Study notes on "Trigonometry" for SSC CGL CHSL EXAM

Trigonometry 

Hello, Students, SSC CHSL exam is going on and SSC CGL Pre 2017 is scheduled in the month of June/July 2017. Now It's Important to learn and revise all the important Formulas of advanced maths. We'll provide you all the tricky notes and formulas. these notes are based on the type of questions that are asked in SSC CGL exam. 

 Sector

π radian = 180°
If an arc of length ‘s’ subtends an angle θ radian at the centre of a circle of radius, r then s = rθ.

P – Perpendicular

B – Base

H – Hypotenuse

How to Solve Trigonometry Questions for SSC CGL 2017

Dear Students, SSC CGL Pre 2017 Exam is scheduled tentatively in the month of JUNE/JULY 2017. we are providing all types of Quant quizzes and the TRICKS, FORMULAS and STUDY NOTES. We will cover all the topics of Quant. Stay tuned for more Study Notes. 

FORMULAE FOR MAXIMA AND MINIMA

Important Geometry Formula For SSC CGL Exam 2017

Dear Readers, Here We are providing a Study Notes of Quantitative Aptitude in accordance with the syllabus of SSC CGL. These notes are based on the Important formula of Circle. This will help you to solve more Questions of Geometry in very less time. 

Important Formula of Algebra For SSC CGL EXAM 2017

Important Formula of Algebra For SSC CGL EXAM 2017

Dear Readers, Here We are providing a Study Notes of Quantitative Aptitude in accordance with the syllabus of SSC CGL. These notes are based on the Important formula of  Algebra. This will help you to solve more Questions of  Algebra in very less time.

Theory Based Repeated Question of Geometry FOR SSC CGL EXAM

Theory Based Repeated Question of Geometry FOR SSC CGL EXAM

Dear Readers, Here we are providing Theory Based  Repeated  Question of Geometry in ssc cgl exam. This will help you to give the answer orally. So you can save for another Questions

⇒ Circum radius of right angled triangle is?

Ans. Half of hypotenuse

⇒ Distance of vertices for any triangle from circumcentre is known as?

Ans. Circum radius

⇒ In a right angled triangle the circumcentre of the triangle lies?

Ans. On midpoint of the hypotenuse

⇒ The perpendiculars drawn from the vertices to the opposite sides of a triangle, meet at the point whose name is.

Ans. Orthocenter

⇒ Orthocentre of right angle triangle lies at

Ans. At right angle vertex

⇒ Orthocentre of obtuse triangle lies.

Ans. Outside the triangle

⇒ If the orthocenter and the centroid of a triangle are the same, then the triangle is 

Ans. Equilateral triangle

⇒ In a triangle, if three altitudes are equal then the triangle is

Ans. Equilateral

⇒ The sum of three altitudes of a triangle is 

Ans. Less than the sum of side

Quant Quiz For SSC

Quant Quiz For SSC Exam

Dear reader here we are providing some question on quant aptitude which can be help in your upcoming exams.
1.    The selling price of 10 oranges is the cost price of 13 oranges. then the profit percentage is :
(1) 30%
(2) 10%          
(3) 13%                               
(4) 3%


2.   A shop man bought pens at the rate of 7 for Rs10 and sold them at the profit of 40%.how many pens would a customer get for Rs 10.
(1) 6                                   
(2) 4
(3) 5                                   
(4) 3

3.   A train running at 36 km/hr passes another train completely in 12 s, which is half of its length, running in the opposite direction at 54 km/hr. If it also passes a railway platform in 1.5 min, what is the length of the platform (in meters)?
(1) 700                               
(2) 860                        
(3) 900                               
(4) 1, 000   
       
4.   Two rice varieties costing Rs 20 per kg and Rs 30 per kg were mixed as 2 : 3 and sold so as to gain 10%. What was the SP of the mixture (Rs/kg)?
(1) 31.2                              
(2) 28.6                       
(3) 30                                 
(4) 26      
        
