p and q are positive integers. What is the number of positive divisors of p?
I. $$p = q^{10}$$
II. q is a Prime number
TS ICET 2019 Question Paper Shift-2 (23rd May)
In questions numbered 1 to 20. a questionis followed by data in the form of two statements labeled as Iand II. You must decide whetherthe data given in the statements are sufficient to answer the questions. Using the data make an appropriate choice from (1) to (4) as per the following guidelines:
Ifp and g are positive integers whose productis 72. then what is the value of p+ q?
I. p>q
I. $$\mid p-q\mid$$=1
If n and m are integers, is n > m?
I.3n+2m=11
II.n-m=1
Is there positive integer n divisible by 35?
I.15 divides n.
II.28 divides n.
What is the value of $$\sin \theta + \cos \theta$$?
I.$$\sin 2 \theta = \frac{1}{2}$$
II.$$\cosec \theta + \sec \theta = 5$$
In the triangle POR, whatis the length of the side OR?
I.PQ=8 cm ,PR=5 cm
II.Area of a triangle PQR=10 Sq.cm.
How muchis the loss percent?
I.The loss is 20% of the selling price.
II.The cost price is Rs.250
If n is an integer and 10I.The sum of the digits in 7 is 12.
II.One digit in 7 is 3 times the other.
For two sets A and B, what is $$n(A \cap B)$$?
I. $$n(A) = 10$$ and $$n(B - A) = 9$$
II. $$n(A - B) = 7, n(B - A) = 9$$ and $$n(A \cup B) = 19$$
What percent of 16 is x?
I.200 percent of x 1s less than 1.
II.x is 5 percent of 10.
What is the value of $$x^{2} - y^{2}$$?
I. $$(x - 2018)^{2} + (y + 2019)^{2} = 0$$
II. $$(x + 2018)^{2} + (y - 2019)^{2} = 0$$
What is the value of x?
I. $$3^{48} \equiv x (mod 10)$$
II. $$0 \leq x \leq 9$$
Will B take more than 9 hours to complete the job alone?
I.A works faster than B.
II.A and B can togetherfinish the job in 6 hours.
What is the area of the rhombus?
I.Each of its sides is 120 cm.
II.Each of its opposite angles are $$60^\circ$$.
In the figure given below, what is the value of $$\alpha+\beta+\gamma+\delta$$ ?
_5nUboov.png)
I. $$\alpha + \beta + \gamma + \delta$$
II. $$\theta + \phi = 90^\circ$$
What is the day of the week was 31st December of that year?
I.In that year the first of March was Monday.
II.That year was a leap year.
A, B, C, D and E are sitting around a circulartable facing the centre. Who is sitting to the immediate left of C ?
I.Only A is between E and B.
II.D is to the immediate left of B.
Whatis the area of the sector 4 of the circle?
I. The sector 4 makes an angle $$60^\circ$$ at the centre.
II. Length of the arc of the sector A is $$\frac{110}{21}$$cm.
What is the area ofthe right angled triangle?
I.Its longest side is 6 cms.
II.One of its angle is $$45^\circ$$.
Whatis the value of $$8a^{3}+b^{3}-27c^{3}$$
I. abc = 10
II.2a + b = 3c
In each of the 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.
100 : 111 :: 144 : .........
182: ....... :: 210: 380
........ :122::168:290
12:132::14: .......
12 : 1872 :: ...... : 2366
corden : zrogbq: : ....... :pxivro
COUNSEL: BITIRAK: : GUIDANCE : ........
$$D \times I : 19 \times 9 :: K \times F : .........$$
3:13::17: ........
1331 : 11 :: ....... : 22
In the following questions pick the odd thing out:
Each of the questions from36 to 45 followa definite pattern. Observe the same and fill in the blanks with suitable answers.
6, 10, 18. 30, 46, 66, ........
$$11\frac{1}{9},12\frac{1}{2},....... 16\frac{2}{3},20$$
E,G, K, ......... ,Q,s,.........
768921350, 68921350, 6892135, 892135, .........
11, 30, 128,346, ........
11,22,35,50,67, .......
18,20,17,21,16,22,15,.......
$$\left\{\frac{1}{5},\frac{1}{6},\frac{1}{7}\right\},\left\{\frac{1}{8},\frac{1}{11},\frac{1}{14}\right\},\left\{\frac{1}{17},\frac{1}{22},\frac{1}{27}\right\}, .......$$
$$(a+b), (a^{2} - b^{2}), (a + b)^{2} (a-b), (a^{2} - b^{2})^{2}, (a+b)^{3} (a-b)^{2}, ............$$.
CGK,OSW,AEI .......
Study the following table carefully and answer the questions.
