35180.Raju starts walking towards south. After walking 20 m he turns towards North and Walks 8 m. Again he turns towards East and walks 5 m. How far and in which direction is he from his starting point.
15 m, South
17 m, North-West
7 m, East
13 m, South-East
Explanation:
$ x^{2}=(12^{2})+(5^{2})=169$
$x=13m southeast$
35182.The sides of 14 Squares are 11 cm, 12 cm, 13 cm, .......... 24 cm, then find the total area of 14 squares.
3515 cm 2
4515 cm 2
2115 cm 2
3215 cm 2
Explanation:
$\dfrac{n(n+1)(2n+1)}{6}$
$Area of square=a^{2}$
$11^{2}+12^{2}+13^{2}+...+24^{2}$
$=[1^{2}+2^{2}+3^{2}+....+24^{2}]-[1^{2}+2^{2}+3^{2}+...+10^{2}]$
$=\dfrac{24\times25\times49}{6}-\dfrac{10\times11\times21}{6}$
$=4900-385$
$=4515$
35184.A Train travelled a certain distance at a uniform speed. If the train had been 7 km/hr faster, it would have taken 14 hours less than the scheduled time. If the train were slower by 3 km/hr then it would have taken 10 hours more than the scheduled time. Find the distance covered by the train.
600 Km
700 Km
800 Km
900 Km
Explanation:
$\frac{d}{x}-\frac{d}{x+7}=14---->(1)$
$\frac{d}{x-3}-\frac{d}{x}=10----->(2)$
$\frac{ d[x+7-x]}{x(x+7)}=14 $
$7d=14x(x+7)$
$d=2x(x+7)------>(3)$
$\frac{d[x-(x-3)]}{x(x-3)]}=10$
$3d=10x(x-3)$
$d=\frac{10}{3}x(x-3)----->(4)$
$From (3) & (4)$
$2x(x+7)=\dfrac{10}{3}x(x-3)$
$2x+21=5x-15$
$2x=36$
$x=18kmph$
$(1)----->\dfrac{d}{18}-\dfrac{d}{25}=14$
$\dfrac{25d-18d}{450}$
$=14$
$d=900km$
35186.Find the average of first n natural numbers
$\dfrac{n(n+1)}{2}$
$\dfrac{n(n+1)(2n+1)}{2}$
$\dfrac{(n+1)}{2}$
n2
Explanation:
$Average=\dfrac{n((n+1)/2)}{n}$
$=\dfrac{n+1}{2}$
35188.A gardener wanted to reward a girl for her good deeds by giving some apples. He gave 2 apples on the first day, 4 on the second day, 8 on the third day, 16 apples on the fourth day and so on for ten days. How many apples did she get from the gardener at the end of the tenth day
1024
2060
1760
2046
Explanation:
2+4+8+...+1024
$2+2^{2}+2^{3}+...+2^{10}$
$s_{n}=\dfrac{a[r^{n}-1]}{r-1}$
=$\dfrac{2[2^{10}-1]}{2-1}$
=2[1024-1]
=$2\times 1023$
=2046
2+4+8+...+1024
$2+2^{2}+2^{3}+...+2^{10}$
$s_{n}=\dfrac{a[r^{n}-1]}{r-1}$
=$\dfrac{2[2^{10}-1]}{2-1}$
=2[1024-1]
=$2\times 1023$
=2046
35190.Using the clay, Malar makes a cone, a hemisphere and a cylinder have equal bases and the heights of the cone and a cylinder are equal. They same as the common radius then find the ratio of their respective volumes
1:2:3
1:2: 4
1:2: 5
1:2: 6
Explanation:
volume of cone :volume of hemisphere :volume of cylinder
$\dfrac{1}{3}\pi r^{2}h:\dfrac{2}{3}\pi r^{3}:\pi r^{2}h$
