Is $$a > b $$?
I. $$a^{16} < b^{16}$$
II. $$a^{21} < b^{21}$$
AP ICET 2019 Question Paper Shift-1 (26th April)
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:
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
What is the value of $$3a + 2b$$ ?
I. $$\frac{a}{b} = \frac{2}{3}$$
II. $$2a - 3b = 10$$
How many sons does A have ?
I. Bis D’s brother and sonof A.
II. D's father has three children.
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
What is the GCD of positive integers a and b?
I. a and b differ by 1.
I. a > b
What is the value of $$\mid x \mid$$?
I. $$x^4 - 4x^2 + 4 = 0$$
II. $$x$$ is even
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
Is $$x > y$$?
I. $$\mid x \mid < 3$$
II. $$\mid y \mid > 3$$
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.
What is the LCM of the positive integers m, n?
I. GCD of m, n is 9.
II. m + n = 108
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
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
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.
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.
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 $$29^{th}$$.
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.
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.
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
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.
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 : ........
15 : 224 :: 17 : ........
17 : 306 :: 19 : .........
7 : 77 :: 13 : .......
Foot : Inch :: Year : ........
6, 15, 35, 77, 143, ......
ABC, BDF, CFI, DHL, .........
D3B, H7F, L11J, P15N, .......
$$\frac{6}{5}, \frac{35}{12}, \frac{143}{24}, \frac{323}{36}, \frac{667}{52}, ............$$
MILK : 54 :: CURD : ........
In the Following questions pick the odd thing out.
The following question followg definite pattern. Observe the same and fill in the blanks with suitable answers.
BZE, DYH, HWN, ........
7, 10, 16, 28, ......... 100
4T, 16W, 52U, ..... 484V
E3V. I4R, G12T, K45P, ........
3, 4, 12, 39, 103, .........
6, 24, 60, 120, ........
75, 79, 72, 80, 69, 81, ........
1, 2, 6, 22, 86, ........
0, 6, 24, 60, .......... 210
$$\frac{1}{2}, \frac{4}{3}, \frac{13}{5}, ..........., 11$$
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?
what percentage of growth did the party A gain 1995 overthe previous election?
Howm any more seats did the party A get overthe party B inall elections put together?
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
The percentage of his monthly income spent on the head D corrected to two decimals, is
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
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
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
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?
How many watched exactly two programmes?
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’
The code for ‘APICET” is
“SYSTEM” is coded as
‘USVV" is decoded as
"BKREV" is decoded as
For the following questions answer them individually
If ‘BEAT’ is coded as ‘EHDW’, the code for ‘ROAD’ is
If ‘SAFE’ is coded as ‘“OWBA’. then whatis the code for ‘CROW’?
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
In a certain code ‘BEST’ and ‘PORT’ are coded as 51 and 84 respectively. then in the same code ‘WORD’ is coded as
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
The number of leap years in between the years 2018 and 2126 is
The angel between hour hand and the minute hand of a clock when the time is 5.40 is
If two hands of a clock coincide (are together) every 64 minutes. the time gained, in minutes, by that clock in a day is
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
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?
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
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
If $$\triangle$$ denotes multiplication, * denotes subtraction, $$\triangledown$$ denotes addition and $$\oplus$$ denotes
division then $$10 \triangledown 8 \oplus 2 * 5 \triangle 3 = ?$$
If $$x * y = \frac{1}{x} + \frac{1}{y}$$ for all $$x, y \epsilon R - \left\{0\right\}$$ then $$(4 * 5) * (3 * 2) =$$
For $$m, n \epsilon R$$, define $$m * n = m + n - 2$$ and $$m \oplus n = \frac{mn}{2}$$ then $$(3 * 5) \oplus (9 * 7) = ?$$
$$(3^{2x + 4} \times 9^{4x + 2}) \div (9^{x + 4} \times 3^{2x + 2}) = 9^5 \Rightarrow x = ?$$
If $$x = \sqrt{7} - \sqrt{6}$$ then $$x^4 + \frac{1}{x^4} =$$
$$5(x^2 + y^2 + z^2) = 4(xy + yz + zx)$$ then $$x : y : z$$
$$yz : zx : xy = 1 : 2 : 3 \Rightarrow \frac{x}{yz} : \frac{y}{zx} =$$
$$\sqrt{4 + \sqrt{4 + \sqrt{4 + \sqrt{4 + ........ \infty}}}} = $$
$$\sqrt{8 + 2\sqrt{15}} =$$
If 11 divides 29x03 then x =
Solution
Any number is divisible by 11 if,
The sum of odd placed number - sum of even placed number will be divisible by 11, then the number will be divisible by 11.
$$3+x+2-(0+9)=x-4$$
It will be divisible by 11, if $$x-4=0$$
Or $$x=4$$
How many integers are there from 200 to 400 which are multiples of 7?