The numbers given in the table represent the number of students from various schools playing different games.
If 20% of the students playing football from school ‘A’ also play Badminton, then the total number of students playing Badminton from School ‘A’ is.
The number of students playing Basketball from School ‘C’ is approximately what percent of the numberof students playing basketball from School ‘E’?
The difference between the average numberof students playing all the games from school ‘B’ and the numberof students playing badminton from that schoolis:
The Pie chart given below shows the percentage-wise break up of students studying various specializations A.B.C.D.E and F in M.B.A. course in a university. The total numberof students howtook admission in MBA in that university is 8000. Study the chart carefully and answer the questions given below.
The total number of students studying the specializations in C, D and F is
Students studying B as specialization forms approximately what percent of students studying A as specialization?
The total numberof students studying E as specialization.
The ratio of the students studying C as specialization to students studying F as specialization is.
If x : y represent the ratio of the numberofstudents studying F and C to the numberof students studying D, then x - y =
Study the following data and answer the questions.
"In a study of 1500 rivers the following data were reported: 520 rivers were polluted by sulphur compounds, 335 were polluted by phosphates, 425 were polluted by crude oil, 100 were polluted by both crude oil and sulphur compounds; 180 were polluted by both sulphur compounds and phosphates; 150 were polluted by both phosphates and crude oil and 28 were polluted by sulphur compounds, phosphates and crude oil."
The number of the rivers polluted by at least one of the three impurities is
The number of the rivers polluted by exactly one of the three impurities is
In a certain code, the $$r^{th}$$ letter of the English alphabet is coded as $$r + 10(\equiv mod 26)^{th}$$ letter cyclically. For example, $$4^{th}$$ letter D is coded as $$14^{th}$$ letter N and $$24^{th}$$ letter X is coded as $$8^{th}$$ letter H (because $$r + 10(\equiv mod 26)$$). The reverse process is used for decoding. Basing on this coding and decoding, answer questions.
‘ARMY’is coded as
‘SEVEN’ is coded as
Which word is coded as ‘MYVN’*?
The code for ‘TSICET’ is
Which word is coded as ‘GKB’?
In a certain code language, '481' means "sky is blue", '246' means "sea is deep" and '698' means "sea looks blue". Using this information answer the quesions.
What is the code for “deep”’?.
The code for ‘sea sky looks’ is
The code for ‘Sky blue is deep’ is:
692 is the code for
What is the code for “blue sea” ?
For the following questions answer them individually
What day of the week was $$26^{th}$$ January 1983?
If a clock takes 22 seconds to strike 12. how many secondswill it take to strike 9?
At what time between 2 O clock and 3 O clock will the two hands in a clock be at right angle to each other?
Introducing a man. a woman said “he is the only son of my mother’s mother”, Howis the woman related to the man?
Reaching the place of meeting 15 minutes before 8.30 a.m. Ram found himself half an hourearlier than the man who was 40 minutes late to the meeting. Then the scheduled time of the meeting is.
If $$t_1$$ is the time elapsed between 9:25 a.m to 2:50 p.m, and if $$t_2$$ is the time elapsed between 10:10 a.m to 5:15 p.m then $$t_1 : t_2 =$$
Six persons P. O, R. S, T and Uare sitting around a roundtable facing the centre of the table. Tis between P and S, R is to the immediate left of U and to the immediate mght of O and O is to the immediate mght of S. Who is sitting between R and S?
