What is the integer n ?
I. n is a multiple of 5
II. n and n + 1 are prime numbers
AP ICET 2018 Question Paper Shift-1 (2nd May)
In the following questions each question is followed bydata 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 the integer n odd ?
I. $$n^3$$ is even
II. $$(n + 1)^3$$ is divisible by 3.
What is the area of triangle $$\triangle ABC$$?
I. $$\triangle ABC$$ is isosceles
II. $$\triangle ABC$$ is inscribed in a circle with center A
What is the average of a, b, c, d and e?
I. a + b + c = 20 - d - e
II. d + e = 8
Is the positive integer n is divisible by 48?
I. n is a multiple of 12
II. 32 divides n
Is PQRS a sqaure ?
I. PR > QS
II. PQ = QR = RS = SP
What is the total number of students in the class in which 24 are boys?
I. The student strength in the school is 284
II. The ratio of boys and girls in the class is 4: 3
What is distance between A and B ?
I. A person P walked from A to B in 50 minutes at a speed of 6 Kmph
II. A person Q took 10 minutes to reach B from A on a motorcycle.
How many women are needed to complete the work in 10 days?
I. 6 men and 8 women can complete the work in 8 days.
II. 4 women and 3 men can complete the work in 16 days.
What is the total interest on principal amount Rs.20,000 for two years period?
I. The rate of interest is 8% per annum.
II. It is compounded every quarterly.
Is the triangle with sides a, b and c equilateral?
I. $$a^2 = b^2 + c^2$$
II. $$a < b + c$$
How much amount is needed to fence the circularfield?
I. The radius of the field is half of its diameter.
II. The diameter of the field is 200 mts and the cost of fencing is Rs. 10 per meter.
In a triangle $$ABC, \angle B = 90^\circ$$. Then what is $$AB : BC : CA ?$$
I. $$\tan C = \frac{1}{2}$$
II. $$\sin^2 A + \cos^2 A = 1$$
What is the length of the train?
I. The train crosses a man standing onthe platformin 15 seconds.
II. The train crosses its own length in 25 seconds.
What is the slope of the line l in the xy - plane?
I. l passes through origin.
II. l passes through (1, 4)
What is the area of the triangle whose sides are a, b and C?
I. a + b = 14
II. b + c = 18
In how many days a piece of work can be completed by three men A, B and C?
I. Individually A and B can do the same amount of work in a day.
II. C can do double the amount of work than that of A.
What is the product of divisors of the natural number n?
I. $$d_1, d_2, ......... d_k$$ are all the positive divisors of n
II. n > 2
For real numbers x and y what is the value of x + 2y?
I. x > 0, y > 0
II. $$x^2 + 4y^2 + 4xy = 0$$
What is the ratio of the length to the diagonal of a rectangle whose dimensions are a and b?
I. $$4a^2 + 9b^2 = 12 ab$$
II. a > 0, b > 0
In each of the Following 10 questions a sequence of numbersorletters that followa definite pattern is given. Each question has a blank space. This has to befilled by the correct answer from the four given options to complete the sequence without breaking the pattern.
216 : 6 :: 512 : ..........
8 : 72 :: ....... : 819
15 : 223 :: ........ : 287
8 : 36 :: 12 : .........
POSH : SHOP :: ......... : LEAP
2 : 64 :: ...... : 729
AEI : CHK :: EIM : ..........
EI : 59 :: ....... : 1121
HOSPITAL : PATIENTS :: SCHOOL : ........
C : X :: F : ......
In the Following questions pick the odd thing out.
The following questions follow a definite pattern. Observe the same and fill in the blanks with suitable answers.
9 , 28, 126, ........, 1332
P3C, RSF, T8I, V12L, ........
99, 80, 63, 48, ......, 24, 15
C, D, G, K, M, .........
1, 2, 6, 15, 31, ......., 92
7, 13, 21, 31, 43, ....., 73
-1, 6, 25, 62, .........., 214,
$$\frac{1}{3}, 1\frac{1}{3}, 4\frac{5}{6}, 7\frac{1}{3} ..........$$
3, ......, 22, ............, 116
DFIK, GILN, JLOQ, ..........
The graph shown below gives the sales of the weapons during the years 2008 to 2016. Study the graph and answer the following questions.
During which year, the sales witnessed a sharp down fall?
During which year the sales witnessed a sharp rise?
During which year consecutive sales witnessed down fall?
The following pie chart shows the marks obtained by a student in five subjects. The total marks obtained by him in all the five subjects are 900. Study this chart and answer the following questions.
Marks obtained by him in mathematics is
The marks obtained by him in physics is
The approximate percentage of marks obtained by him in Englishin total marks is
The total marks obtained by him in two languages together is
The percentage of marks obtained by him in Telugu alone in the total marks
In the Venn diagram given below, n (A) = 24, n (B) = 30, and n (C) = 36. Study this diagram and answer the Following questions.
$$n(A \cup B) =$$
$$n(A \cup B \cup C) =$$
The numbers 0 to 9 are coded as follows by considering the exceptions given below:
Exception (1): If a number starts and ends with non zero odd digits, then the first and last digits should be coded as P and Q respectively.