Solution
The numbers which are divisible by 7, in between 200 to 400 are given below,
$$203,210, 217..........399$$
We know for the AP series,
$$\Rightarrow t_n=a+(n-1)d$$
$$\Rightarrow 399=203+7(n-1)$$
$$\Rightarrow 7(n-1)=399-203=196$$
$$\Rightarrow n-1=\dfrac{196}{7}$$
$$n=28+1=29$$
The smallest positive integer which when divided by 6, 9, 12 and 15 leaves 5 as remainder in each case is
Solution
As per the given question,
The given numbers $$6,9,12,15$$
It is giving remainder 5, if we are dividing a by these given number.
So, the required number is=LCM of the given number +5
Hence the required number =$$180+5=185$$
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?
Solution
As per the given question,
The first type of oil have 462 liters
2nd type of oil have 286 liters
3rd type of oil have 187 litrs of oil
Hence $$462=2\time 3\times 7 \times 11$$
$$286=2\times 11\times 13$$
$$187=11\times 17$$
Hence the required capacity= $$11 liter$$
The number of tin required $$=\dfrac{462}{11}+\dfrac{286}{11}+\dfrac{187}{11}$$
Hence, the number of tin of 11 liter capacity required $$=42+26+17=85$$
$$\left(1 - \frac{1}{7}\right)\left(1 - \frac{1}{8}\right)\left(1 - \frac{1}{9}\right)\left(1 - \frac{1}{10}\right) .................. \left(1 - \frac{1}{51}\right) =$$
$$0.2\overline{34} =$$
The increasing order of $$a = \sqrt{7} - \sqrt{6}, b = \sqrt{3} - \sqrt{2}, c = \sqrt{6} - \sqrt{5}, d = \sqrt{2} - 1$$ is
The smallest among $$\frac{9}{1}, \frac{8}{9}, \frac{5}{6}$$ and $$\frac{7}{8}$$ is
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
Solution
Let he have the total amount of x Rs.
Percentage of money gave to charity $$=\dfrac{12x}{100}=0.12x$$
The remaining amount $$=x-0.12x=0.88x$$
Now money gave to charity=80%
Hence the remaining amount $$\dfrac{0.88x\times 20}{100}=264$$
$$=0.176x=264$$
Hence $$x=\dfrac{264}{0.176}=1500$$
Hence, The amount of money he have in the begining $$=1500Rs.$$
When 40% of a number is added to 84. if the resultant is the number itself. then that number is
Solution
Let the number is x
Now, as per the condition given in the question,
$$\Rightarrow \dfrac{40x}{100}+84=x$$
$$\Rightarrow 0.4x+84=x$$
$$\Rightarrow x-0.4x=84$$
$$\Rightarrow 0.6x=84$$
$$\Rightarrow x=\dfrac{84}{0.6}=\dfrac{840}{6}=140$$
$$x=140$$
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?
Solution
As per the given question,
The cost price of one book $$=\dfrac{100}{11}$$
The sale price of one book $$=\dfrac{110}{10}$$
Hence the required percentage $$=\dfrac{(11-9.09)\times 100}{9.09}$$
$$=\dfrac{1.91\times 100}{9.09}=21% Profit$$
To successive profits of 8% and 10% are equal to a single profit of
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
Solution
The partnership ratio of P and Q $$=9:7$$
As per the question, at the end of the 8 months, Q withdraw his amount,
The ratio in the profit is given as 9:4
So, we know that profit sharing ratio $$=\dfrac{C_P\times T_P}{C_Q\times T_Q}$$
$$\Rightarrow \dfrac{9}{4}=\dfrac{9\times T_P}{7\times 8}$$
$$\Rightarrow \dfrac{9}{4}=\dfrac{9\times T_P}{56}$$
$$T_P=\dfrac{56}{4}=14$$
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
Solution
as in the given question,
total profit$$=55000$$
shared profit of P,Q,R will be$$=x+4x+5x$$
then,sum of profit will be$$\Rightarrow x+4x+5x=55000$$
$$x=5500$$
then,the profit of $$P=1\times 5500$$
profit of Q $$=4\times 5500=22000$$
difference of profit between Q and P=Profit of Q-Profit of P
$$\Rightarrow 22000-5500=16500$$
So the difference of profit between Q and P is 16500
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
Solution
Part filled without leak in 1 hour $$= \dfrac{1}{9}$$
Part filled with leak in 1 hour $$=\dfrac{1}{10}$$
Work done by leak in 1 hour$$=\dfrac {1}{9}-\dfrac{1}{10}=\dfrac{1}{90}$$
We used subtraction as it is getting empty.