If $$\alpha$$ denotes multiplication, $$\beta$$ denotes division, $$\gamma$$ denotes addition and $$\delta$$ denotes subtraction, then,
$$6 \delta \left[\left\{(6 \gamma 4)\beta 8\right\}\alpha 2\right] =$$
For any real numbers a and b. if a*b=a+b—ab then
(1*2)*(3*4)=
If Z denote the set of integers then the number of elements in the set $$A = \left\{(a,b) : 2a^{2} + 3b^{2} = 25 ;a, b \epsilon Z \right\}$$ is
$$x^{y}=y^{x}\Rightarrow \left(\frac{x}{y}\right)^{\frac{y}{x}} =$$
Solution
given that
$$x^{y}=y^{x}$$
so we can write that $$y = x^\frac{y}{x}$$
and substituting the value to
$$x^\frac{y}{x}$$
we get $$\frac{x}{x^\frac{y}{x}^\frac{x}{y} $$
= {x^$$\frac{x}{y}$$ $$frac {x^1}$$
x^$$\frac{x}{y}-1$$ answer
$$x^{x\sqrt{x} = \left(x\sqrt{x}\right)^x} \Rightarrow x = .............$$
Solution
$$x^{x\sqrt{x} = \left(x\sqrt{x}\right)^x} \Rightarrow$$
$$\frac{1}{a} : \frac{1}{b} : \frac{1}{c} = 3 : 5 : 7 \Rightarrow a : b : c =$$
Solution
$$\frac{1}{a} : \frac{1}{b} : \frac{1}{c} = 3 : 5 : 7 \Rightarrow a : b : c =?$$
now we have from above eq $$a:\frac{1}{3},b:\frac{1}{5},c:\frac{1}{7}$$
let take LCM of 3,5 and 7 we get lcm=105
now we have $$a:b:c:=\frac{1}{3}times105:\frac{1}{5}times105:\frac{1}{7}times105$$
after solving we get
$$a:b:c:=35:21:15$$ answer
If for the natural numbers $$a, b, c, a^{3} + b^{3} + c^{3} = 8072$$ and $$a : b = b : c = 3 : 2$$, then $$a =$$
Solution
$$a,b,c,a^{3}+b^{3}+c^{3}=8072$$ and $$a:b=b:c=3:2$$ then $$a= ? $$
let $$\frac{a}{b}=\frac{3}{2}times\frac{3x}{3}$$ and $$\frac{b}{c}=\frac{3}{2}times\frac{2x}{2}$$
then we get
$$a=9x,b=6x,c=4x$$
now put the value of a,b,and c in equation $$a,b,c,a^{3}+b^{3}+c^{3}=8072$$
now we have eq $${9x}^3+{6x}^3+{4x}^3=8072$$
then we get $${729x^3+216x^3+64x^3}=8072$$
then $$1009x^3=8072$$
$$x=2$$
put the value of x and we get
$$a=18,b=12,c=8$$ answer
$$\frac{1}{\sqrt{5} - 1} - \frac{1}{2 - \sqrt{3}} + \frac{1}{\sqrt{3} - \sqrt{2}} - \frac{1}{\sqrt{2} - 1} + 1 =$$
$$\sqrt{18 + x \sqrt{2}} = \sqrt{12} + \sqrt{6} \Rightarrow x =$$
Solution
$$\sqrt{18 + x \sqrt{2}} = \sqrt{12} + \sqrt{6} \Rightarrow x =$$
Take square both side
$$({\sqrt{18 + x \sqrt{2}}})^2 = ({\sqrt{12} + \sqrt{6}})^2 \Rightarrow x =$$
$${18 + x \sqrt{2}} = 12 + 6 + 2 * \sqrt{12} * \sqrt{6} \Rightarrow x =$$
$${18 + x \sqrt{2}} = 18 + 2 * \sqrt{6} * \sqrt{2} * \sqrt{6} \Rightarrow x =$$
18 will be eliminated from both the sides.
$${x \sqrt{2}} = 2 * \sqrt{6} * \sqrt{2} * \sqrt{6}$$
x =2 * 6
x = 12
Hence, option C is correct.
When a positive integer is divided by 783 the remainder was 48. What will be the remainder when the same numbersis divided by 29 ?
Solution
Let the number be N.
As the number leaves 48 as remainder when divided by 783, then
N = 783 x k + 48 (Here, k is an integer)
N = 29 x 27 x k + 29 + 19
N = 29 (27k + 1) + 19
Let 27k + 1 = m
then N = 29m + 19
So, remainder = 19
Hence, option C is correct.
The numbers of divisors of 1248 other than 1 and the numberitselfis:
Solution
Factors of 1248 = 2 x 2 x 2 x 2 x 2 x 3 x 13
It can be written as
1248 = $$2^{5}$$ x $$3^{1}$$ x $$13^{1}$$
Factors are written in the form: $$2^{p}$$ x $$3^{q}$$ x $$13^{r}$$
Total number of divisors = (p+1) x (q+1) x (r+1)
= (5+1) x (1+1) x (1+1)
= 6 x 2 x 2 = 24
1 and the number itself are excluded, then
24 - 2 = 22
So, the number of divisors will be 22.
Hence, option C is correct.
What is the least number which whensubtracted from 3000 is exactly divisible by 7. 11, 13 ?
Solution
Take L.C.M. of 7, 11, 13
L.C.M. (7, 11, 13) = 1001
3000 = 1001 x m + k (where k is remainder)
Put value of m = 2
3000 = 1001 x 2 + k
3000 = 2002 + k
k = 998
So, the least number which when subtracted from 3000 is exactly divisible by 7, 11, 13.
Hence, option D is correct.
What is the largest number which will divide 1354. 1866 and 2762 leaving 10 as remainderin each case?
Solution
Since 10 is remainder in each case, subtract 10 from every number.