5.   A circle of radius 8 cm has its radius decreased by 2 cm. What is the approximate percentage decrease in area?
(1) 25%                             
(2) 50%                      
(3) 38%                             
(4) 43.75%   
  
6.   In a school, there are 3600 students. The ratio of boys to girls is 4 : 5. If twenty percent of the boys and sixty percent of the girls like to play hockey, then how many students do not like to play hockey?
(1) 1520                             
(2) 1250                      
(3) 2008                             
(4) None of these

7.   The ratio of the present ages of Sonu and Monu is 7: 6 respectively. Eight years ago the respective ratio of their ages was 5 : 4. What will be Monu’s age four years from now?
(1) 28 years                       
(2) 32 years    
(3) 24 years                       
(4) 30 years    

8.  The sum of three consecutive odd numbers is 20 more than the smallest number. What is the middle number?
(1) 7                                   
(2) 9                
(3) 11                                 
(4) 5   
             
9.   A invests Rs. 24000 to start a business. Four months later B joins him by investing Rs. 31000 and after another two months C joins them by investing Rs. 40000. At the end of one year the business earns a profit of Rs. 12028. What is C's share in the profit?
(1) Rs. 4464                      
(2) Rs. 3844   
(3) Rs. 3720                      
(4) Rs. 3270   

10.  2 men can complete a piece of work in 6 days. 2 women can complete the same piece of work in 9 days, whereas 3 children can complete the same piece of work in 8 days. 3 women and 4 children worked together for 1 day. If only men were to finish the remaining work in 1 day, how many total men would be required?
(1) 4                                   
(2) 8                
(3) 6                                   
(4) 2

Answers with solutions:
1.(1) 
Profit percentage = (13-10)*100/10 = 30%

2. (3) 
The S.P. of 7 pens = 10*140/100 = Rs 14
∴The S.P. of I pens = 14/7 = Rs 2
∴The pens for Rs 10 = 10/2 = 5

3. (1)
Crossing time = l1+ l2 / relative speed
l1 = x
l2 = x/2
Relative speed = 36 + 54 = 90 km/hr = 90 x 5/8 = 25 m/s
Time = 12 sec
12 = x + x/2 / 25
x = 200 m
Now train crossing the platform
l1 = 200 m,    l2 = length of platform = y
Time = 1.5 min = 90 sec
Speed = 36 km/hr = 10 m/s
90 = 200 + y / 10
Y = 700 m

4.  (2) 
CP of the mixture = 20 x 2 + 30 x 3  / 5   = 26
SP = 1.1 x 6 = 28.6

5.  (4) 
Original area of the circle = π (8)2 = 64 π
New area of the circle = π (6)2 = 36 π

% decrease in area = 64 π  - 36 π / 64 π x 100 = 43.75%

6.  (4) 
Total Students in school = 3600
Number of boys = 4/9 x 3600 = 1600
Number of boys who like hockey = 20% of 1600 = 320
Number of girls = 2000
Number of girls who like hockey = 60% of 2000 = 1200
Number of students who do not like hockey = (1600 – 320) + (2000 – 1200) = 2080 

7.  (1)
Let the present ages of Sonu and Monu be 7x and 6x. Now
7x – 8 /6x – 8 = 5/4
x = 4
Present age of Monu = 24 years
Monu’s age four years from now = 24 + 4 = 28 years

8.  (2)
 Let the numbers be x, x + 2 and x + 4. Then
x + (x + 2) + (x + 4) = x + 20
x = 7
So the middle number is 9.