So total time to empty the cistern is 90 hours
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?
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
Solution
Car A starts at 8AM with the speed of $$65kmph$$
Car B starts at 9AM with the speed of $$70kmph$$
Both starts from the point P,
Let after the time t, both the car will meet.
$$d=65\times t---------(i)$$
$$d=70\times (t-1)-------(ii)$$
From the equation (i) and (ii)
$$65\times t=70\times t-70$$
$$5\times t=70$$
Hence t=14 hour.
Hence both the car will meet 10PM
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
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?
Solution
Let P will complete the work in 15 days
P can do the work in one day $$=\dfrac{1}{15}$$
Q can finish the work in 20 days.
Q can do the work in one day $$\dfrac{1}{20}$$
Let R can do the work in x days.
R can do the work in one day $$\dfrac{1}{x}$$
If P, Q and R working together, then they can finish the work in 5 days.
Hence, working together, then can do the work in one day $$\dfrac{1}{15}+\dfrac{1}{20}+\dfrac{1}{x}=\dfrac{1}{5}$$
$$\Rightarrow \dfrac{1}{x}=\dfrac{1}{5}-\dfrac{1}{15}-\dfrac{1}{20}$$
$$\Rightarrow \dfrac{1}{x}=\dfrac{1}{5}-\dfrac{7}{60}$$
$$\Rightarrow \dfrac{1}{x}=\dfrac{5}{60}=\dfrac{1}{12}$$
Hence x=12 days. So , R can finish the work in 12 days.
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?
Solution
5 men in 6 days in 6 hours per day$$=5\times 6\times 6=180$$hours
Therefore, 180 hours will be taken to produce 10 toys
Therefore 1 toy$$=\dfrac {180}{10}=18$$hours
16 toys can be prepare in$$=16\times 18=288$$hours
When,12 men prepare 16 toys$$=\dfrac {288}{12}=24$$hours per day
Then by working 8 hours per day it will be$$=\dfrac {24}{8}=3$$days
Therefore in 3 days 12 men can prepare 16 toys for working 8 hours a day.
If the area of an equilateral triangle is $$4\sqrt3$$ sq.cm.. then its perimeter, in centimetres, is
Solution
Let a is the length of the side of the equilateral triangle.
We know that the area of the equilateral triangle $$=\dfrac{\sqrt{3}a^2}{4}$$
So, $$\dfrac{\sqrt{3}a^2}{4}=4\sqrt3$$
$$a^2=4\times 4 $$
$$a=4$$
Hence, perimeter of the triangle $$=3a=12$$cm
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?