1354 - 10 = 1344
1866 - 10 = 1856
2762 - 10 = 2752
HCF (1344, 1856, 2752) = 64
So, 64 will be the greatest number.
Hence option C is correct.
If the recurring decimal number $$3.7\overline{84}$$ is equal to the rational number $$\frac{p}{q}$$ and $$GCD(p, q) = 1$$,then $$p + q =$$
Solution
Let x = $$3.7\overline{84}$$
We can write it as
x = 3.7848484...
Multiply the equation with 10 on both the sides
10x = 37.8484... equation 1
Multiply equ 1 with 100 on both the sides
1000x = 3784.8484... equation 2
Subtract equation 1 from equation 2
1000x - 10x = 3784.8484... - 37.8484...
990x = 3747
x = $$\frac{3747}{990}$$
where $$\frac{3747}{990}$$ is in $$\frac{p}{q}$$ form
For $$GCD(p, q) = 1$$
$$\frac{3747}{990}$$ = $$\frac{1249}{330}$$
p + q = 1249 + 330
= 1579
Hence, option B is correct answer.
3+$$\frac{1}{4+\frac{1}{5+\frac{1}{6}}}$$
Solution
3+$$\frac{1}{4+\frac{1}{5+\frac{1}{6}}}$$
3+$$\frac{1}{4+\frac{1}{\frac{31}{6}}}$$
3+$$\frac{1}{4+\frac{6}{31}}$$
3+$$\frac{1}{\frac{124+6}{31}}$$
3+$$\frac{31}{130}$$
$$\frac{421}{130}$$
Hence, option A is correct.
The largest among the following numberts:
Solution
$$\sqrt{2}$$, $$\sqrt[3]{3}$$, $$\sqrt[5]{5}$$, $$\sqrt[7]{7}$$
$${2^\frac{1}{2}}$$, $${3^\frac{1}{3}}$$, $${5^\frac{1}{5}}$$, $${7^\frac{1}{7}}$$
Now, take L.C.M. of denominators of power
L.C.M. of (2, 3, 5, 7) = 210
$${2^\frac{1*105}{2*105}}$$, $${3^\frac{1*70}{3*70}}$$, $${5^\frac{1*42}{5*42}}$$, $${7^\frac{1*30}{7*30}}$$
$${2^\frac{105}{210}}$$, $${3^\frac{70}{210}}$$, $${5^\frac{42}{210}}$$, $${7^\frac{30}{210}}$$
$$\sqrt[210]{{2}^{105}}$$, $$\sqrt[210]{{3}^{70}}$$, $$\sqrt[210]{{5}^{42}}$$, $$\sqrt[210]{{7}^{30}}$$
The largest power is of 2. So, $$\sqrt{2}$$ will be the largest number.
Hence, option A is correct.
Which of the following statements is true ?
Solution
As, the denominators are 4, 6, 8, 9 in each option
take L.C.M. of 4, 6, 8, 9 = 72
Now, make all the denominators equal to 72.
Since 1 is common in each question, we can ignore it,
Option A: $$1\frac{1*18}{4*18}>1\frac{5*12}{6*12}>1\frac{7*9}{8*9}>1\frac{8*8}{9*8}$$
$$1\frac{18}{72}>1\frac{60}{72}>1\frac{63}{72}>1\frac{64}{72}$$
(condition does not satisfy)
Option B: $$1\frac{1*18}{4*18}>1\frac{7*9}{8*9}>1\frac{8*8}{9*8}>1\frac{5*12}{6*12}$$
$$1\frac{18}{72}>1\frac{63}{72}>1\frac{64}{72}>1\frac{60}{72}$$
(condition does not satisfy)
Option C: $$1\frac{8*8}{9*8}>1\frac{7*9}{8*9}>1\frac{5*12}{6*12}>1\frac{1*18}{4*18}$$
$$1\frac{64}{72}>1\frac{63}{72}>1\frac{60}{72}>1\frac{18}{72}$$
(condition satisfies)
Option D: $$1\frac{8*8}{9*8}>1\frac{5*12}{6*12}>1\frac{1*18}{4*18}>1\frac{7*9}{8*9}$$
$$1\frac{64}{72}>1\frac{60}{72}>1\frac{4}{72}>1\frac{63}{72}$$
(condition does not satisfy)
Hence, option C is correct.
40 liters of milk contains 10% of water. How many liters of water are to be added to increase the water content to 20%?
Solution
Given: Amount of mixture = 40L
Water content in the mixture = 10% of 40 = 40 x $$\frac{10}{100}$$ = 4L
So, milk content in the mixture will be = 40 - 4 = 36L
Let the amount of water need to be added to make the water content to 20% be xL.
