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If sinθ + sin^{2}θ = 1, then the value of cos^{12}θ + 3 cos^{10}θ + 3 cos^{8}θ + cos^{6}θ – 1 is:
sinθ + sin^{2}θ = 1 ⇒ sinθ = cos^{2}θ
Given : cos^{12}θ + 3 cos^{10}θ + 3 cos^{8}θ + cos^{6}θ–1
= (cos^{4}θ + cos^{2}θ)^{3} – 1 = (sin^{2}θ + cos^{2}θ)^{3} – 1 = 1 – 1 = 0
The height of an equilateral triangle is 4√3 cm, then what will be the area of the equilateral triangle?
Height = 4√3 cm
Thus, side of equilateral triangle = 8 cm.
Area of equilateral triangle
If 10 men can do ork in 6 days and 15 women can do the same in 5 days, Then 8 men and 5 women can together do the work in :
If the work is to be finished in 5 days, number of women required = 15
If the work is to be finished in 6 days, number of women required =[15×5]/6 = 25/2
So that 10 men = 25/2 women
or 5 women = 4 men
8 men + 5 women = 8 men + 4 men = 12 men
Now 10 men can finish the work in = 6 days
∴ 12 men can finish the work in [6×10]/12=5 days
The average of two numbers is 8 and that of another three numbers is 3. The average of these five numbers is
Which of the following is obtained after the rationalization of the expression 1/(√2+√3+√5) ?
If sin θ=8/17, where 0^{o}<θ<90^{o}, then tan θ+sec θ is:
Using pythagorus theorem
AC^{2} = AB^{2} + BC^{2}
(17)^{2} = AB^{2} + (8)^{2}
AB^{2} = 289  64
AB =
AB = 15
OA, OB, OC are 3 lines in a plane which meet at O. If the angles ∠AOB, ∠BOC, ∠COA are 2x, 5x, 8x respectively (where x is a positive angle), then x equals:
2x + 5x + 8 = 360°
15x = 360°
The value of tan 31° tan 33° ... tan 59° is equal to:
tan 31°. tan 32°. tan 33° .... tan 59°
= tan 31°.tan 32°. tan 33° ... tan 57°. tan 58°. tan 59°
= tan 31º. tan 32°. tan 33° ... cot 33°. cot 32°. cot 31° = 1
[tan (90°θ) = cotθ and tanθ cotθ =1]
If x = 81, then the value of (x1/4 1) (x1/4+1) is:
A man sells two scooters for Rs.12000 each. He makes a profit of 20% on one and a loss of 20% on the other. The profit/loss, on the whole, is
SP1 = 12000
profit = 20%
∴ CP1 = 12000/120 x 100 = Rs.10,000
SP2 = 12000
Loss % = 20%
∴ CP = 12000/80 x 100 = Rs.15,000
Total CP = 25000
Total SP = 24000
Loss = Rs.25000 – Rs.24000 = Rs.1000
(or)
If the selling price of the two items is equal and the percentage of profit on one equals the percentage of loss on the other, then, the result is always loss and the percentage of loss is (loss%2/100).
Hence, in the present case, loss percentage = (20)2/100 percent = 4%.
Loss = 4/96 × Rs.24000 = Rs.1000
A train covers a certain distance in 50 minutes, if it runs at a speed of 48 km/hr on an average. The speed at which the train must run so that time of journey becomes 40 minutes?
Distance travelled in one hour = 48 km.
∴ Distance traveled in 50 minutes
The time to be reduced is 40 min.
Required speed
The pie chart given here shows expenditures incurred by a family on various items and their savings, which amount to Rs. 8,000 in a month.
Study the chart and answer the questions based on the pie chart.
How much expenditure is incurred on education?
The pie chart given here shows expenditures incurred by a family on various items and their savings, which amount to Rs. 8,000 in a month.
Study the chart and answer the questions based on the pie chart.
The ratio of the expenditure on food to the savings is:
Expenditure on food
=(120/300)×40,000= Rs. 16,000
Required ratio = 16000 : 8000 ⇒ 2 : 1
A solid metallic cone of height 10 cm and radius of base 20 cm is melted to make spherical balls each of 4 cm diameter. How many such balls can be made?
Volume of cone = 1/3πr2h
=(1/3)×π×(20)^{2}×10
=400×10
=(π/3)×4000=(4000/3)π
Volume of spherical balls = 4/3πr^{3}
=(4/3)×π×(2)^{2}
= 32/3π
∴ Spherical balls are formed from the cones.