Exception (2): If a number starts and ends with non zero even digits, then first and the last digits should be coded X and Y respectively.
What is the code for 389167
What is the code for 278140 ?
Which one of the following numbers is represented by BADGE
Which of the following numbers are represented by XABCFY?
(A) 215096 (B) 815094 (C) 315094
What is the code for 1538428 ?
In a code language ‘SILVER’ is coded as ‘QGNXCT’ and ‘SHYAM’ as ‘QJWYK’. Using this information find the coding and decoding process and answer the following questions.
Which is code for ‘DELHI’
Which string of letters is coded as ‘FOUR’
What is the code for ‘EIGHT’?
Which string of letters is coded as ‘FLIGHT’
What is the code for ‘KILL’
For the following questions answer them individually
What is the day of the week was it on $$5^{th}$$ November 1987 if it was Mondayon $$4^{th}$$ April 1988?
At what point of time after 3'O clock the hour hand and the minute hand are at right angles for the first time?
A watch which gains uniformly, is 5 minutes slow at 7'O clock in the morning on a Sunday and it is 5 minutes 48 sec fast at 7 pm on the following Sunday. Which day was it correctly showing?
P is the father of R and is the son of Q and T is the youngest brother of P. If R is the sister of S, howis Q related to T?
Reaching the meeting place 20 minutes before 8.50 hrs, Satish found himself 30 minutes earlier than the man who comes 40 minutes late. What was the scheduled time of the meeting?
There is a metro train between stations X and Y every 15 minutes. An announcement was made at station that next train will depart in another 11 minutes as the previous train left at 2.18 PM. At what time was the announcement made?
Nine persons J, K, L, M, N, O, P, Q and R are sitting in a row facing the same direction. L is at the right of M andat the third place at the right of N. K is at one end of the row. Q is seated adjacent to both O and P. O is at the third place at the left of K. J is next to left of O. Which one of the followingis true?
If $$\Box$$ and $$\rightarrow$$ are defined by $$a \Box b = \frac{a - b}{a + b}$$ and $$a \rightarrow b = ab$$ then $$\frac{(66 \Box 6) \rightarrow 66}{55 \Box 5} =$$
By applying which one of the following meaning of arithmetical signs will the value of $$700 - 10 \div \frac{1}{2} \times 35 + 70 = 0$$
If $$\rightarrow$$ stands for addition
$$\leftarrow$$ stands for subtraction
$$\uparrow$$ stands for division
$$\downarrow$$ stands for multiplication
🡕 stands for equal to
Then which one of the following is true.
If $$f(x, y) = x^n . y^n$$ and $$f\left(4x, \frac{y}{2}\right) = k.f(x, y)$$ then k =
If $$2^x = 4^y = 8^z$$ and xyz = 288, then, x + y + z =
Solution
$$2^x = 4^y = 8^z$$
$$2^x=2^{2y}=2^{3z}\ $$
=> $$x=2y=3z\ $$
Let $$x=2y=3z\ =k$$
xyz = 288
=> k*k/2 *k/3 = 288
=> k^3 = 1728 => k =12
x=12, y=6 and z = 4
x+y+z=22
If $$25x^2 + 13y^2 + z^2 = 30xy + 4yz$$ then $$x : y : z =$$
A, B and C are co-workers in a company and their total salary is Rs. 94,000/-. The salaries of A and B are in the ratio 5 : 6; that of B and C are in the ratio 3:2. If the salaries of C and A are in the ratio 4:5 then the salary of B ( in thousands of rupees) is
Solution
Given, total salary of A, B and C = Rs. 94,000
A : B = 5:6
B : C = 3:2 = 6:4
$$\Rightarrow$$ A : B : C = 5:6:4
$$\therefore\ $$Salary of B $$=\frac{6}{5+6+4}\times94000=\frac{6}{15}\times94000=$$ 45,000
If $$\sqrt{15 - 2\sqrt{35} - 2\sqrt{15} + 2\sqrt{21}} = \sqrt{a} - \sqrt{b} + \sqrt{c}$$ then $$a^2 - c^2 =$$
$$\sqrt{21 - 4\sqrt{5} + 8\sqrt{3} - 4\sqrt{15}} =$$
Solution
$$\sqrt{21 - 4\sqrt{5} + 8\sqrt{3} - 4\sqrt{15}} =$$ = $$\sqrt{2^2+\left(-\sqrt{\ 5}\right)^2+\left(2\sqrt{\ 3}\right)^2+2\cdot2\cdot-\sqrt{5}+2\cdot\left(-\sqrt{\ 5}\right)\left(2\sqrt{3}\right)+2\cdot\left(2\sqrt{3}\right)\cdot2}=$$
Which is in the form $$a^2+b^2+c^2+2ab+2bc+2ca\ =\ \left(a+b+c\right)^2$$
hence $$\sqrt{21 - 4\sqrt{5} + 8\sqrt{3} - 4\sqrt{15}} =$$ = $$2-\sqrt{\ 5}+2\sqrt{\ 3}$$
When a number is divided by 75, the remainder is 28. The remainder when the same number is divided by 25 is
Solution
The number will be of the form (75k+28)
75k+28 = 75k+25+3 = 25(3k+1)+3 = 25p+3
$$\therefore\ $$The remainder when (75k+28) is divided by 25 = 3
Hence, the correct answer is Option C
Sum of all integers lying between 200 and 400 that are multiples of 7 is
Solution
The integers between 200 and 400 divisible by 7 are 203,210...... 399
$$\therefore\ $$Required Sum = 203 + 210 +....+399
$$=7[29+30+.....+57]$$
$$=7[\frac{29}{2}\left(29+57\right)]$$
$$=7[\frac{29}{2}\left(86\right)]$$
$$=7\times29\times43$$
$$=8729$$
Hence, the correct answer is Option D
A, B and C respectively take 27, 36 and 45 seconds to run around a track. All of them start at a point P on the track simultaneously. The number of rounds made by C when all of them meet next at P is
Solution
LCM of 27, 36, 45 = 540
A, B, C will again meet at P after every 540 seconds.