put r=h then,
$\dfrac{1}{3}\pi r^{3}:\dfrac{2}{3}\pi r^{3}:\pi r^{3} $---->(1)
multiply (1) by 3 then,
$\dfrac{1}{3}\times 3 :\dfrac{2}{3}\times 3 : 1\times 3$
1:2:3
volume of cone :volume of hemisphere :volume of cylinder
$\dfrac{1}{3}\pi r^{2}h:\dfrac{2}{3}\pi r^{3}:\pi r^{2}h$
put r=h then,
$\dfrac{1}{3}\pi r^{3}:\dfrac{2}{3}\pi r^{3}:\pi r^{3} $---->(1)
multiply (1) by 3 then,
$\dfrac{1}{3}\times 3 :\dfrac{2}{3}\times 3 : 1\times 3$
1:2:3
35192.Spherical metal ball of radius 6 cm is melted and casted into small spherical balls having diameter 6 mm. How many small balls can be casted
8000
1000
6000
2000
Explanation:
$\dfrac{\dfrac{4}{3}\pi R^{3}}{\dfrac{4}{3}\pi r^{3}}$
$=\dfrac{60\times 60\times 60}{3\times3\times3}$
$=20^{3}$
=8000 smaller balls
$\dfrac{\dfrac{4}{3}\pi R^{3}}{\dfrac{4}{3}\pi r^{3}}$
$=\dfrac{60\times 60\times 60}{3\times3\times3}$
$=20^{3}$
=8000 smaller balls
35194.The radii of two circular ends of a frustum shaped bucket are 15 cm and 8 cm. If its depth is 63 cm, find the capacity of the bucket in litres (Take $\pi=\dfrac{22}{7}$)
2.6994 litres
26.994 litres
269.94 litres
2699.4 litres
Explanation:
capacity of bucket=$\dfrac{1}{3}\pi h[R^{2}+r^{2}+Rr]$
=$\dfrac{1}{3}\times\frac{22}{7}\times 63[225+64+120]$
=$22\times 3\times 409$
=$26994cm^{3} [1 litre=1000c m^{3}]$
=26.994litre
capacity of bucket=$\dfrac{1}{3}\pi h[R^{2}+r^{2}+Rr]$
=$\dfrac{1}{3}\times\frac{22}{7}\times 63[225+64+120]$
=$22\times 3\times 409$
=$26994cm^{3} [1 litre=1000c m^{3}]$
=26.994litre
35196.The present age of A and B are in the ratio 4: 5 and after five years they will be in the ratio 5:6 then their sum of present age is
55 years
45 years
35 years
25 years
Explanation:
present age of A & B=4:5
After 5 years the ratio will get 5:6
so, 1 unit=5 years
A+B=9Units
=9*5=45years
present age of A & B=4:5
After 5 years the ratio will get 5:6
so, 1 unit=5 years
A+B=9Units
=9*5=45years
35198.If A and B can do a work in 6 days. B and C can do it in 12 days, C and A can do it in 4 days how many days it would take to finish the same work by all the three together?
8 days
4 days
10 days
2 days
Explanation:
Implementing given statement in terms of equations,we get,
A + B=1/6; as both do 1/6 work in 6 days.
similarly, B + C=1/12;
A + C=1/4;
now adding above equations we get,
==>2(A + B +C)=1/6 + 1/12+1/4;
==>2(A + B +C)=(2+1+3)/12; as, lcm= 12,
==>2(A + B +C)=6/12;
==>(A + B +C)=6/24;
==>(A + B +C)=1/4;
hence they all work in 4 days to complete
Implementing given statement in terms of equations,we get,
A + B=1/6; as both do 1/6 work in 6 days.
