours. If both A and B are opened at the same instant, the total time taken to fill that empty tank,in hours, is
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A train travels a distance of 60 km in 40 minutes. If its velocity is decreased by 15 km/hour, then the time required by that train to travel the same distance, in minutes, is
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A person travels from A to B at a speed of 75 kin/hour in a car and returns from B to A by reducing his speed by 15 km/hour. If the total time taken is 3 hours, then the distance between A and B, in kilometers, is
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Two persons A, B can together complete a piece of work in 12 days, B and C together complete the same work in 8 days. If A, B, C work together, then that work can be finished in 6 days. Then the number of days B alone can finish the same work is
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A, B, C can individually complete a work in 20 days, 15 days, 12 days respectively. B and C start the work and they worked for 3 days and left. Then the number of days required by A to finish the remaining work is
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If the length of the hypotenuse of right angled Iscoceles triangle is 12 cm , then the area of the triangle in sqaure centimeters is
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If the length of the diagonals of a rhombus are 18 cm and 24 cm then the area of a rhombus in square centimeters is
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A cylindrical bar of height 1 metre and base radius 0.75 metres is melted and cast as a sphere and cast as a sphere. Then the diameter of a sphere in meters is
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Two boxes have square bases. Thesides of these bases are in the ratio 2 : 1. If the heights of the boxes are in the ratio 1 : 2 respectively, then the ratio of the volumesofthe boxes in that order is
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The radius of a coneis 3 times the radius of a cylinder and their heights are same. Then the ratio of their volumesin that order is
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A window is in the shape of a rectangle surmounted by a semicircle. If the length of the rectangle is 6 feet and the radius of the semicircle is 2 feet, then the area of the window,in square feet, is
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11 cubic meters of steel is cast in to cylindrical bars of diameters 10 cm and the length 1.4 metres. Then the number of such bars that can be cast with the given metal is (Take $$\pi = \frac{22}{7})$$
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The difference between the largest three digit natural number x satisfying x=(mod 8)and the smallest three digit natural number y satisfying y = 2(mod 5) is
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If $$3^{48} = x(mod 10)$$ and if $$0 \leq x \leq 9$$ then $$x =$$
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If p and q are two statements, then which oneofthe followingis a tautology ?
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Which of the following is equivalent to the statement $$P \rightarrow Q$$?
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Set A has 5 elements and set B has 10 elements. Then the possible maximum number of elements in $$A \cup B $$ is
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Let A be non empty set and P(A) be the power set of (A). Let R be a relation defined on P(A) by $$ X R Y \Leftrightarrow X \subseteq Y \forall X, Y \epsilon P(A)$$. Then R is not
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If a function $$f : R \rightarrow R$$ is defined by $$f(x) = x^{2} + 1$$, then $$f^{-1}(26) =$$
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If the line passes through the points (3,-5) and (-2, 7), then x is the intercept is
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The length of the intercept made by the line which passes through the points (2, 5) and (-4, 8) between the coordinate axesis
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If $$\theta$$ lies in the first quadrant and $$5 \tan \theta = 4$$, then $$\frac{5 \sin \theta - 3 \cos \theta}{\sin \theta + 2 \cos \theta} =$$
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If $$\theta +\phi = \frac {\pi}{4}$$, then $$(1 + \tan \theta) (1 + \tan \phi) =$$
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$$(\cos^{2}15^\circ - \cos^{2} 75\circ) (\sin 65^\circ . \cos 35^\circ — \cos 65^\circ . \sin 35^\circ) =$$
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Two poles of height 15 metres and 30 metres stand upright on a play ground .If the feet of the poles are 36 meters a part , then the distance between their tops are
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If the polynomial $$ax^{4} + bx^{3} + 3x^{2} - 4x - 4$$ is divisible by $$(x^{2} - 1)$$ then $$(a, b) =$$
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If $$(x - \alpha)$$ and $$(x - \beta )$$ are the two factors of the polynomial $$f(x) = ax^{2} + bx + c$$,then the quadratic polynomial whose factors are $$(x - \frac{1}{\alpha})$$ and $$(x - \frac{1}{\beta})$$ is
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If $$63 \times 65 \times 67 \times 69$$ is divided by 12 then the remainder obtained is
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A polynomial in x leaves remainders 8, 4 when divided by (x + 2) and (x - 2) respectively. If the same polynomialis divided by $$x^{2} - 4$$ then the remainder is
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If x + y = 12 y + z = 20 and z + x = 18 then x - y + z =
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A Person has a certain number of two rupee coins and some five rupee coins.If the total number of coins is 16 and thwe value of coins is ₹50 ,then the number by which the number of two rupee coins exceeds number of five rupee coins is
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If thew first and sixth terms of geometric progessions are $$\frac{2}{3}$$ and 162 respectively then the $$8^{th}$$ term of the progression is