Then, $$\frac{4+x}{40+x}$$ x 100 = 20
x = 5L
Hence, option C is correct.
The salary of an employee was increased by 20% and then reduced by 10%. What was the net change in the employee’s salary?
Solution
Solution
Let original salary be Rs.100
After increment of 20% on original salary (Rs.100)
Salary = (100+20)/100 x Rs.100 = 1.2 x Rs. 100 = Rs. 120.
After decrement of 10% on increased salary (Rs.120)
Salary = (100-10)/100 x Rs.120 = 0.9 x Rs. 120 = Rs. 108.
So the final salary stands at Rs. 108
Net change w.r.t. original salary = Rs. (108-100) = Rs. 7
% change = (Rs.8/100) x Rs.100 = 8% Answer
If an article is sold at a loss of 9%instead of loss of 15%a dealer gets Rs. 420 more. The cost price of the article (in Rs.) is
Solution
Solution:
Old loss % = 15
New loss % = 9
Difference in loss percentages = 15-9 = 6%
This 6%(of CP)loss corresponds to monetary loss of Rs 420.
1% of CP corresponds to Rs. 420/6 = Rs.70
100% of CP = Rs. 70 * 100 =Rs. 7000 Answer
A person buys a car at 20%discount of the original price and sells it at 20% higherthan the original price. The percentage gain in this transaction iS
Solution
Solution
Let Original price of the car be Rs. 100
After 20% discount car's price = (100-20)/100 x Rs.100 = 0.8 x Rs. 100
= Rs. 80.
So CP for Man = Rs.80
Car was sold at 20% higher price,
So SP = (100+20)/100 x Rs. 100
= 1.2 x 100 = Rs. 120
SP for man = Rs. 120
Profit % = (SP-CP)/CP
=(120 - 80) / 80
= 50 % Answer
In a business P. O and R invested ₹7,200,₹ 12,600 and ₹ 9,600 respectively. What is the share of R (in ₹) in a total profit of 6,860 ?
Solution
Solution:
The ratio of investments of P,O and R is 7200:12600:9600.
The standard ratio will be 12:21:16.
So for every profit of Rs.(12+21+16) , R will get Rs. 16.
i.e. So for every profit of Rs.49,R will get Rs. 16.
for Profit of Re 1, R will get Rs.(16/49)
For Profit of Rs 6860, R will get Rs. (16 /49 ) x 6860
= Rs. 2240. Answer
P and O enterinto a partnership with capitals in the ratio of 3:4. At the end of 10 months P with draws. If they share profit in the ratios 5:6 for how many months O’s capital was used ?
Solution
Solution
Let Ps and Os initial investment be 3x and 4x respectively.
P's investment was for 10 months so it will be proportional to (3x)(10) = 30x
let Q's investment be for 'm' months, so its proportional investment will be (4x)(m).
So according to investment profits will be divided in the ratio 30x : 4mx = 30:4m
A/q
=> 30:4m = 5:6
=> 30/4 =
=> m= 9
Hence O invested for 9 months.
A pipe canfill a tank in 15 hours. Another pipe can empty the full tank in 20 hours. If both the pipes are opened together the number of hours required to fill the tank is
Solution
Solution:
Let total capacity of the tank be 60 units [LCM of 15,20]
First pipe fills 60 units (full tank) in 15 hrs. Hence in 1 hr. it fills (60/15) =4 units
Second pipe empties 60 units (full tank) in 20 hrs. Hence in 1 hr. it empties (60/20)units = 3 units or fills (-)3 units.
If both the pipes are opened simultaneously, total tank filled in 1 hr = 4 + (-)3 units = 1 unit.
So to fill full capacity (60 units), time taken = (60/1) = 60 hrs.
Two pipes P and O can fill a tank in 12 minutes and 15 minutes respectively. If both are opened together and P is closed after 3 minutes then the time required to fill the tank (in minutes) is
Solution
Solution:
Let total work be 60 units [LCM of 12,15]
P does 60 units in 12 minutes. Hence in 1 minute P does (60/12)units = 5 units.
O does 60 units in 15 minutes. Hence in 1 minute O does (60/15)units = 4 units.
Total work in 1 minute = 9 units
Now, for the given scenario,
First,
P and O work for 3minutes together @ 9 units/min
Work done = (9 x 3) units = 27
Work remaining =Total units of work - work done = 60-27 =33 UNITS .
Then,
O work alone @ 4 units/min.
Time taken = (Work remaining / speed) = 33/4 mins. = 8.25 minutes
Total time = 3+8.25 = 11.25 minutes or 11$$\frac{1}{4}$$ minutes
A Person runs 200 meters in 20 seconds. Whatis his speed in kmph?