Solution
As per given in the question,
Let,the length be $$7x$$ and breadth be $$5x$$
We know that the area of the rectangle $$=length\times breadth$$
So, $$3500=7x\times 5x$$
$$\Rightarrow 3500=35\times x^2$$
$$x=10$$cm
We know that the perimeter of the rectangle $$ =2(length+breadth)$$
hence, perimeter $$=2(7x+5x)$$
$$\Rightarrow 2\times 12x$$
$$\Rightarrow 24\times 10=240$$
therefore,the perimeter of the rectangle is 240 cm
If the surface area of a cube is 726 sq.cm., then its volume. in cubic centimeters, is
Solution
given,
surface area of cube$$=6\times a^2$$
according to the given condition,
$$6\times a^2$$=726
$$a^2$$=$$\frac{726}{6}$$
a=11
hence,volume of cube will be=$$a^3$$
=$$11^3$$
=1331 cubic cm
Therefore the volume of the cube is 1331 cubic cm
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
Solution
given,
radius of sphere=10 cm
volume of each spherical ball=$$\frac{volume of sphere}{8}$$
$$\frac{4\times \pi\times r^3}{3}$$=$$\frac{1}{8}$$ $$\frac{4\times \pi\times 10^3}{3}$$
$$r^3$$=$$\frac{1000}{8}$$
$$r^3$$=$$\frac{10^3}{2^3}$$
r=$$\frac{10}{2}$$
r=5
surface area of each ball=$$4\times \pi\times r^2$$
=$$4\times \pi\times 5^2$$
=$$4\times 25\times \pi$$
=$$100\pi$$
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
Solution
Let, Length be l, breadth be b
As per the condition given in the question,
$$b = l \times \dfrac{3}{4}$$
$$\Rightarrow 4b = 3l or 3l-4b = 0 ---------(i) $$
$$\Rightarrow 2(l+b) = 1050$$
$$\Rightarrow l+b = 525$$
$$\Rightarrow l = 525 - b ------- (ii) $$
Put the value of "l' from equation (ii) in the equation (i)
$$ \Rightarrow 3(525 - b) - 4b = 0$$
$$ \Rightarrow 1575-3b-4b = 0$$
$$ \Rightarrow 1575 = 76$$
$$ \Rightarrow b = 225m ------(iii)$$
Put the value of b from equation (iii) in the equation (ii)
$$ l = (525-b)$$
$$ l = (525-225)$$
$$ l = 300m$$ ------------(iv)
Area of plot in square metres will be = l \times b
Put the value of l and b from equation (iii) and (iv)
$$A = 300 \times 225$$
$$A = 67,500$$
Therefore, area of the plot is square metre is 67500 metres
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
Solution
Let, the hight of triangular field be = h
Then base = 3x
Now cost per hectare 73.44 is Rs 991.44
So, area of field = $$ \dfrac{991.44}{73.44}$$
$$ \Rightarrow 13.5$$
we know that area of triangle = $$ \dfrac{1}{2} \times b \times h$$
Then,
$$ \Rightarrow \dfrac{1}{2} \times 3h \times h = 13.5$$
$$ \Rightarrow 3h^2 = 27$$
$$ \Rightarrow h^2 = \dfrac{27}{3}$$
$$ \Rightarrow h^2 = 9$$
$$ \Rightarrow h = 3$$
In meters it will be
$$ \Rightarrow (h \times 100)m$$
$$ \Rightarrow (3 \times 100)m $$
$$ \Rightarrow 300m$$
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
Solution
As per given question,
volume of cuboid=72 cu. mts
Let the length of the cuboid be$$=x$$
breadth$$=\dfrac{2}{3}\times x$$
then height$$=\dfrac{3}{4}\times \dfrac{2}{3}\times x$$
as we know volume of cuboid$$= length \times breadth \times height$$
$$\Rightarrow x\times \dfrac{2}{3}\times x \dfrac{1}{2} \times x$$
$$\dfrac{1}{3}\times x^3=72$$
$$x^3=216$$
x=6
then length=6
breadth$$=\dfrac{2}{3}\times 6=4$$
height$$=\dfrac{3}{4}\times \dfrac{2}{3} \times 6=3 $$
as we know suface area of cuboid$$=2(lb+bh+hl)$$
surface area$$=2(6\times 4+4\times 3+3\times 6) $$
surface area= 108 sq.mts
$$1212_{(7)} = x_{(10)} \Rightarrow x =$$
$$101_{(2)} + 110_{(2)} =$$
$$P \rightarrow (Q \rightarrow P) \Rightarrow $$
The negation of the statement $$p \vee (\sim p \wedge q)$$ is
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
If n(A) = 5, then the number of relations on A which are not symmetric is
Let $$f$$ be defined on $$[0, 7]$$ and $$g(x) = \mid 2x + 1 \mid$$. Then the domain of $$(fog)(x)$$ is
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
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
Solution
As per the given in the question,
Ratio of intercept $$=\dfrac{1}{3}$$
So, $$x=k$$ and $$y=3k$$
So, the co-ordinates of intersection point on the x and y axis (k,0) and (0,3k)
So, equation of line
$$\Rightarrow (y-0)=\dfrac{3k-0}{0-k}(x-k)$$
$$\Rightarrow y=-3(x-k)$$
Now, this line is passing through the point (-2, 3)
Hence, $$3=-3(-2-k)$$
$$\Rightarrow 3=6+3k$$
$$\Rightarrow k=-1$$
Hence the line equation will be
$$\Rightarrow y=-3x-3$$
$$\Rightarrow 3x+y+3=0$$
$$\tan 480^\circ + \sec 510^\circ + \cosec 750^\circ + \cot 765^\circ =$$
$$\frac{\sin 150^\circ - 5 \cos 300^\circ + 7 \tan 225^\circ}{\tan 135^\circ + 3 \sin 210^\circ} =$$
If $$\sec \theta + \tan \theta = \frac{2}{3}$$, then $$\sin \theta =$$
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
The smallest value of x for which $$\left(\frac{12}{x} + 36\right)(4 - x^2) = 0$$ is
If $$\alpha$$ and $$\beta$$ are the roots of the equation $$8x^2 - 3x - 27 = 0$$, then the value of $$\left(\frac{\alpha^2}{\beta}\right)^{\frac{1}{3}} + \left(\frac{\beta^2}{\alpha}\right)^{\frac{1}{3}} =$$
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
Solution
The given number in the question is $$=2035$$
Now, after subtracting x from the given number, new number will be $$2035-x$$
When we are dividing the $$2035-x$$ by $$9,10,15$$ it is leaving the remainder 5.