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Three numbers are in an arithematic progession. their sum is 3 The third number is greater than first number by 16 ,then the product of those three number is
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The term independent of x in the expansion of $$\left(3x^{3} - \frac{4}{x}\right)^8$$
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If P is the sum of odd terms and Q is the sum of even terms in the expansion of $$(x + y)^n$$ then $$P^{2} - Q^{2} =$$
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If A is a 3 x 3, square matrix and if A Adj $$A = \begin{bmatrix}4 & 0 & 0\\0 & 4&0 \\ 0 & 0 & 4\end{bmatrix}$$, then det(2A) =
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$$\lim_{x \rightarrow 5} \frac{x^{2} - 3x - 10}{x^{2} - 7x + 10} =$$
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If $$x = t - \frac{1}{t}, y = t + \frac{1}{t}$$ where t is a parameter then $$\frac{dy}{dx} =$$
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If A is a square matrix and A^{T} denotes transpose then the matrix $$A. A^{T}$$ is always
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When a piece of wire is bent in the form of equilateral triangle then the area of the triangle is $$121 \sqrt{3} cm^{2}$$. If the same piece of wire is bent in the form circle , then the area of the circle in square centimeters is (Take $$\pi = \frac{22}{7})$$
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The sum of all the internal angles of a regular hexagon, in radians, is
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If two circles of radii, 7 cm and 10 cm respectively touch each other internally, then the distance between their centres, in centimeters, is
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If the mid points of the sides AB and AC of a triangle ABC are (4, -2), (-8, 14) respectively, then the length of the side BC, in units, is
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The distance between the lines $$\frac{x}{3} + \frac{y}{4} = 1$$ and 8x + 6y = 5 in units, is
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The mean of 6 observations is calculated as 24 and later it was noted that one of the observations is wrongly taken as 24 intstead of -24 then the correct mean is
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The median of 15 observations is 32 .Each of the obeseravation is greater than the median are increased by 8 and each of the observations leaas than the median are decreased by 6 Then the median of new data is
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The mode of the following distribution: 19, 13, 16, 13, 19, 24, 13, 9, 24, 13, 26 is
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If the standard deviation of the first n natural numbers is t then $$12t^{2} + 1 =$$
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If the standard deviation of a variable x is 12 then the variance of the variable 2x + 17 is
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If 3 coins are tossed, then the probability of getting at least 2 heads is
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When two unbiased dice are thrown , the probability that they show up different numbers is
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In a bivariate distribution $$X_i, y_i, i = 1, 2, ....., 8$$, if $$d_i$$ is the deviation between the the ranks of $$X_i$$ and $$Y_i$$ and and $$\sum_{i = 1}^{8} d_i^{2} = 21$$ then the coeffefficient of rank correlation between $$X_i$$ and $$Y_i$$ is
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If 5 boys and 4 girls sit in a row at random then the probability the boys and girls sit alternatively is
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When a leap year is selected at random then the probability that it has exactly 52 Sundays is
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Choose the correct answer :
A situation in which goods or shares are plentiful and buyers can keep prices down is called
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A differnce in wages between industries or between categories of Employees in the same industry referred to as
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A large corportion formed by the merging of separate firms is known as
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Celebraties who endorsed a product reffered to as
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Stocks ,Shares ,Bonds are collectively known as
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A computer language that is used to create websites is known as
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connection of networks that can be joined together is possible through
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ISDN stands for
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ELDstands for
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The connection between a computer and another piece of equipmentis
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Choose the Correct Answer.
A: “How is your business ?”
B: “I’m broke!”
B’s answerindicates that
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A: "you should not have spoken so harshly to him. you know that the faulty was yours "
B:"I know. I'll have to eat humble pie "
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A: " I have two tickets for the movie tommorrow .Will you come with me ? "
B: "could you invite some one else ? movies give me a headache ."
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"I dont think his jokes ever come off"
The speakers implies that the jokes were
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The passive form of the sentence "They are not going to play the match today " is
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A: “I’m sorry I couldn’t come to your party as I was out of town.”
B: “It’s alright. Don’t worry about it”.
In this conversation, the speaker “B”is
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“When it comes to grammar, she’s really on the ball.”
