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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
⇒ (∆BDE) = 1/4 × (∆ABC)
And ∆BDE = ∆PED
[ ∵ both triangles lie on the same base DE and between two parallel lines DE and BP.]
∴ (∆PED) = 1/4 × (∆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 △ABC
and BD be perpendicular on hypotenuse AC then
1 / P^{2} = 1 / 6^{2} + 1 / 6^{2}
P^{2} = 6^{2} / 2 => p = 3√2.
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?
×3 ↓ : ↓ ×3 → time
Length = 9m : 12m
Time = D / S = L_{1} + L_{2} / S_{1} + S_{2} = 9 + 12 / 4 + 3 = 2 / 14 + 3
= 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 = 1/5
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.
Q. 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.
Q. 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 × 5 / 18m/sec.= 50 / 3m⋅/sec
T = 30sec
Length = S × T = (50 / 3 × 30)m
I = 500m
The supplement of an angle is onefourth of itself. Determine the angle and its supplement.
Then, the measure of its supplementary angle is (180 − x^{∘}). It is given that, 180^{∘ }− x = 1 / 4 × x
⇒ (180^{∘} − x) = x
⇒ 720 − 4x = x
⇒ 5x = 720
⇒ x = 144
Thus, the measure of the angle is 144^{∘} 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 + 3 x 5 = 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?
33.33 = 1 / 3 → 1 / 2 = 50% [1 / 2 = 1 / 3  1]
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?
I, I(1 + r/100)^{1}, I(1 + r/100)^{2}, I(1 + r/100)^{3}, I(1 + F/100)^{4} respectively
Given, (1 + r/100)^{3} = 13310
and (1 + r/100)^{4} = 14641
2) divided by (1), we get (1 + r/100) = 14641 / 13310 = 1.1
∴ Sum of the first three years interests = 13310 / (1.1)^{3} + 13310 / (1.1)^{2} +13310 / (1.1)^{1}
= 13316 / 1.331 + 13316 / 2.21 + 13316 / 2.1
= 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
1  1/2 = 1/2
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 ratio 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
If a + b + c = 1, then Find (1 + a) (1 + b) (1 + c)?
a = 1 / 3, b = 1 / 3, c = 1 / 3
a + b + c = 1
1 / 3 + 1 / 3 + 1 / 3 = 1
3 / 3 = 1
1 = 1
put the value of a, b, c (1 + a)(1 + b)(1 + c)
(1 + 1 / 3)(1 + 1 / 3)(1 + 1 / 3)
4 / 3 × 4 / 3 × 4 / 3
64 / 27 = 2.37
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?
= 260 − 39 = 221
2^{nd} discount
S.P = Rs.221 − 20%Rs.221
= 221 − 44.2 = 176.8
Sales tax = 5 / 100 × 1768 / 10
= 8840 / 1000
= 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 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 22 x 1/2 % on it. The cost price of the article is :
S.P. at 10% loss = Rs0.9x
According to question if it is sold by Rs 9 more there will be gain of 25 / 2%
0.9x + 9 = x ×
0.9x + 9 = 225x / 200
⇒ 180x + 1800 = 225x
⇒ 225x − 180x = 1800
⇒ 45x = 1800
∴ x = Rs.40
Alternate solution, Let the CP of the article =100
x × 22.5 = 9
x = 9 / 22.5
= 18 / 45
Required, ⇒ CP × x
⇒ 100 × 18 / 45
⇒ 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 = 102cu.cm
1cu.m = 100cu.cm
102cu.m = 102 × 100
100cu⋅cm = 1 litre
1cu⋅cm = 1 / 1000
10200cu⋅cm = (1 / 1000) × 10200
= 10.2 litres
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 = a^{2} / 2a^{2} = 1 : 2
If secθ + tanθ = p, the p^{2}  1 / p^{2} + 1 = ?
In the given figure, if ∠ABC = 90°, and ∠A = 30°, then ∠ACD =
= 90° + 30°
= 120° (exterior angle)
A certain sum of money yields ₹ 1261 as compound interest for 3 years at 5% per annum. The sum is
2^{x − 1}(1 + 2^{2}) = 320
2^{x − 1} = 320
2^{x − 1} = 320 / 5 = 64
2^{x − 1} = 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 the 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 : ?
4 x 4 x 4 = 64
2 x 8 x 4 = 64
6 x 2 x 4 = 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?
Triangles are  ABC, CLM, CKJ, DEF, GHI, GNO.
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 right of Tina. What is the position of Pooja from the right side?