$$\therefore\ $$Number of rounds made my C in 540 seconds = $$\frac{540}{45}$$ = 12
Hence, the correct answer is Option A
State a pair of numbers, whose sum is 184 and whose greatest common divisor is 23
Solution
53 is not divisible by 23, hence option A is eliminated
79 is not divisible by 23, hence option C is eliminated
84 is not divisible by 23, hence option D is eliminated
The rational numbers with recurring decimal expansion $$0.\overline{12}$$ is
Solution
Let a = $$0.\overline{12}$$ ........(1)
$$\Rightarrow$$ 100a = $$12.\overline{12}$$ ........(2)
Solving equation(2) - equation(1)
99a = 12
$$\Rightarrow$$ a = $$\frac{12}{99}$$
$$\Rightarrow$$ a = $$\frac{4}{33}$$
$$\Rightarrow$$ $$0.\overline{12}$$ = $$\frac{4}{33}$$
Hence, the correct answer is Option D
If $$p$$ is the smallest prime with $$7p > 5$$ and q is the largest prime with $$7q < 497$$ then the rational number $$\frac{p}{q} =$$
Solution
Given, $$7p > 5$$
$$\Rightarrow$$ $$p>\frac{5}{7}$$
$$\Rightarrow$$ $$p>0.714$$
The smallest prime number greater than 0.714 is 2
$$\Rightarrow$$ $$p=2$$
$$7q < 497$$
$$\Rightarrow$$ $$q<71$$
The largest prime number less than 71 is 67
$$\Rightarrow$$ $$q=67$$
$$\therefore\ $$ $$\frac{p}{q}=\frac{2}{67}$$
The greatest among $$\frac{3}{5}, \frac{6}{7}, \frac{5}{8}, \frac{7}{9}$$ is
Solution
$$\frac{3}{5}$$ = 0.6
$$\frac{6}{7}$$ = 0.8
$$\frac{5}{8}$$ = 0.62
$$\frac{7}{9}$$ = 0.77
$$\therefore\ $$The greatest among $$\frac{3}{5}, \frac{6}{7}, \frac{5}{8}, \frac{7}{9}$$ is $$\frac{6}{7}$$
Hence, the correct answer is Option B
If $$a = \sqrt[3]{4}, b = \sqrt[4]{5}, c = \sqrt[4]{7}$$ and $$d = \sqrt[3]{9}$$, then their correct ordering is
Solution
a = $$\sqrt[\ 3]{4}\ =\ \sqrt[\ 12]{256}$$
b = $$\sqrt[\ 4]{5}\ =\ \sqrt[\ 12]{125}$$
c = $$\sqrt[\ 4]{7}\ =\ \sqrt[\ 12]{343}$$
d=$$\sqrt[\ 3]{9}\ =\ \sqrt[\ 12]{6561}$$
hence b<a<c<d
In a fraction if the numerator is increased by 20% and the denominator is decreased by 10% the fraction becomes $$\frac{16}{21}$$. Then the original fraction is
Solution
Let numerator = x
and denominator = y
New numerator = 1.2x
New denominator = 0.9y
Given,
1.2x/0/9y = 16/21
=> x/y = 4/7
The total number of students in the class with 36 boys and the rest 55% girls is
Solution
Given, number of boys in the class = 36
Percentage of girls in the class = 55%
$$\Rightarrow$$ Percentage of boys in the class = 45%
Let total students in the class = x
$$\Rightarrow$$ 45% of x = 36
$$\Rightarrow$$ $$\frac{45}{100}$$x = 36
$$\Rightarrow$$ x = 80
$$\therefore\ $$Total number of students in the class = 80
Selling two items each at Rs 240/-, a merchant gets, a profit of 20% on one of them and incurs a loss of 20% onthe other. In the whole transaction the merchant gets
Solution
SP1 = 240
CP1 = 240/1.2 =200 Rs
SP2=240
CP2 = 240/0.8 = 300
Total SP = 480 and total CP = 500
Loss % = 20/500 = 4%
A sales man writes the price of each article he sells as 50% above the cost price. He allows some discount and makes a profit of 20% still. The rate of discount is
Solution
Let CP = 100 Rs
According to the problem,
MP = $$\frac{150}{100}\times100$$ = Rs 150
Profit% = 20%
SP = $$\frac{120}{100}\times100$$ = Rs 120
Discount = 150 - 120 = Rs 30
Discount% = $$\frac{30}{150}\times100$$ = 20%
Hence, the correct answer is Option A
A started a business with B joining him investing 60% more than the investment of A after 4 months. If B gets Rs 20,000/- more in the year-end profit then the total profit (in lakhs of rupees)
A, B, C enter into a business partnership such that 3 times the capital of A is equal to 4 times the capital of B which is equal to 5 times the capital of C. The ratio of their capitals is