The speaker implies that
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Fill in the blanks with the appropriate phrase/verb/preposition.
A: “Are you going to the bank today ?”
B: “No. I've already to the bank.”
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I hope the enquiry will ....... truth
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The workers .......... their resignation when their demands were not met by the managing committee
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Here is the watch you asked .....
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The loan will be repaid ........ two months
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It ...... raining for a while , but now its raining again.
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They are ......... the whole family for Christmas.
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A subordinate has to abide .......... the decisions ofhis superiors.
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Read the following passage and answer questions :
In times of social fragmentation, vulgarity often becomes a wayoflife. To be shocking becomes more important than to be civil or creative or truly original. Given the degree of vulgarity in our society, cynicism seems almost irresistible. But cynicism represents a secession from society, a dissolution of the bonds between people and families and communities, an indifference to the fate of anything, beyond the self Cynicism is deadly. It bites everything it can reach-like a dog with a foot caughtin a trap. And then it devours itself. It drains us of the will to improve; it diminishes our public spirit; it saps our inventiveness; it withers our souls. Cynics often see themselves as merely being world-weary. There is no new thing under the sun, the cynics say. They claim their weariness is wisdom. Butit is usually mere posturing . Their weariness seems to be most effective when they consider the aspirations of those beneath them, who have neither powernor influence nor wealth. For these unfortunates, nothing can be done, the cynics declare. Hope is considered an affrontto rationality : the notion that the individual has a responsibility for the community is considered a dangerousradicalism. Ultimately, however, the life of a cynic is lonely and self - destructive. It is our human nature to make connections with other human beings. The gift of symapthy for another is one of the most powerful sentiments we ever feel.If we do not have it, we are not have human .Indeed it is so powerful that the cynics who denies it goes to war with himself.
What is Considered normal in today's society?
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What have divisions in the society led to
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Why cynism dangerous
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What charecterises the behaviour of a cynic ?
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What quality makes us human?
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Read the following passage and answer questions
Production may not be a dominant ideological leverage in economic decision making, but it cannot be altogether dismissed from economic calculations at whatever level. The difference that globalization has brought about is not that it has made production concerns immaterial, but that the leading factor is now the consumer and production must do what it can to meet the demands of the market. So every nowand again, one comes up against serious production problems at the national level which are resolved at the global level by importing skills or machinery. Thus while it is true that consumer tastes are getting more homogenized across the world, production facilities have not kept up. Economic difficulties at the national level arise from this mismatch.
What cannot be kept out of economic calculations ?
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What is the most prominent consideration today ?
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Which word does the writer use to describe buyer’s tastes ?
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What has caused the change in approach to economic decision-making ?
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At the national level, whatis the effect of the discrepancy between production and demand ?
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Read the following passage and answer questions
The land in Egypt is very fertile when it ts irrigated, and water for irrigation has to come mainly from the one big river which Egypt has, namely, the Nile. Therefore, most of the farming is done near this river. As the Nile nears the sea, it splits into several branches to form a delta. The land here is very flat; ploughing and irrigation are easy andit is, therefore, the most highly cultivated arca. Further inland, away from the sea, only the strips of land on either side of the river are cultivated, There are, of course, a few irrigation projects and model farms, but a large proportion of the Egyptian country side remains a dry, sandy desert. In the delta, the main crops are cotton, rice, fruit such as banana, dates, figs and melons, and vegetables. Cattle, buffalo, and goats are also kept for milk and meat. Further inland, however, where the land is not so flat, and water is scarce, the cultivation is less intense; in this part of the country, there is a scarcity of fresh food, such as fruit and vegetables, because there is not enough water to grow it. Sugarcane and wheat are the main crops here. In the huge, barren deserts, there are wandering herdsmen who keep goats and camels. Thusit is clear that vast areas of land are lying unused at present only because ofthe lack of irrigation. The country can double its production if the irrigation projects multiply.
What is the meaning of ‘irrigation’ ?
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What does the Nile form whenit reaches the sea ?
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What are cultivated towards the interior of the city ?
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Who are the ‘wandering herdsmen’ ?
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How can agricultural production be increased in Egypt ?
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Choose the correct meaning for the word given:
bulwark
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cower
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plebiscite
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bizarre
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Platitude
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feign
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Fill in the blank choosing the correct word:
Conspirators were satirically called ............ men.
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The ........ of informationin the organization will be given high priority.
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Bitter experiences make us ............ though wiser.
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The ......... of the flowers enhanced the beauty of the garden.
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