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D and E are the midpoints of AB and AC of ∆ABC, BC is produced to any point P; DE, DP and EP are joined. then, area of:
DE ∥ BC
DE = 1/2 BC
⇒ ar(∆BDE) = 1/4 × ar(∆ABC)
And ∆BDE = ∆PED
[ ∵ both triangles lie on the same base DE and between two parallel lines DE and BP.]
∴ ar(∆PED) = 1/4 × ar(∆ABC)
One side other than the hypotenuse of right angle isosceles triangle is 6 cm. The length of the perpendicular on the hypotenuse from the opposite vertex is:
Let √B be right angle in ΔABC
and BD be perpendicular on hypetenuse AC then
The speeds of two trains are in the ratio 3 : 4. They are going in opposite directions along parallel tracks. If each takes 3 seconds to cross a telegraph post, find the time taken by the trains to cross each other completely?
x 3 ↓ : ↓ x 3 ⟶ time
Length = 9m : 12m.
= 3 sec.
A mother is 3 times faster than her daughter. If the daughter completes a piece of work in 15 days, how long will it take for both mother and daughter to complete the same work?
Mother’s one day work = ⅕
Both can complete their work = 1/5+1/15 = (3+1)/15 = 4/15
Hence, required days= 15/4 days .
Study the following table carefully to answer the questions that follow.
Number of soldiers (in thousands) joining five different forces during six different years.
The total number of soldiers joining BSF in the years 2004, 2005 and 2006 was approximately what percent of the total number of soldiers joining Navy over all the years together?
= 13400
Total no. of soldiers joining in Navy = 10900
Required Percentage= (13400/10900)×100 = 123%
Study the following table carefully to answer the questions that follow.
Number of soldiers (in thousands) joining five different forces during six different years.
What was the ratio of the number of soldiers joining Army in the year 2008 to the number of soldiers joining coast guard in the year 2006?
If tan (5x – 10°) = cot (5y + 20°), then the value of (x+y) is:
tan (5x – 10°) = tan (90° – {5y + 20°})
5x – 10° = 90° – (5y + 20°)
5x + 5y = 90° + 10° – 20°
5x + 5y = 80°
x + y = 16°
If a train, with a speed of 60 km/hr, crossed a pole in 30 second, the length of the train (in meters) is:
S = 60 x 5/18 m./sec. = 50/3 m./sec.
T = 30 sec.
Length= S x T =
l = 500m.
The supplement of an angle is onefourth of itself. Determine the angle and its supplement.
⇒(180° x) = x
⇒ 720  4x = x
⇒ 5x = 720
⇒ x = 144
Thus, the measure of the angle is 144°,the and the measure of its supplement.
= 180° 144° = 36°.
3 years ago the average age of a family of 5 members was 17 years. A baby having been born, the average age of the family is the same today. The present age of the baby is
= 17 × 5 = 85 years
Three years hence,
Total age of 5 members = 85+3x5 = 85+15 = 100 years
Sum of present ages of 6 members = 17 × 6 = 102 years
Present age of baby= 102 – 100 = 2 years
A ladder leans against a vertical wall. The top of the ladder is 8 meter above the ground. When the bottom of the ladder is moved 2 meter farther away from the wall, the top of the ladder rests against the foot of the wall. What is the length of the ladder?
Let the length of the ladder be x meter. We have
8^{2} + y^{2} = x^{2} and (y + 2) = x
Hence, 64 + (x  2)^{2} = x^{2}
⇒ 64 + x^{2} — 4x + 4 = x^{2}
⇒ 68 = 4x ⇒ x = 17 meter
The length of a Rectangular plot is decreased by 33.33%. By how much % the breadth of the plot will be increased so that the area remains constant?
A man deposited a certain amount in a fixed deposit at r % p.α., interest being compounded annually. If the interest accrued for the fourth and fifth years are Rs 13310 and Rs 14641. what is the total interest accrued for the first three years?