Solution
Let the capitals of A, B, C are a, b, c respectively
According to the problem, 3a = 4b = 5c
Let 3a = 4b = 5c = t
$$\Rightarrow$$ a = $$\frac{t}{3}$$, b = $$\frac{t}{4}$$, c = $$\frac{t}{5}$$
$$\therefore\ $$Ratio of their capitals = a : b : c
= $$\frac{t}{3}$$ : $$\frac{t}{4}$$ : $$\frac{t}{5}$$
= $$\frac{1}{3}$$ : $$\frac{1}{4}$$ : $$\frac{1}{5}$$
= $$\frac{60}{3}$$ : $$\frac{60}{4}$$ : $$\frac{60}{5}$$
= 20 : 15 : 12
Two pipes A and B canfill an empty tank independently in 20 minutes and 30 minutes respectively. To fill the empty tank both of the pipes were opened at a time and after 4 minutes tap A is closed. The total time (in minutes) takes to fill the tank is
Solution
Let the capacity of tank = 60litres
Speek of A = 60/20 = 3litres/min
Speed of B = 60/30 = 2 litres/min
In 4 min, A will fill 12l and B will fill 8 l. Total 20 litres
Left = 40 litres
Time required by B to fill remaining = 40/2 = 20 min
Total time = 24min
A pipe A can fill a tank 3 times faster than a pipe B and takes 28 min less time than pipe B to fill a cistern. If both pipes are opened simultaneously, the time (in minutes) to fill that tank is
If the ratio of the speeds of three trains is 3:4:5 thenthe ratio of the times taken by them to cover the same distance is
Solution
Time and speed are inversely proportional
hence ratio of times = $$\frac{1}{3}:\frac{1}{4}:\frac{1}{5\ }$$
Multiply by 60, we get 20:15:12
600 meters long train is running at the speed of 72 kmph. If it crosses a tunnel in 1 minute. then the length of the tunnel (in meters) is
Solution
Let length of the tunnel = x
Length of the train = 600 m
Speed of the train = 72 km/h = 72 x $$\frac{1000}{3600}$$ m/sec = 20 m/sec
Time = 1 min = 60 sec
Speed = $$\frac{\text{distance}}{\text{time}}$$
$$\Rightarrow$$ 20 = $$\frac{600+\text{x}}{60}$$
$$\Rightarrow$$ x + 600 = 1200
$$\Rightarrow$$ x = 600 m
$$\therefore\ $$Length of the tunnel = 600 m
A can do a work in 12 days while B needs 16 days to do the same work. After working 4 days together, B left the work. The number of days for A alone to complete the remaining work is
If 5 men or 9 women can finish a piece of work in 19 days, then the number of days for 3 men and 6 women to finish the same work is
Solution
Let the total work = W
Number of days required for 9 women to finish the work = 19 days
$$\Rightarrow$$ Work done by 9 women in 1 day = $$\frac{W}{19}$$
$$\Rightarrow$$ Work done by 1 woman in 1 day = $$\frac{W}{19\times9}$$
5 men or 9 women can finish the work in 19 days
$$\Rightarrow$$ 5 men = 9 women
$$\Rightarrow$$ 1 men = $$\frac{9}{5}$$ women
3 men and 6 women = 3($$\frac{9}{5}$$women) + 6 women = $$\frac{27}{5}$$ women + 6 women = $$\frac{57}{5}$$ women
Work done by $$\frac{57}{5}$$ women in 1 day = $$\frac{57}{5}\times\frac{W}{19\times9}$$ = $$\frac{W}{15}$$
Number of days required for $$\frac{57}{5}$$ women to complete the work = 15 days
$$\therefore\ $$Number of days required for 3 men and 6 women = 15 days
In a circle of radius 7 cms, a sector is of $$\frac{77}{3}$$ sq.cms area. Then the sectorial angle is (Taking $$\pi = \frac{22}{7}$$)
Solution
Area of sector = $$\frac{\theta}{360}\cdot\pi\ r^2=\frac{77}{3}$$
=> $$\frac{\theta}{360}\cdot\frac{22}{7}\cdot7^2=\frac{7}{3}$$
=> angle = 60
The length of a rectangle is thrice its breadth and its perimeter is 96 cm. The area (in square centimetres) of the rectangle is
Solution
Let length = 3b and breadth =b
Permiter = 2(b+3b) = 96
=> 4b= 48 => b=12
Hence l = 36 and b = 12
Area = 36*12 = 432
A rain of 2cmfall on a land of 1 sq.km. If 50% of rain water has been driven into a pool having base of dimensions (200 m X 10 m), then the increase (in meters) of water level of the pool