Solution
Solution
Method 1
Distance = 200 m
Time = 20s
Speed in m/s = (200/20) m/s
= 10m/s
Now Important pointer to remember
5m/s = 18 km/h
So 10m/s = 36kmph Answer
Method 2
20 s for 200m.
1 Hr. (20 x 3 x 60 s) for (200 x 3 x60) m
1 Hr for 36000m
1 Hr for 36 km
Hence speed 36kmph Answer
Running at $$\frac{5}{4}$$ of his usual speed a person improveshis timing by 30 minutes. What was his usual time in hours?
Solution
Solution:
Let old speed and time be S1 and T1.
Let new speed and time be S2 and T2.
A/q,
S2=(5/4)S1 = 1.25 S1 .....Eqn (i)
T1 - T2 = 30minutes = 0.5 hr.....Eqn (ii)
As Distance remains constant ; S x T = constant;
S1 x T1 = S2 x T2
S1 x T1 = (1.25 S1) x T2......from Eqn.(i)
T1/T2 = 1.25
T1= 1.25 T2
and T1- T2 = 0.5 hr .........from Eqn.(ii)
1.25T2 - T2 = 0.5Hr
0.25 T2 = 0.5 Hr.
T2 = 2 Hr.
T1 = old time = T2 + 0.5 Hr. = 2.5 Hr.Answer
P’s workis twice as much as Q. If both work togetherthey finish a job in 12 days. If P works alone the number of days needed to complete that work?
Solution
Solution:
A/q
Let Q's efficiency be x%.
Then P's efficiency is 2x%
Total efficiency (if they work together) = (x + 2x)%= 3x %
With 3x% efficiency, time taken = 12 days.
So, with x% efficiency time taken = 13 x 3 = 36 days..... (Efficiency is indirectly proportional to Time taken)
So time taken if P works alone @ 2x % is = 36/2 days
= 18 days. Answer
A, B. C completed a work and received %.1800 as their wages. A worked for 6 days. B for 4 days and C for 9 days. If their wages are in the ratio of 5:6:4 the amount received by B (in rupees)is
Solution
The length and the breadth a rectangular field are in the ratio 3 : 2. The cost of fencing the field at the rate of ₹ 50 per meter is ₹ 25.000/-. The area of the field in square meters is
Solution
The circumference of a circle is 352 meters. Taking the approximate value of $$\pi$$ to be $$\frac{22}{7}$$,the area of the circle in square meters is
Solution
The radius of the base of a cylinder is $$\frac{1}{3}$$ of the radius of the base of a cone .If their heights are equal, then the ratios of their voulumes is
Solution
Three metal cubes of sides 6. 8 and 10 cms are melted and formed into a single cube. If there is no loss of metal in the process what is the side of the big cube (in cms) ?
Solution
A semi-circle is constructed on each side of a square of side 2m. Thenthe whole area of the figure (in sq.m) is
Solution
The difference between the circumference and radius of a circle is 111 cm. Then the area of the circle (in $$cm^{2}$$)?
Solution
Two poles of height 15 meters and 30 meters are erected in a playground at a distance of 36 meters between them. The distance between their tops (in meters) is
Solution
The numberequal to $$(254)_{5}$$ in ternary system is
Solution
The sum $$(1010)_{2}$$+$$(102)_{3}$$
Solution
For any two statements p, q, the contrapositive of $$p \Rightarrow q$$ is
For any two statements p, g the converse of $$\sim p \Rightarrow q $$ is
If a N denotes the set $$\left\{ax : x \epsilon N \right\}$$ then $$3N \cap 7N =$$
If $$R = \left\{(a, b) \epsilon R^{2} : a - b + \sqrt{2}\right\}$$ is irrational then the relation R on $$R^{2}$$ is:
If f(1) = 1 and $$f(n) = 2 \sum_{k-1}^{n-1} f(k),(n > 1)$$ then $$\sum_{k-1}^{m} f(k)$$ =
The sum of the intercepts made by the lme 7x+2y=28 on the coordinate axes is
A line l passing through the point (1, -2) is perpendicularto the line x+2y+1=0. Thenthe point of intersection of 1 and x + 2y + 1 = 0 1s:
$$\cos(A + 45^\circ) + \sin(A - 45^\circ) =$$
$$\cos^{2} A = \sin A \tan A \Rightarrow \cot^{6} A - \cot^{2} A =$$
$$\frac{\cos \theta}{7} = \frac{\sin \theta}{6} \Rightarrow 7 \cos 2 \theta + 6 \sin 2 \theta = $$
The angle of elevation of a tower from a point 40 meters from foot of the tower is $$\cot^{-1}\left(\frac{3}{5}\right)$$. Then the height (in meters) of the tower is
The quadratic polynomial in x which whendivided by x - 1, x + 2, x + 1 leave remainders 3, 24, 9 respectively is
If x + a is the highest common factor of $$x^2 + bx + c$$ and $$x^2 + dx + e$$, then the value of a is
If p(x) is a quadratic polynomial suchthat P(1) = 7, p(-1) = 3, p(0) = 4, then p(10) =
The remainder when $$x^4 + 4x^3 - 5x^2 - 6x + 7$$ is divided by x - 3, is
If a number x exceeds its reciprocal by $$2\frac{2}{3}$$, that $$x^2 =$$
A fraction becomes $$\frac{5}{7}$$ if 2 is added to both its numerator and denominator. However. if 17 is subtracted from both numerator and denominator the fraction becomes $$\frac{8}{15}$$. If 1 is added to its numerator and denominator, the fraction becomes.