Therefore, interests or 1^{st}, 2^{nd},3^{rd},4^{th} and 5^{th} years will be:
respectively.
Given, (1)
And (2)
(2) divided by (1), we get
∴ Sum of the first three years interests
= 10000 + 11000 + 12100
= Rs. 33100
A person earns Rs. 5000 as an interest in 5/2 years on a certain sum invested with a company at the rate of 10% per annum. Find the sum invested by a person in the company?
Hence
A is twice as fast as B and B is one third as fast as C. If they together can complete work in 30 days. In how many days, A, B and C individually can do the same work?
B, means their ratio is 2: 1.
Condition 2 B is one third as fast
as C, means their ratio is 1: 3. Then we can say, the ration of A, B and C is as follows
According to condition 1,
A : B = 2 : 1
According to condition 2;
B : C = 1 : 3
Thus, Ratio of A : B : C = 2 : 1 : 3
This ratio denotes the working efficiency of A, B and C which means;
A, B and C can do = (2 + 1 + 3 = 6) work/day
Now we can calculate total work i.e.
Total work = Total days × Per day work
Total work = 30 × 6 = 180
A can do the same work in;
= (Total work / Efficiency of A) = 180 / 2 = 90 days
B can do the same work in;
= (Total work / Efficiency of B)
180 / 1 = 180 days
C can do the same work in;
= (Total work / Efficiency of C) = 180 / 3 = 60 days
Thus, A, B and C can individually complete the same work in 90, 180 and 60 days, respectively.
Then a + b = 5 + 5 (∴ ab= 25 and a=b)
=10
Let observe the value of a,b,c
a + b + c = 1
1 = 1
put the value of a, b, c
(1 + a) (1 + b) (1 + c)
The price of a shirt is ₹260 but the shopkeeper successively discount 15% & 20%. The net sales price is subject to a sales tax of 5%. What does the buyer pay?
S.P= Rs.260  15% Rs.260
= 260  39 = 221
2^{nd} discount
S.P= Rs.221  20% Rs.221
= 221  44.2 = 176.8
= Rs.8.84
Amount paid by buyer
= Rs. 176.8 + Rs. 8.84
= Rs. 185.64.
A cistern from inside is 12.5 m long, 8.5 m broad and 4 m high and is open at the the ,,.top. Find the cost of cementing the inside of a cistern at Rs. 24 per sq. m
i.e, area of four walls + area of the floor
= 2 x (21) x 4 + (106.25)
= 274.25 m^{2}
∴ cost of cementing = 24 x 274.25 = Rs. 6582
A goat is tied to a pole fixed at a corner outside a room with a square base in a grass field. It is tied using a 14 m long rope. The side of the base of the room is 21 m. Find the area of the field over which the goat can graze (in sq. m).
Let the goat be tied at P.
The area over which the goat could graze = sum of the areas of the regions A and B = Area of a
sector of radius 14 m and central angle 270°
An article is sold at a loss of 10%. Had it been sold for Rs. 9 more, there would have been a gain of on it. The cost price of the article is :
S.P. at 10% loss = Rs 0.9x
According to question if it is sold by Rs 9 more there will be gain of 25/2 %
⇒ 180x + 1800 = 225x
⇒ 225x  180x = 1800
⇒ 45x = 1800
∴ x = Rs. 40
Alternate solution.
Let the CP of the article = 100
x x 22.5 = 9
Required,
⇒ CP x x
⇒
⇒ 40
A water tank is 6 m long, 5 m broad and 3.4 m high. Find the capacity of the tank in litres?