One cubic meter of aluminium is used to prepare a sheet of 10000 square meters. The thickness (in cm) of the sheet is
Solution
Let thickness = a meters
According to the problem,
a x 10000 m$$^2$$ = 1 m$$^3$$
$$\Rightarrow$$ a x 10000 = 1 m
$$\Rightarrow$$ a x 10000 = 100 cm
$$\Rightarrow$$ a = $$\frac{1}{100}$$ cm
$$\Rightarrow$$ a = 0.01 cm
Hence, the correct answer is Option D
The area of a parallelogram is 128 sq.cm and its altitude is twice the base. Then the base (in cms) is
Solution
Given, h = 2b
Area of parallelogram = base x height
$$\Rightarrow$$ b x h = 128
$$\Rightarrow$$ b x 2b = 128
$$\Rightarrow$$ b$$^2$$ = 64
$$\Rightarrow$$ b = 8 cm
$$\therefore\ $$Base of parallelogram = 8 cm
A rectangular plot of perimeter 46 meters has area of 120 sq. meters. The length (in meters) of its diagonal is
Solution
Let length = l
Breadth = b
Given, lb=120 and l+b = 23
Squarring on both sides, $$l^2+b^2+2lb\ =\ 529$$
$$l^2+b^2=\ 529\ -\ 2\left(120\right)$$
=> $$l^2+b^2=\ 289$$
Lenth of diagonal = $$\sqrt{l^2+b^2\ }=\ \sqrt{\ 289}\ =17$$
A paper is in square form with a side 20cm. Two semicircles are drawn on its opposite sides as diameters. If these semicircles are cut down. the area (in sq.cm) of the remaining part of the paper is
$$3214_{(7)}$$ in decimal system is
Solution
$$3214_{(7)}$$ = $$4\left(7^0\right)+1\left(7\right)+2\left(7^2\right)+3\left(7^3\right)=\ 1138$$
$$\therefore\ $$In decimal system, $$3214_{(7)}$$ = $$1138_{(10)}$$
Hence, the correct answer is Option A
For any integer $$k$$ let $$k^{*} = 2k - 5$$. Then the number of elements in the set $$S = \left\{x : (x^{*})^{*} = x \right\}$$ is
If p and q are statements then $$\sim(p \vee q)$$ is equivalent to
A tautology, among the following is
If $$E_n = \left]\{x \epsilon R: -\frac{1}{n} < x < 0\right\}$$ for $$n = 1, 2, 3, ............ $$ then $$\bigcap_{n=1}^{\infty}E_n =$$
The number of functions from {a, b, c, d, e} into {1,2} is
If $$f(x) = \frac{x - 1}{x + 2}$$; x ≠ -2, then $$f^{-1}(4) =$$
Solution
$$f^'\left(x\right)=\frac{\left(\left(x-2\right)1\ -\left(x-1\right)1\right)}{\left(x-2\right)^2}=$$
The equation of the line passing through(-4, 3) and parallel to the line joining the points (1, -3) and (-5, 1) is
The equation of a straight line passing through the intersection of the lines x + 2y - 19 = 0 and x - 2y - 3 = 0 and at 5 units distance from(-2, 4) is
$$\sin 0^\circ + \cos 30^\circ - \tan 45^\circ + \cosec 60^\circ + \cot 90^\circ =$$
Solution
$$\sin 0^\circ + \cos 30^\circ - \tan 45^\circ + \cosec 60^\circ + \cot 90^\circ $$ =$$0+\frac{\sqrt{\ 3}}{2}-1+\frac{2}{\sqrt{\ 3}}+0\ =\ \frac{\left(7-2\sqrt{\ 3}\right)}{2\sqrt{\ 3}}=\frac{\left(7\sqrt{\ 3}-6\right)}{6}$$
If $$\sin \theta = -\frac{1}{2}$$ and $$\cot \theta = -\sqrt{3}$$ then the minimum value that $$\theta$$ can take is
$$\sin^2 \frac{\pi}{4} + \sin^2 \frac{3\pi}{4} + \sin^2 \frac{5\pi}{4} + \sin^2 \frac{7\pi}{4} =$$
Two boys who are oneither side of a tower of 100 meters height observe that the angles of elevation of the top of the tower are $$30^\circ$$ and $$45^\circ$$. The distance (in meters) between the boys is
For a ≠ b, if the quadratic expression $$x^2 + ax + b$$ and $$x^2 + bx + a$$ have a common factor, then the relation between a and b is
If f(x) and g(x) are polynomials of degrees 3 and 2 respectively then f(g(x)) is of degree
If two of the factors of the polynomial $$x^3 + x^2 - 10x + 8$$ and x - 1 and x - 2 then the third factors is
Solution
If x+a is factor of a polynomial f(x), then f(-a) should be zero
f(-4) = $$\left(-4\right)^3+\left(-4\right)^2-10\left(-4\right)+8=0$$
Hence x+4 is the third factor.