9.  (3)
 The ratio of their investments = 24000 x 12: 31000 x 8 : 40000 x 6 = 36 : 31:30
Since the ratio of investment is also the ratio of profit,
C’s share = 30/97 x 12028 = 3720

10. (2) 
2 M x 6 = 2 W x 9 = 3 C x 8
2 M = 3 W = 4 C
The ratio of efficiency of man, woman and children = 1/2: 1/3: 1/4 = 6: 4: 3
Let the work done by a man, a woman and a children in one day be 6 units, 4 units and 3 units respectively.
So the total work to be done = 2x6x6 = 72 units
Work done by 3 women and 4 children in one day = 3 x 4 + 4x 3 = 24 units
Remaining work = 72 – 24 = 48 units
Number of men required to complete the remaining work in one day = 48/6 = 8

Quant Quiz On D.I

Quant Quiz On D.I

Directions—(Q. 1–5) Study the following graph carefully to answer the questions—

The following Bar graph gives the number of products manufactured and sold by a company over the years. 2004 to 2009 Value in Thousand.

1. What is the difference in the number of products manufactured by the Company in the year 2009 and 2008 ?
(1) 4000   
(2) 5000  
(3) 3500
(4) None of these

2. The number of products sold by the company in the year 2004 is what per cent of the number of products manufactured by it in that year ? (Rounded off to two digits after decimal)
(1) 71.43   
(2) 67.51 
(3) 81.67  
(4) 56.29  

3. What is the per cent increase in the number of products manufactured by the company in the year 2006 from the previous year ? (Rounded off to two digits after decimal)
(1) 19.25   
(2) 33.33 
(3) 10.45  
(4) None of these

4. What is the respective ratio of the number of products not sold by the company in the year 2007 to those not sold in the year 2005 ?
(1) 3 : 1   
(2) 6 : 5  
(3) 1 : 3
(4) 5 : 6  

5. What is the  average number of products manufactured by the company over all the years together ?
(1) 36550  
(2) 39480 
(3) 41220  
(4) 43330  
(5) 34420

Directions—(Q. 6–10) Study the following graph carefully to answer the questions that follow—
The following line graph gives distance (in km) travelled by five different trucks in a day.

6. What is the respective ratio of the distance travelled by Truck A to the distance travelled by Truck D?
(1) 17 : 19  
(2) 11 : 15 
(3) 19 : 17 
(4) 15 : 11  

7. What is the average distance travelled by all the Trucks together ?
(1) 510 km   
(2) 515 km 
(3) 425 km  
(4) None of these

8. If Truck C covered the given distance at the average speed of 55 km/hr, what was the time taken by it to cover this distance?
(1) 12 hours 
(2) 10 hours 
(3) 8 hours 
(4) 6 hours  

9. The distance travelled by Truck A is approximately what per cent of the total distance travelled by Truck E and C together ?
(1) 44   
(2) 50  
(3) 52   
(4) 58  

10. If the time taken by Truck B to cover the given distance was 8 hours, what was the average speed of the truck ?
(1) 51.75 km/hr  
(2) 45•25 km/hr 
(3) 52•25 km/hr  
(4) 43•75 km/hr

Solutions (1-5):
1. (2) 

2. (1) Required percentage = 25/35 * 100 = 71.43%

3. (4) Required percentage =  (42.5 - 37.5)/37.5 *100 = 13.33%

4. (3) Required ratio = (45 – 42.5) : (37.5 – 30) = 1 : 3

5. (4) Required average = (35000 + 37500 + 42500 + 45000 + 47500 + 52500)/6  =43330 (approx).

Solutions (6-10):

6. (3) Required ratio = 475 : 425 = 19 : 17

7. (4) Total distance travelled by all trucks = 475 + 350 + 550 + 425 + 525 = 2325 km
Average distance = 2325/5 = 465 km .

8. (2) Time taken by truck C = 550/55 = 10 hours.

9. (1) Required percentage = 475 / (550 + 525)  = 44% (approx).