Volume = 6 x 5 x 3.4
Volume = 102 cu. Cm
1 cu. m = 100 cu. Cm
102 cu. m = 102 x 100
= 10200 cu. Cm
1000 cu. cm = 1 litre
1 cu. Cm =
10200 cu. cm = x 10200
= 10.2 liters
The ratio of the area of a square to that of the square drawn on its diagonal is :
Its area = a^{2}
Area of square on the diagonal = (√2a)^{2} = 2a^{2}
Required ratio
In the given figure, if ∠ABC = 90°, and ∠A = 30°, then ∠ACD=
= 90° + 30°
= 120° (exterior angle)
A certain sum of money yields Rs. 1261 as compound interest for 3 years at 5% per annum. The sum is
2^{x1} + 2^{x+1} = 320
2^{x 1} (1 + 2^{2}) = 320
2^{x1} = 320/5 = 64
2^{x1} = 2^{6}
x  1 = 6
x = 7
= sin^{2} 25° + cos^{2} 25° = 1
A is twice as good as workman as B. Together, they finish the work in 14 days. In how many days can it be done by each separately?
So A:B = 2:1
Also (A+B)'s oneday work = 1/14
To get days in which B will finish the work,
let's calculate work done by B in 1 day
=(1/14)x(1/3) = 1/42
So B will finish the work in 42 days and A will finish the work in 21 days.
There are several chickens and rabbits in a cage (with no other types of animals). There are 72 heads and 200 feet inside the cage. How many chickens and rabbits are there?
No. of rabbit = y
No. of legs = 2x + 4y = 200
x + 2y = 100 → 1
No. of heads = x + y = 72 → 2
1  2
y = 100  72 = 28
= 72  28 = 44
Hence the correct answer is option A
Find the next term in the given series?
BY, DW, GT, KP, ?
Read the following statements. The conclusions are given in the options, you have to read the conclusions and then decide which one of them among the options definetly does not follow.
Statements:
1. Some tables are chairs.
2. No Chair is a couch.
3. All sofas are couch.
All sofas are not chairs. So some sofas being not chairs is true.
So Option 1 is true.
Option 2 is also true
Option 3 is also true.
Option 4 is false.
Which of the following will be the mirror image of the given question figure (x), if the mirror is placed along the line MN. Choose the correct mirror image among (I), (II), (III) and (IV) given
If in a certain code, GLACIER is coded as 6293017 and FRUIT is coded as 47806, then how will FILTER be coded as in the same code?
And,
So, we get,
Harish is standing to the northwest of Kishore. Raju is standing to the southeast of Prem. Prem is standing to the southeast of Kishore. Manu is standing to the east of Kishore. What is the direction of Raju with respect to Harish?
Raju Southeast of Harish
In the following question, select the related numbers from the given alternatives.
9246 : 1926 ∷ 3968 : ?
4*6=24 → 24+2= 26
Becomes 1926.
Similarly,
3*9=27 → 27+1= 28
6*8=48 → 48+2= 50
Becomes 2850.
Arrange the given words in the sequence in which they occur in the dictionary and then choose the correct sequence.
1 Arraign 2 Arrest 3 Arrive 4 Array
In order to complete the set, which one of the following set of letters should be placed at the gaps sequentially?
_QOMKI_
A Faulty watch loses 5 minutes in 2 hours. It was set right at 6 o' clock in the morning. At 6 o' clock in the morning on the next day, what was the time shown in the faulty watch?
In 2 hours, the faulty watch loses 5 minutes
In 24 hours, the faulty watch loses 60 minutes or 1 hour
Time shown in the faulty watch will be 05:00 a.m.
In a certain code, BOTANY is written as Q3M. How is RHYTHM written in that code?
B (2) + O (15) = 17 → Q
T (20) + A (1) = 21 = 2 + 1 = 3
N (14) + Y (25) = 39 = 26 + 13 = M
So, R (18) + H (8) = 26 = Z
Y (25) + T (20) = 45 = 4 + 5 = 9
H (8) + M (13) = 21 → U
Hence, the required code is Z9U
Each question given below consists of a statement, followed by two arguments numbered I and II. Decide which of the arguments is a 'strong' argument and which is a 'weak' argument and choose the corresponding option as your answer.
Should the age of drinking be reduced from 21 years to 18 years?