If the remainders when the polynomial f(x) is divided by $$x - 1$$ and $$x + 1$$ are 3 and 4 respectively. then the remainder when f(x) is divided by $$x^2 - 1$$ is
If 5 is subtracted from each of the two numbers their ratio becomes 1:2. while 1 is added to each. their ratio becomes 8:13. Then the difference between those numbers is
Solution
Let the numbers be x, y
Given, $$\frac{\left(x-5\right)}{y-5}=\frac{1}{2}$$ => 2x-y =5
Given, $$\frac{\left(x+1\right)}{y+1}=\frac{8}{13}$$ => 13x-8y = -5
Solving we get x=15 and y= 25
Diference = 10
The point (x, y) in the plane for which 6x + 6y = 5xy and 6y - 6x = xy is
Solution
Given, equation of planes is
6x + 6y = 5xy .......(1)
6y - 6x = xy .........(2)
Solving equation (1) + equation (2)
12y = 6xy
$$\Rightarrow$$ 12y - 6xy = 0
$$\Rightarrow$$ 6y(2-x) = 0
$$\Rightarrow$$ y = 0 or 2-x = 0
$$\Rightarrow$$ y = 0 or x = 2
From equation (1)
When y = 0, 6x + 0 = 0 $$\Rightarrow$$ x = 0
When x = 2, 6(2) + 6y = 5(2)y $$\Rightarrow$$ y = 3
$$\therefore\ $$Required point is (2,3)
In an arithmetic progression the $$8^{th}$$ and $$19^{th}$$ terms are respectively 17 and 39. The $$25^{th}$$ term of it is
Solution
Given, $$8^{th}$$ and $$19^{th}$$ terms of the arithmetic progression are 17 and 39
$$\Rightarrow$$ a+7d = 17 and a+18d = 39
Solving the above two we get 11d = 22
$$\Rightarrow$$ d= 2 and a = 3
Hence 25th term = a+24d = 3 + 24(2) = 51
$$1 + \frac{3}{4} + \frac{5}{16} \frac{7}{64} + ......... \infty =$$
The term independent of x in the binomial expansion of $$\left(x - \frac{1}{x^2}\right)^3n$$ is
The coefficient of $$x^8$$ in $$\left(x - \frac{2}{x}\right)^{20}$$ is
If the system of equations $$3x - 2y + z = 0, \lambda x - 14y + 15z = 0, x + 2y + 3z = 0$$ has non-trivial solution, then $$\lambda$$ is a root of the equation
$$A = \begin{bmatrix}4 & 0 & 0 \\0 & 5 & 0 \\0 & 0 & 6 \end{bmatrix} \Rightarrow A^{-1} =$$
$$\lim_{x \rightarrow 0}\frac{1 - \cos 4x}{1 - \cos 5x} =$$
If $$y = \sqrt{x + y}$$ then $$\frac{dx}{dy} =$$
Solution
Given, $$y = \sqrt{x + y}$$
Squaring on both sides, we get
$$y^2=x+y$$
$$\Rightarrow$$ $$x=y^2-y$$
$$\Rightarrow$$ $$\frac{dx}{dy} = 2y^{2-1}-y^{1-1}$$
$$\Rightarrow$$ $$\frac{dx}{dy} = 2y-1$$
Hence, the correct answer is Option D
If each interior angle of a regular polygon is $$135^\circ$$, then the number of sides of the polygon is
Solution
Each interior angle of the regular polygon = $$\frac{\left(n-2\right)180^{\circ\ }}{n}$$
Given, each interior angle of the regular polygon is $$135^\circ$$
$$\Rightarrow$$ $$\frac{\left(n-2\right)180^{\circ\ }}{n}=135^{\circ\ }$$
$$\Rightarrow$$ $$4\left(n-2\right)\ =3n$$
$$\Rightarrow$$ $$\ 4n-8=3n$$
$$\Rightarrow$$ $$n=8$$
$$\therefore\ $$Number of sides of the polygon = 8
ABCD is a quadrilateral and P, Q, R and S are the mid-points of AB, BC, CD and DA respectively. Then PQORS is a
A parallelogram and a triangle have same base and the third vertex of the triangle lies on the side parallel to base. If the area of the triangle is 36 sq.cms then the area (in square cms) ofthe parallelogram is
The area (in sq. units) of the triangle formed by points (2, 3), (3, 4) and (4, 2) is
Solution
Area of triangle formed by points (2, 3), (3, 4) and (4, 2) = $$\frac{1}{2}\left|x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right|$$
$$=\frac{1}{2}\left|2\left(4-2\right)+3\left(2-3\right)+4\left(3-4\right)\right|$$
$$=\frac{1}{2}\left|2\left(2\right)+3\left(-1\right)+4\left(-1\right)\right|$$
$$=\frac{1}{2}\left|4-3-4\right|$$
$$=\frac{1}{2}\left|-3\right|$$
$$=\frac{3}{2}$$
PQR is a right angled triangle where P and R are the points (2, 4) and (6, 10) respectively and $$\angle Q = 90^\circ$$. Then the circumcentre of the triangle is
Solution
In a right-angled triangle, circumcentre is the centre of the hypotenuse.