The sum of first three terms of a geometric progression is $$\frac{13}{12}$$ and their product is -1. Then the fourth term is
How many first few terms of the geometric progression 3, 6, 12, 24.... add up to 765?
The coefficient of $$x^5$$ in the expansion of $$\left(\frac{4x}{5} - \frac{5}{2x}\right)^9$$ is
$$10_{C_0} + 10_{C_2} + ........ + 10_{C_{10}} =$$
$$\begin{bmatrix}-1 & 2 \\1 & -1 \end{bmatrix} \begin{bmatrix}x \\y \end{bmatrix} = \begin{bmatrix}4 \\5 \end{bmatrix} \Rightarrow 3x - 4y =$$
The system of equations:
x + y + z = 3
2x + 5y + 4z = 11
5x + 2y + z = 10 has
$$\lim_{x \rightarrow 0}\left(\frac{e^{5x} - e^{3x}}{e^{4x} - e^{x}}\right) =$$
$$(x + y)^{a + b} = x^ay^b \Rightarrow \frac{dy}{dx} =$$
In a $$\triangle ABC , \angle B = 55^\circ, \angle C = 45^\circ$$ and bisector of $$\angle A$$ meets BC at a point D. Then $$\angle CAD =$$
If the point A, B, C and D are Concyclic, then $$\angle ABc + \angle ADC =$$
A circle touches all the four sides of a quadrilateral ABCD as shown below. If AB = 3 cm. BC = 4 cm and CD = 5 cm then AD =
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The points A (5, 2), B (6, -15), C (0, 0) are vertices of the triangle which is
If three vertices of a rectangle are (4, 1), (7, 4) and (13, -2) then the fourth vertex is
The arithmetic mean of 10 observations is 48. If two more observations 65 and 75 are added to the data. then the arithmetic mean of the entire data of 12 observations is:
Solution
The mean of 10 observation is 48
Likewise the mean if the two added observation is 70(65+75/2=70)
Using Alligation method:
Step 1: 10 2
48 70
?
Step 2: 48 70
?
5 : 1
Step 3: 5+1=22
1=11/3
so as 1=11/3,so 5=55/3
putting those values we get ,
Step4: 48 70
?
55/3 : 11/3
Step 5: 48 70
155/3 OR 15 2/3
55/3 11/3
The median of first 2n natural numbers is
Fora data the medianis 53.5 and the meanis 53.8. Then mode of the data is
The standard deviation of first 25 natural numbers is
The variance of first n natural numbers is
If the sum of squares of the deviations of ranks of two players in n sports is $$\frac{2n(n + 1)}{3}$$, then the coefficient of rank correlation is
If A and B are two events in a random experiment with the probabilities $$P(A) = \frac{3}{8}, P(B) = \frac{1}{3}$$ and $$P(A \cap B) = \frac{1}{4}$$, then $$P(\overline{A} \cap \overline{B}) =$$ Here $$\overline{A}$$ is the complementary event of A
If a numberis selected at randomout of the first 120 natural numbers, then the probability that it is a composite number is
Solution
1 is neither composite nor prime no,
Eliminating the remaining prime no from the first 120 natural numbers we get 89 numbers which are composite numbers,
Hence, 89/120
If three vertices are selected at random fromthe vertices of an octagon, then the probability that no two of their three vertices are adjacent to each other is
If four boys and five girls sit in a row at random, then the probability that all boys sit together is
Choose the correct meaning for the word given:
Restive
Wield
Whimsical
Vociferous
Uprising
Rampant
Fill in the blank choosing the correct word:
The ........... wealth of India tempted many foreign invaders.
The disaster was .........., thanks to timely action.
The havoc caused by the storm was .........
The welfare measures ............. by the Government benefited the entire society.