similarly, B + C=1/12;
A + C=1/4;
now adding above equations we get,
==>2(A + B +C)=1/6 + 1/12+1/4;
==>2(A + B +C)=(2+1+3)/12; as, lcm= 12,
==>2(A + B +C)=6/12;
==>(A + B +C)=6/24;
==>(A + B +C)=1/4;
hence they all work in 4 days to complete
35200.A and B can complete a work individually in 12 days and 18 days. They started doing the work together but after 4 days. A had to leave and B alone completed the remaining work. The whole work was completed in
30 days
20 days
12 days
8 days
Explanation:
work done by A,B &C in 1 day=2[A+B+C]=$\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{4}$
$=\dfrac{2+1+3}{12}$
$=\dfrac{6}{12}$
$=\dfrac{1}{2}$
$[A+B+C]'s 1 day work=\dfrac{1}{2\times 2}=\dfrac{1}{4}$
35202.A function f:(-7,6) $\Rightarrow$ R is defined as follows 
what is the value of $\dfrac{4f(-3)-2f(4)}{f(-6)-4f(1)}$ ?
what is the value of $\dfrac{4f(-3)-2f(4)}{f(-6)-4f(1)}$ ?
$\dfrac{2}{7}$
$\dfrac{7}{2}$
2
$\dfrac{1}{2}$
Explanation:
f(-3)=x+5=-3+5=2
f(4)=x-1=4-1=3
f(-6)=$x^{2}+2x+1$=36-12+1=25
f(1)=x+5=1+5=6
f(-3)=x+5=-3+5=2
f(4)=x-1=4-1=3
f(-6)=$x^{2}+2x+1$=36-12+1=25
f(1)=x+5=1+5=6
$\dfrac{(4\times 2) -(2\times 3)}{18-4(6)}$
=$\dfrac{8-6}{25-24}$
=235204.Mala and Latha each had a number of bangles. Mala said to Latha “If you give me 4 of your bangles, my number will be thrice yours". Latha replied "If you give me 36, my number will be thrice yours". What is the total bangles together with them?
70
80
90
100
Explanation:
From given question,M+4=3(L-4)
M+4=3L-12
M=3L-16------>(1)
then L+36=3(M-36)
L+36=3M-108
L+36=3(3L-16)-108
L+36=9L-48-108
8L=192
L=24
put L value in equation (1)
M=3L-16
M=72-16
=56
Total Bangles=56+26=80
From given question,M+4=3(L-4)
M+4=3L-12
M=3L-16------>(1)
then L+36=3(M-36)
L+36=3M-108
L+36=3(3L-16)-108
L+36=9L-48-108
8L=192
L=24
put L value in equation (1)
M=3L-16
M=72-16
=56
Total Bangles=56+26=80
35206.Match List I with List II and select the correct answer using the codes given below :
| List I-planets | List II - Revolution Periods |
|---|---|
| (a) Mars | l. 88 days |
| (b) Earth | 2. 225 days |
| (c) Mercury | 3. 687 days |
| (d) Venus | 4. 365 days |
3 4 2 1
3 4 1 2
2 4 3 1
2 4 1 3
35210.Identify the irrigation canal which originate from the Harike Barrage in Ferozepur district of Punjab
Bhakra canal
Indira Gandhi canal
Sirhind canal
Bist Doab canal
35212.Assertion (A) : Extra-Tropical cyclones are formed in mid-latitudes.
Reasoning (R): The warm and cold fronts converge in mid-latitudes.
Reasoning (R): The warm and cold fronts converge in mid-latitudes.
Both (A) and (R) are true and (R) is the correct explanation of (A)
Both (A) and (R) are true but (R) is not the correct explanation of (A)
(A) is true but (R) is false
(A) is false but (R) is true
35216.Who won the IAAF best female Athletic of the year award in 2016?
Yelena Isinbayeva
Almaz Ayana
Shelly Ann Fraser Pryce
Valerie Adams
35218.Match the Field with Nobel Prize Winners 2016 and select the correct answer using the codes given below :
| Field | Nobel Prize Winner |
|---|---|
| (a) Peace | 1. Jean Pierre Sauvage, Fraser Stoddart, Bernad L. Feringa |
| (b) Medicine | 2. Yoshinori Ohsumi |
| (c) Physics | 3. Juvan Manuel Santos |
| (d) Chemistry | 4. David Thouless, Duncan M. Haldane, Michael Kesterlitz |
3 4 2 1
1 3 2 4
3 2 4 1
4 3 1 2