Hence circumcentre = $$\frac{\left(6+2\right)}{2},\ \frac{\left(10+4\right)}{2}=\left(4,7\right)$$
If the arithmetic mean of a, b, c, d and 18 is 17 then the arithmetic mean of at+2b, b+2c, e+3d and 2a-1 is
The median of 462, 378, 448, 364, 528, 486, 534, 386 is
Solution
Ascending order of the given numbers is 364, 378, 386, 448, 462, 486, 528, 534
$$\therefore\ $$Median of the given numbers = $$\frac{448+462}{2}$$ = 455
Hence, the correct answer is Option C
The mode of the observations 10, 13, 16, 13, 19, 24, 13, 9, 24, 13, 26 is
Solution
The mode is defined as the entity that repeats the maximum number of times
In the given observations, 13 is repeating thrice which is maximum.
$$\therefore\ $$Mode of the given observations = 13
The standard deviation of five consecutive positive integers is
Solution
five consecutive positive integers = 1,2,3,4,5
Mean = 3
Standard deviation = $$\sqrt{\frac{\left(\ \left(3-1\right)^2+\left(3-2\right)^2+\left(3-3\right)^2+\left(3-4\right)^2+\left(3-5\right)^2\right)}{5}}$$ = $$\sqrt{\ 2}$$
The standard deviation of the first five even natural numbers is
Solution
first five even natural numbers = 2,4,6,8,10
Mean = 6
Standard deviation = $$\sqrt{\frac{\left(\ \left(6-2\right)^2+\left(6-4\right)^2+\left(6-6\right)^2+\left(6-8\right)^2+\left(6-10\right)^2\right)}{5}}$$ = $$\sqrt{\ 8}=2\sqrt{\ 2}$$
In the calculation of the rank correlation coefficient $$(\rho)$$ of 9 pairs of observations $$(x_i, y_i)$$, it is found that the sumof the squares of the deviations of the corresponding ranks is 144. Then $$\rho =$$
A number is selected from $$S = \left\{1,2,3,......,30\right\}$$ at random. The probability that the number has no square factor other than one is
P and Q are two sets such that n(P) = 5 and n(Q) = 3. A relation from P to Q is selected at random. Then the probability that the relation is not a function is
When two dice are thrown, the probability of getting the sum 9 is
Solution
When two dice are thrown, the possible cases of getting a sum of 9 are (3,6) (4,5) (5,4) (6,3)
Number of favourable cases = 4
Total possibilities = 6 x 6 = 36
$$\therefore\ $$Required probability = $$\frac{4}{36}$$ = $$\frac{1}{9}$$
Hence, the correct answer is Option C
Bag I contains 4 white and 3 black marbles while bag II contains 3 white and 5 black marbles. One marble is drawn at random frombag I and put in bag II without seeing it. The probability that a marble drawnfrom bagII is a black one is
Choose the correct meaning of the word given:
procrastination
grumble
devious
tepid
impromptu
acquiesce
Fill in the blank choosing the correct word:
The war left a .......... of destruction behind.
She drove around the neighborhoodin an/a .......... display of her newly acquired wealth.
Administration becomes easy if procedures are ................
Having noticed that crimes were on the rise, the government asked the courts to .................. their judgment
Choose the correct answer:
The person who purchases or sells shares on behalf of the client is a .........
PERT stands for
The standard layout on English language keyboard is
CRR stands for ...........
The programmeused to change assembly to machine languageis called a/an
Which of the following allowa user to add components and capabilities to a system?
Data integrity refers to ...........
To remove someone froma list of contacts on social networking website is called
A partner in a business who manages unlimited liability is called ..............
A company’s agreement with a foreign firm for manufacturing its products for royalties is called ...........