I. Yes, because alcohol is not as harmful to health as smoking is.
II. Yes, because if an 18year old adult can have the right to vote and get married, he can also have the right to drink
Each question given below consists of a statement, followed by two arguments numbered I and II. You have to decide which of the arguments is a 'strong' argument and which is a 'weak' argument.
Statement: Should luxury hotels be banned in India?
Arguments:
I. Yes. They are places from where international criminals operate.
II. No. Affluent foreign tourists will have no place to stay.
P remembers that his joining date in office is after 18th October, but not on any oddnumbered date. Q remembers that P is joining in October. R, who is P's friend remembers that P is joining before 21st October. Then, on which date is P joining?
Identify the diagram that best represents the relationship among the given classes.
Human, children, Male
In the following question, select the odd letters from the given alternatives.
G(7) N(14) O(15)
D(4) H(8) I(9)
I(9) R(18) S(19)
M(13) Y(25) Z(26)
Select the related letters/words/numbers from the given alternatives
AK : FP : EO : ?
8x4x2=64
4x4x4=64
2x8x4=64
6x2x4=64 not 48
In the following question, a figure (x) is given having a pattern, whose two portions marked as A and B are missing. Below the figure, four patterns (i), (ii), (iii) and (iv) are given, among which two of them fit A and B correctly. Select the option which matches both A and B correctly.
How many triangles are present in the given figure?
Find out from amongst the four alternatives as to how the pattern would appear on the sheet when the sheet is folded at the dotted line and is punched as given
Each question given below consists of a statement, followed by two arguments numbered I and II. Decide which of the arguments is a 'strong' argument and which is a 'weak' argument and choose the corresponding option as your answer.
Should sex education be made compulsory at all schools?
I. Yes, because parents are not capable of educating their children.
II. No, because this leads students astray.
In a queue, Tina is standing 8th from the left and 9th from the right. Pooja is to the immediate left of Sara, who is 8th towards the right of Tina. What is the position of Pooja from the right side?
Position of Sara =8+8=16th from left
Position of Pooja =161=15th from left
Position of Pooja from right =1615+1=2 from right
Three positions of a same cube are shown below. Which number appears on the face opposite to '5'?
We get 
C is the wife of B and B is the son of K. F is the brother of C, and A is the nephew of F. J is the father of F. Q is the daughter of F. How is C related to K?
National Education Day is celebrated on November _____.
National Science Day is celebrated every year on:
India has been elected as a Member of the ________ for another 4year term (20192022) recently.
The third edition of Indian Ocean Conference was held in 
literature, was Persian, albeit the language of religion was Arabic.
Which of the following crops are suitable for growing on black soil?
The sultan who described himself as “The second Alexander”(SikanderieSani’ ) was?
Sher Shah defeated Humayun and captured Gaur in the battle of:
How many National Parties are there in India(as on Jan 2019)?
The addition of a neutron to the nucleus of an atom
Which catalyst is used in conversion of sucrose into glucose and fructose?
Which of the following belong to phylum coelenterata?
What happens If an egg with shell is placed in a microwave oven?
When a Red Glass Plate and a Blue Glass plate combined, it will transmit ______?
If a bus starts from rest, then the passenger will ….?
Which of the following enzyme is not secreted in the small intestine?
The unit of Young’s Modulus of Elasticity in MKS system is?
Choose the one which is different or odd from the following.
A person bakes a cake. It turns out to be hard and small in size. Which ingredient has he forgotten to add that would have caused the cake to rise and become light?
Why the clear nights are cooler than the cloudy nights?
Melting point of cast iron (in ∘C ) is in the range of
Where shall the water boil at the lowest temperature?
Which of the following type of rays does NOT penetrate Earth's atmosphere?
Quartz is a metamorphic rock. What is the chemical name of quartz?
The resistance of a conductor is inversely proportional to:
Graphite and heavy water are two common moderators used in a nuclear reactor. The function of the moderator is to:
Which of the following substance is also called brain alcohol?
Which mosquito is responsible for Japanese encephalitis?
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