Now, the LCM of the number $$90$$
Now, when we are dividing the 2035 by 90, then it is leaving the remainder 55.
But as per the condition, the remainder should be 5. hence the required number $$=55-5=50$$
If the remainder obtained whena certain integer x is divided by 5 is 2, then which one of the following is never an integer?
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
Solution
Let the present age of Rahim $$=x$$ years
So, the present age of David$$=x-6$$
and the present age of Amar$$=x-6-8=x-14$$years
After the 8 years, age of Rahim will be $$x+8$$
After the 8 years, age of Amar will be $$x-14+8=x-6$$
As per the condition given in the question, $$x+8=2(x-6)$$
Hence, $$2x-x=12+8$$
$$x=20$$years
Hence, the present age of David $$=20-6=14$$years
4 years ago, the age of David $$=14-4=10$$years.
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
Solution
10 consecutive integers are:-
$$ x,(x+1),(x+2), (x+3), (x+4),--------(x+9)$$
sum of the 5 least number of the set is 265
$$\Rightarrow x+(x+1)+(x+2)+(x+3)+(x+4) = 265$$
$$\Rightarrow 5x+10 = 265$$
$$\Rightarrow 5x = 255$$
$$\Rightarrow x = \dfrac{255}{5}$$
$$\Rightarrow x = 51$$
Therefore, the sum of 4 greatest number of the set will be
$$\Rightarrow (x+6)+(x+7)+(x+8)+(x+9)$$
$$\Rightarrow 4x+30$$
$$\Rightarrow 4\times 51+30$$
$$\Rightarrow 204+30$$
Hence the sun of the greatest number will be 234
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
Solution
Let the terms of the GP are $$\dfrac{a}{r},a, ar$$
Where a is the first term and r is the common ratio.
As per the condition, $$\dfrac{a}{r}+a+ar=26------------(i)$$
$$\dfrac{a}{r}(1+r+r^2)=26$$
Now, squaring both side,
$$\dfrac{a^2}{r^2}(1+r+r^2)^2=676$$
As per the the second condition,
$$(\dfrac{a}{r})^2+a^2+(ar)^2=364$$
$$\dfrac{a^2}{r^2}(1-r+r^2)(1+a^2+a^2r^2)=364-------------(ii)$$
From equestion (i) and (ii)
$$\Rightarrow \dfrac{1-r+r^2}{1+r+r^2}=\dfrac{364}{676}$$
$$\Rightarrow \dfrac{1-r+r^2}{1+r+r^2}=\dfrac{7}{13}$$
$$\Rightarrow 13 - 13r + 13r^2 = 7 + 7r + 7r^2$$
$$\Rightarrow (3r-1)(r-3) =0$$
So,$$r=3$$ and $$r=\dfrac{1}{3}$$
Now, substituting the value of r=3,
So, $$a(1+r+r^2)=26$$
$$a(1+3+9)=26$$
$$a(13)=26$$
$$a=\dfrac{26}{13}=2$$
Hence, the product of these numbers $$=a\times \dfrac{a}{r}\times ar =a^3=6^3=216$$
The sum of all the natural numbers between 100 and 1000 which are multiples of 5 is
Solution
The natural number between 100 and 1000 are $$105, 110, 115......995$$
It is making an arithmetic series.