A: Ihear. youare tripped for promotion.
B: It is on the cards.
The conversation implies that
His hard work brought him the reputation of being a cut ............ the rest of his colleagues.
A: How big is your new house?
B: It is hardly bigger than the old one.
In this conversation, B says that .............
“The CEO is coming today. It is a red letter day for us”.
The underlined phrase means ..............
A: No one expected him to stand first; by topping the list he proved to be a dark horse.
The underlined phrase means ..............
Please ........... the word in a dictionary.
I ........... ice cream.
Fill in the blanks with the appropriate word /phrase/verb/preposition:
It will take some time for the wound to ............
Many of my friends .......... at the funeral.
Much water has .......... under the Godavari Bridge.
One should not .............. a man because he is not rich.
The robbers made ............ with substantial booty.
The chairman had to finally ............ to the demands of the employees.
They couldnot refrain ............ illegal activities.
India is also ......... Bharath.
Read the following paragraphand answerthe following questions.
Try walking into an office of any small time entrepreneur, businessman ortrader, chances are that you mayfind a slogan adorning the reception area — “Customer satisfaction is our motto”. Nothing profoundinthat, manyof us have sometimes seen such slogans prominently on advertisements and billboards for decades. The more business — savvy types have dispensed with it long ago, categorizing it as cliché and not in the tune with the times.
What is not so clichéd and ordinary is the fact that very few of our business practitioners have actually molded their profession around this philosophy — Knowinglyor unknowingly. Let me explain — have you as a customer been subjected to sales calls by DSA’s (Direct Sales Agents) of reputable banks proclaiming that you are the luck one who has been cleared for a loan of some preposterous amount? Yes indeed, most of us
have at some point orthe other. You decide to be polite and decline the offer in the most affable manner and hopethat is the end of your transactions with the bank’s sales agent. Think again — high probability that for the next several days you shall get multiple calls from the similar direct personnel of the so-called reputable bank, all offering the same product that you had declined just the other day, you may be lucky not to have them visit your homeoroffice, again offering the same product. When you confront them with the fact that someone had already approached you from their office earlier with a similar offering and that you have declined it for the umpteenth time. they feign ignorance and
unashamedly blame it on some internal operational gaffe which theyare not responsible for.
Sophisticated business organizations removed the slogan because ................
The example the writer gives of business not following what they preach is that ...........
The word that suggests that the offer made through the sales representative is absurd is ...........
The initial reaction of a customer who receives a call fromthe agent is ...........
The writer’s main focus here is to show how ...........
Read the following paragraph and answer the following questions.
When I first visited Bangalore in the sixties it was a garden city. With its parks, one a forest in the centre of the city, its lakes, its avenues covered with a green canopy of rain trees, its altitude of three thousand feet above sea-level and the temperate climate that goes with the height. it became a victim of its own natural assets. At the beginning of the twentieth century the Indian Institute of Science was founded there and just before independence came the Raman ResearchInstitute. They gave Bangalore a reputation for excellence in science which attracted nationalized hi-tech industries like Hindustan Aeronautics as well as the private sector. Then followed the IT wallahs. To add all those
pressures post-independence Bangalore also became the capital of one of India’s largest and progressive states. Bangaloreans who once boasted of their garden city nowdo not use that term for obvious reasons. Their homes for the future, fuelled by the city’s readiness to move on to the national, even international platform. have been belied, at least for the moment, by their innumerable travails like environmental pollution,
haphazard expansion and piece-meal planning.
‘one’ in the second sentence refers to ............
What caused the loss of the city’s tranquility?
For “obvious reasons” implies that the city
Which one of the following is not one of the current problems mentioned by the writer about the city he is describing?
Which one reason does the writer not give for the city to get a reputation for excellence in science?
Read the following paragraphand answerthe following questions.
Union Budget 2018 has been on expected lines. aimed at appeasing farmers and others in rural areas, as well as small industry. When it comes to most tare proposals, it has disappointed everybody except senior citizens and Micro. Small & Medium Enterprises (MSMEs). Inits last full budget before the next general elections. the BJP-led NDA governmenttargets its vote banks in rural areas and the agriculture sector, promising them a lot. In direct taxes, however, where it was expected bring in a lot of reforms and exemptions. it has done precious little.
If all classes of tax payers, the salaried employee has been left almost high and dry with the finance minister announcing there would be no change in the personal income-tax rates. There was a lot of expectation that the personal income tax exemption limit would be raised. That has not happened with GST becoming a reality, most citizens are being made to pay taxes on almost every purchase and in most cases, the taxes are
higher than before. That is why there were expectations that the finance ministers would put more money into the taxpayer’s hands by lowering personal taxes. None of these has happened.
According to the passage the Union Budget 2018 has not disappointed ...........
In the area of direct taxes the budget has done ............
The main reason for citizens ending up paying taxes on almost every purchase is the introduction of ................
Which statement is true about the budget ?
The expression ‘left high and dry’ means ..........