10. (4) Speed of truck B = 350/8 = 43.75 km/hr

                                        

Quant Quiz For SSC

Quant Quiz For SSC Exam

1.    A man rows 20 km downstream and 16 km upstream taking 4 hours each time. What is the speed of current?
(a) 0.4 kmph
(b) 0.5 kmph
(c) 0.6 kmph
(d) 0.1 kmph

2.    On selling an item for Rs 20 a man gains 25%. In order to gain 40% what will be the increase in it’s selling price.
(a) Rs 3.40
(b) Rs 3 
(c) Rs 2.62
(d) Rs 2.40 

3.    The sum of money that will give Rs 2 as simple interest per day at the rate of 8% per annum is
(a) Rs 9125
(b) Rs 7236
(c) Rs 6382
(d) Rs 9262 

4.    X can do a piece of work in 20 days and Y can do it in 10 days. They started together, but after 6 days X leaves off. Y will do the rest work in
(a) 1 day 
(b) 2 days
(c) 7/3 days
(d) 3 days 

5.    A radio is sold for Rs 990 at a profit of 10%. What would have been the gain or loss in percentage had it been sold for Rs 880?
(a) 19/3%  gain
(b) 17/3% loss
(c) 17% gain
(d) 20/9% loss 

6.    In an exam, 60% of the total student passed. If the number of failed students is 320 then the total number of students is
(a) 600 
(b) 700 
(c) 800 
(d) 900  

7.    A cycle is bought for Rs 840 and sold at Rs 920. What is the percentage gain
(a) 10.50%
(b) 8.52%
(c) 7.35%
(d) 9.52% 

8.    If Raj’s salary is 30% more than Amar’s salary, the how many percent is Amar’s salary less than that of Raj’s?
(a) 56% 
(b) 23.07%
(c) 50/3%
(d) 50.6% 

9.     Find the number of ways in which 5 different beads can be arranged to form a necklace.
(a) 120 
(b) 60 
(c) 30 
(d) 12  

10.  A card is drawn from a pack of playing cards, what is the probability of getting either a red or a red queen?
(a) 4/13  
(b) 7/13 
(c) 1/13 
(d) 1/26 

ANSWERS WITH EXPLNATION :
1. (b)
Speed downstream = 20/4 = 5 kmph
Speed upstream = 16/4 = 4 kmph
Speed of current = 1/2 * (5-4)= 0.5 kmph

2. (d)
SP = 20, gain = 25%
CP = 100/125 * 20 = Rs 16
Now, CP = 16, gain = 40%
SP =  140/100 * 16 = 22.40
Increase = 22.4 – 20 = 2.4

3. (a)
Annual intetest = Rs 365 × 2 = Rs 730
Rate = 8%
Sum = (100 * 730)/8 = Rs 9125

4. (a)
(X + Y)’s 6 days’ work = 6 * (1/20 + 1/10) = 9/10
Remaining work = 1 - 9/10 = 1/10
1/10 work is done 2y Y in 10 * 1/10 = 1 day

5. (d)
Let the CP is Rs x.
Then, x * 110/100  = 990
x = 900
Now CP is Rs 900 and SP is 880.
% loss =  20/900 * 100 = 20/9%

6. (c)
Let the number of student is x out of that 40% have failed.
40/100 * x = 320
x = 320 * 100/40 = 800

7. (d)
CP = Rs 840 and SP = Rs 920
Gain = 920 – 840 = Rs 80
gain percentage = 80/840 * 100 = 9.52%

8. (b);
Amar’s salary is less than of Raj 2y
(R/100 + R * 100)% = (30/(100 + 30) * 100)%
(30/130 *100 )% = 300/13% = 23% APPROX

9. (d)
According to formula:  
Number of arrangements = (5-1)!/2 = 12

10. (b)
26/52 + 2/52 = 28/52 = 7/13

Quant Quiz On Number Series

Quant Quiz On Number Series

Directions (1 - 5): What will come in place of the (?) in the following number series?
1.    5, 9, 18, 34, 59, 95, (?)
(a) 272                       
(b) 186           
(c) 140
(d) 144                       
(e) None of these