Choose the correct answer
The package of MS Office that is used to curate documents is known as
A barcode reader is an example for
Algorithm consists of
Which of the following is not an operating system?
Which of the following provide bi-directional communication but in one direction at a time?
The abbreviation ‘NAV’ of mutual funds stands for
A Security agent against a loan is known as
Thinking creatively, abandoning all pre conceptionsis often described as thinking
The Empirical School of Management emphasizes on the
The wage system wherein a definite sum of moneyis paid for a particular of work is known as
A: “Are you worried about Ramya”
B: “No, not atall! I knowshe can give as good as she gets.” ‘B’ implies that
A: “Wethought everything was settled, but now they say theyare not happy.”
B: “So youare back to square one again.” ‘B’ implies that
“Enterit in the register.” Change the above sentence into passive voice.
“I tried to explain, but the managercut me short.” According to the speaker the manager
A: “How your weekend?”
B: “It was a roller coasterride.” ‘B’ implies that the weekend was
“If the room had been brighter, I would have been able to read for a while before bed time.” The speaker implies
“The manager kep this staff at a distance.” The manager implies that the manager
Fill in the blanks with the appropriate phase/verbs/ preposition:
“Are you hungry? Would youcare ............. something to eat?”
His salary is not enough to live ..........
The staff are ........... strike.
In a fit of emotion he ............ his job.
They were asked to ................. the decision of their supervisors.
If you make a mistake on the form, just ............
Engineers .................. a new channel for the streamto follow.
Do her parents ........ about it?
Read the following passage and answer question:
What are the economic impediments to greater financial inclusion? Perhaps the most important is the economic condition of the excluded. World over, the
poor, the small and the remote are excluded. It is not just because the financial system is underdeveloped, but because they are hard to service profitability.
Nevertheless. this is not a reason to abandon hope, but to ask how we can overcome the impediments in the way of inclusion.
The excluded may live in remote areas or may belong to communities or segments of society that undertake economic activity informally-they do not maintain records or have signed contracts or documentation. They often do not ownproperty or have regular established sources of income. As a result. a banker, especially if as is typical. he is not from the local region, will have difficulty getting sufficient information to offer financial products.
Whom does the passage exclude in the category of “the excluded”?
What is the main reason for economic exclusion?
Which is not stated as a common feature of the excluded?
Why does the banker have difficulty in getting sufficient information about his customers?
What does the term ‘impediments’ mean?
Read the following passage and answer questions:
Every Olympic athlete, every leader, and very human being has a little knownbrain part in common: a Quit Switch. Some people out of lifelong habit throwthe quit switch at the first sign of frustration. Their day of phonecalls gets frustrating. so they throw the switch and go for coffee with a co-worker for two hours of sympathetic negativity. Everyone has a Quit Switch. Not everyone knows it. Get to knowit: notice yourself flipping the switch. You can’t quit and you won't quit until you throwthe switch. A humanbeing is built like any animal to persist until a goal is reached. Somewhere along the way, though. we learn about this little switch. Soon, westart flipping the switch. We quit. If you weren’t in the habit of throwing the switch too early. you would achieve virtually any goal you ever set. Whether youflip it early or late is only habit.
The switch flipping habit is misinterpreted as lack of will power, courage, drive or desire, but that is nonsense. It’s a habit and like any otherhabit. it can be replaced with another habit. Make it your habit not to throw the Quit Switch early in any process.
What is a “Quit Switch’?
What are most people unaware of ?
When do people use the ‘Quit Switch’?
Why is it unnatural to ‘Quit’?
Why can the ‘Quit Switch’ be overcome?
Read the following and answer questions:
From the very first day of my stay with him Gokhale made me feel completely at home. He treated me as though I were his younger brother. He acquainted himself with all my requirements and arranged to see that I got all I needed. Fortunately my wants were fewand as I had cultivated the habit of self — help. I needed very little personal attendance. He was deeply impressed with my habit of tending for myself, my personal cleanliness, perseverance and regularity, and would often overwhelm me with praise.
He seemed to keep nothing private from me. He would introduce meto all the important people that called on him. This is howhe introduced Dr. Ray: “This is Prof. Ray who having a monthly salary of Rs. 800. keeps just Rs.40 for himself and devotes the balance to public purposes. He is not. and does not want to get "married.”
To see Gokhale at work was as much a joy as an education. He never wasted a minute. His private relations and friendships were all for public good. India’s poverty and subjection were matters of constant and intense concern to him.
According to the passage. how old is the author?
Why were the author’s requirements few?
How much did Dr. Ray spend every month for purpose?
What does the phrase “called on” in the passage mean?
Identify the false statement about Gokhale.