Sum of the terms of arithmetic series $$S_n=\dfrac{n(2a+(n-1)d)}{2}$$
$$t_n=a+(n-1)d$$
$$995=105+(n-1)5$$
$$n-1=\dfrac{995-105}{5}=178$$
$$n=178+1=179$$
Hence, the required sum $$S_n=\dfrac{179(2\times 105+(179-1)\times 5)}{2}$$
$$S_n=\dfrac{179\times(210+178\times 5)}{2}=550\times 179=98450$$
Hence, the required sum $$S_n=98450$$
The middle term in the expansion of $$\left(x^2 - \frac{1}{2x}\right)^{10}$$ is
The numerically greatest term in the expansion of $$(2 + 3x)^5$$ when $$x = \frac{5}{4}$$ is
If $$A = \begin{bmatrix}3 & -4 \\1 & -1 \end{bmatrix}$$ then $$A^4 - A^3 + A^2 - A =$$
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
$$\lim_{x \rightarrow 0}\frac{e^x - 1}{\sqrt{1 + x} - 1} =$$
$$\lim_{x \rightarrow 3}\frac{x^4 - 81}{2x^2 - 5x - 3} =$$
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 $$\angle BCD =$$
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
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 $$\angle BOC = $$
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
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
The arithmetic mean of 28, 32, 34, 24, 42, 46, 38, 36 is
Solution
The given data is $$28, 32, 34, 24, 42, 46, 38, 36$$
Number of records=8
The arithmetic mean of the given data $$\dfrac{28+32+34+24+42+46+38+36}{8}=35$$
The median of 18, 16, 18, 12, 10, 14, 16 is
Solution
As per the question,
18, 16, 18, 12, 10, 14, 16
Now arranging the data in the increasing order$$=10, 12, 14, 16, 16,18, 18$$
Total number of observations =7
Hence, the $$median =\dfrac{n}{2}+1$$
$$\Rightarrow median=4^{th} terms =16$$
The mode of the following frequency distribution is
The standard deviation of 6, 7, 8, 9, 10 is
The standard deviation of any three consecutive integers is
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
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?
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
The probability that a non-leap year has 53 Mondays is
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
Choose the correct meaning of the word given:
Angst
Exotic
Aberration
Gratuitous
Deferential
Subservience
Fill in the blank choosing the correct word:
Money lenders are often accused of ............., as they are habituated to recovering by force or threats
Once committed to their goals, people work with a missionary ............
When the going gets tough. the tough get ..........
The seven year old boyis the legal .......... of the huge property.
Choose the correct answer:
A technique in computer graphics that makes an image to look smooth froma distance is called
Balance sheet means ............
Company AGMs are meetings of
Whatis the name of the device that connects two computers by means of a telephone line?
Maslow’s hierarchy conceptis a theory of
A terminal that can function only whenit is lined to a computeris called a
The term ‘golden handshake’ refers to the payment made to
Withdrawal of money in excess of the credit balance on a bank accountis called
The term ‘cybersquatting’ refers to
Obtaining information or opinions from a large group of people via the internetis called
The officer told his visitors that there was no room for discussion on the subject they broached. Here ‘no room’ means
Identify the correct statement:
Low paying jobs are a dime a dozen.
The underlined phrase means
A : Did your husband consult youbefore taking up the newventure?
B : No. He is on his own.
B meansthat her husband
Don’t worry. Everything will happen as a matter of course.
The underlined phrase means
Fill in the blank with the appropriate phrase/verb/preposition:
He does not hanker .......... sensual pleasures.
Hetried his best to ........... his point.
She has been looking forward ............... her parents
By mistake, I took him ............. a thief.
‘Procrastination’ means ‘to .............’
He had no hopeleft. as all his plans were .............
The expression. “to go at it hammer and tongs” means, ...............
The answer given by the film star to the question by the press reporters is wide off the mark. The underlined phrase means
The patriot ............... his life for his country.
Never ............. such an amusing show.
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
Students in a classroom
The silence of the students is a mark of
Students must
Which word means ‘feasible’?
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?
For achieving success. which of the following is NOT mentioned as necessary in the passage?
Into what categories have competencies been divided?
Personal competency results in ................
According to the passage. infuture. the identified competencies are going to be .............
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
The speaker of the passage is a ...........
After writing a book, the writer .............. every character in the novel
According to the passage, the writer
Identify the correct statement based onthe last line of the passage