2.    1200, 480, 192, 76.8, 30.72, (?)
(a) 15.91                   
(b) 18.321       
(c) 12.288
(d) 12.234                 
(e) None of these

3.    13, 14, 30, 93, 376, (?)
(a) 1848                     
(b) 1125         
(c) 1150
(d) 1885                     
(e) None of these

4.    505, 528, 574, 643, 735, (?)
(a) 850                       
(b) 888           
(c) 812
(d) 618                       
(e) None of these

5.    13, 16, 14, 17, 15, 18, (?)
(a) 16                         
(b) 15           
(c) 14             
(d) 21                         
(e) None of these

Directions (6-10): Find the wrong one in the series
6.    4, 5, 15, 49, 201, 1011, 6073
(a) 5                           
(b) 15             
(c) 49                       
(d) 201                       
(e) 1011

7.    888, 440, 216, 104, 48, 22, 6
(a) 440                       
(b) 216           
(c) 104                     
(d) 48                         
(e) 22

8.    2, 3, 6, 15, 52.5, 157.5, 630
(a) 3                           
(b) 6               
(c) 15                       
(d) 52.5                     
(e) 157.5

9.    5, 8, 20, 42, 124, 246, 736
(a) 8                           
(b) 20             
(c) 42                       
(d) 124                       
(e) 246

10.  1050, 510, 242, 106, 46, 16, 3
(a) 510                       
(b) 242           
(c) 106                     
(d) 46                         
(e) 16

ANSWER WITH EXPLANATION:

1.    (d):

5,   9,    18,       34,      59,       95     (144)

 +4    +9     +16     +25      +36   +49

2.    (c)

1200*2/5 , 480*2/5, 192*2/5,  76.8*2/5, 30.72*2/5,(12.288)

                                                

3.     (d)

13,          14,       30,       93,       376,      (1885)

       *1+1       *2+2    *3+3    *4+4     *5+5  

4.     (a)

505,        528,        574,        643,        735,        (850)

        +23         +46       +69          +92       +115

5.    (a)

13,      16,      14,      17,    15,       18,       (16)

      +3        -2     +3        -2       +3       -2

6.    (a)  

2^nd term = (1^st term *1+2)= (4*1+2) = 6

3^rd term = (2^nd term*2+3) = (6*2+3) = 15

4^th term = (3^rd term*3+4) = (15*3+4) = 49

5^th term = (4^th term*4+5) = (49*4+5) = 210 and so on

Therefore 5 is wrong

7.   (e)   

2^nd term = (1^st term - 8)/2 = (888-8)/2 = 440

3^rd term = (2^st term - 8)/2 = (440-8)/2 = 216

4^rd term = (3^st term - 8)/2 = (216-8)/2 = 104

5^rd term = (4^st term - 8)/2 = (104-8)/2 = 48

6^rd term = (5^st term - 8)/2 = (48-8)/2 =20

Therefore 22 is wrong

8.    (d)  

2^nd term = (1^st term* 1.5) = 2 * 1.5 = 3

3^rd term = (2^st term* 2) = 3* 2 = 6

4^th term = (3^st term* 2.5) = 6 * 2.5 = 15

5^th term = (4^st term* 3) = 15 * 3 = 45

Therefore 52.5 is wrong

9.   (b)   

2^nd term = (1^st term * 2 - 2) = (5 * 2 – 2)  = 8

3^rd term = (2^st term * 3 - 2 ) = (8* 3 – 2) = 22

4^th term = (3^st term * 2 - 2 ) = (22 * 2 – 2) = 42

5^th term = (4^st term * 3 - 3) = (42 * 3 – 2) = 124 and so on

Therefore 20 is wrong

10.  (c)    

2^nd term = (1^st term - 30)/2= (1050-30)/2= 510

3^rd term = (2^st term - 26)/2= (510-26)/2= 242

4^th term = (3^st term - 22)/2 = (242-22)/2 = 110

Therefore 106 is wrong