Position of Sara = 8 + 8 = 16th from left
Position of Pooja = 16  1 = 15th from left
Position of Pooja from right = 16  15 + 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 wife of B and B is son of K. F is brother of C and A is nephew of F. J is father of F. Q is daughter of F. How is C related to K?
National Education Day is celebrated on November _____.
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 
As soon as the Ghurids invaded northern India in the 12th century, and doubtlessly with the founding of the Delhi Sultanate. The official language of the Ghurids, Delhi Sultanate, the Mughal Empire, and their successor states, as well as the cultured language of poetry and 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)?
Which of the following plant hormones plays main role in separation of leaves?
Florigens  blooming of flowers
Ethylene  Ripening of fruits
Cytokinin  Cell division
Which of the following falls under the category of Abiotic components of environment?
Abiotic factors refer to nonliving physical and chemical elements in the ecosystem.
Biotic factors are living or onceliving organisms in the ecosystem.
A car accelerates to a speed of 17 m/s over a distance of 25 m. The uniform acceleration of the car will be ________.
S = 25 m
v_{f}^{2} = v_{i}^{2} + 2as
(17)^{2} = (0)^{2} + 2(a)(25 m)
289 = 0 + (50)a
289 = (50)a
a = 289/50
a = 5.78 m/sec^{2}
Mass numbers of some common elements
Neon 20
Sodium 23
Silver 108
Which of the following is often regarded as the purest form of carbon?
Which is the second largest gland of the Human body?
____________ states that, properties of elements are a periodic function of their atomic weight.
____________ is the process in which a material changes from a frozen solid to a gas without passing through the intermediate liquid state.
Sublimation is the process in which a material changes from a frozen solid to a gas without passing through the intermediate liquid state.
Condensation is the process by which water vapor in the air is changed into liquid water.
Evaporation is the process by which water changes from a liquid to a gas or vapor.
Decantation is a process to separate mixtures by removing a liquid layer that is free of a precipitate.
Which of the following statements in the context of electromagnetic waves is/are not true?
Electromagnetic waves propagate with the speed of light.
Transmission of energy through a vacuum or using no medium is accomplished by electromagnetic waves. It is caused by the oscillation of electric and magnetic fields.
Which of the following is a watersoluble vitamin?
Vitamin B is a watersoluble vitamin. A vitamin that can dissolve in water. Watersoluble vitamins are carried to the body's tissues but are not stored in the body.
Vitamin A, D, E & K are fat soluble vitamins.
One mole of oxygen atoms contains __________ oxygen atoms.
One mole of oxygen atoms contains 6.023 X 10^{23} oxygen atoms.
A mole corresponds to the mass of a substance that contains 6.023 x 10^{23} particles of the substance. The mole is the SI unit for the amount of a substance and its symbol is mol.
Definition of mole 1 mol of carbon12 has a mass of 12 grams and contains 6.022140857 x 10^{23} of carbon atoms.
A player serves a table tennis ball with a velocity of 25 m/s. If the ball has a mass of 300 g, what is the kinetic energy (KE) in Joule of the ball?
Velocity(V) = 25 m/s
Mass(M) = 300g or 0.3 Kg
K.E = 1/2 M x V^{2}
K.E = 1/2 x 0.3 x 25^{2}
K.E = 93.75 J
1 Kilowatthour = 3.6 x 10^{6} joule
Momentum is the property of a moving body is defined as the product of mass & _________.
Momentum is the property of a moving body & is defined as the product of mass & velocity. The standard unit of momentum magnitude is the kilogrammetre per second.
Newton's second law , illustrates the concept of momentum i.e. The rate of change of momentum of an object is directly proportional to the resultant force applied and is in the direction of the resultant force. The resultant force is equal to the rate of change of momentum.
Hydraulic press & Hydraulic brake work on the principle of _________.
Oiled paper is an example of ____________ material.
Kepler's ___________ law states that square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.
First law i.e. Law of Orbits: All planets move in elliptical orbits, with the sun at one focus.
Second Law i.e. Law of Areas: A line that connects a planet to the sun sweeps out equal areas in equal times.
For a nonpolar covalent compound, the value of electronegativity is ______.
A fog is an aerosol of liquid particles, in particular a low cloud.
Aerosols are dispersions in gases. In aerosols the particles often exceed the usual size limits for colloids. If the dispersed particles are solid, it is called aerosols of solid particles, if they are liquid, they are called aerosols of liquid particles.
____________ do not fall under the category of Metals.
Lotus  Nelumbo nucifera
Rice  Orzya Sativa
Tiger  Panthera tigris
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