∴ Total volume of all spherical cones = Volume of cones.
∴ No. of spherical balls = Volume of cone/Vol of 1 spherical ball
=4000/3
=32/3
=4000/32=125
Sum of the lengths of any two sides of a triangle is always greater than
The sum of the other two sides of a triangle is always greater than the third side.
If D is a point on the side AB of triangle ABC and DE is a line through D meeting AC at E such that ∠ADE = ∠ACB, then AB. AD is equal to:
A man can row 15 km per hour downstream and 9 km per hour upstream. The speed (in km/hour) of the boat in still water is:
The speed of the boat in still water = ½ (Rate downstream + Rate upstream)
The Speed of boat in still water
If x : y = 3 : 4, then the value of (5x  2y)/(7x+2y)
The sum of the numerator and denominator of the certain fractions is 8. If 2 is added to both the numerator and the denominator the value of the fraction increased by 4/35, then the fraction is:
Let fraction be x/y by given condition
The simple interest on a certain principal at the rate of 9.5 percent per annum is Rs 950 for two years. How much will be the additional interest on the same amount for the same period at the rate of 10.5 percent per annum?
S.I. = Rs 950, rate = 9.5%
time = 2 years
∴ sum =(950×100)/(9.5×2)=5000
If the rate of interest is 10.5% then.
Simple Interest=(5000×2×10.5)/100=Rs 1050
∴ additional interest due to change in the a rate of interest =Rs 100
If the angle of elevation of the top of a tower from two points at the distance x and y meter from the base and in the same straight line with it are complementary, then the height of the tower is?
Let AB be tower and C and D be the point of observation on AC.
< ac="" b="θ," />< adb="90" ="" θ,="" ab="h" />
AC = Xm, AD = Y m
So, CD = x  y m.
tan θ = h/x
Kamya purchased an item of 46,000 and sold it at a loss of 12%. With that amount she purchased another item and sold it at a gain of 12%. What was her overall gain/loss?
SP of first article = (46000×88)100=Rs. 40,480
SP for second article = (40480×112)/100=Rs. 45,337.60
∴ Loss = 46000  45337.60 = Rs. 662.40.
The owner of a cell phone shop charges his customer 23% more than the cost price. If a customer paid Rs.7,011 for a cell phone, then what was the cost price of the cell phone?
According to the question,
[(100+23)/100] × x = 7011
Or, x = (7011×100)/123 = 5700
The cost of an article was Rs.75. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the article is:
Effective decrease
= [20 – 20 – 20×(20/100)] % = 4%
∴ Present cost of the article = 96% of Rs.75
= (75×96)/100 = Rs.72
A rectangular box measures internally 1.6 m long, 1 m broad and 60 cm deep. The number of cubical block each of edge 20 cm that can be packed inside the box is:
Volume of rectangular box = 160 x 100 x 60 cm^{3}
and volume of one cubical block = 20 x 20 x 20 cm^{3}
∴ Required number of cubical block = (160×100×60)/(20×20×20) = 120 blocks
The diameter of the curved surface of a bucket are 28 decimeter and 14 decimeter and its height is 12 decimeter. Find its volume.
What will be the area of a rhombus, whose one side is 20 cm and one diagonal is 24 cm?
Diagnols of a rhombus intersect at right angles, so buy using pythagorus theorem,
X2 + 122 = 202
Therefore x =16, so diagonal = 2 x 16 = 32
Area of rhombus
The ratio of two unequal sides of a rectangle is 1 : 2. If its perimeter is 24 cm, then the length of diagonal in cm is:
Let the sides of rectangle be 2x, x cm
∴ Perimeter of rectangle = 2 (2x+x)
2 (2x+x) = 24
or 6x = 24
∴ x = 4 cm
hence length of diagonal = √[(2x)2+x2]
= √5x2
= √(5×16)
=√ 80
= 4√5
8 hours work of a woman is equal to 6 hours work of a man or 12 hours work of a boy. If 9 men working 6 hours daily can complete a work in 6 days, then in how many days 12 men, 12 women and 12 boys working 8 hours daily will complete the same work?
1 man done work in 6×6×9 hours
Since 8W=6M=12B
therefore 12M+12W+12B=27M
therefore 27 men will do work in (6×6×9/27)=12 hours
=12/8=1.5 days
In an examination, the average marks was found to be 50. For deducting marks for computational errors, the marks of 100 candidates had to be changed from 90 to 60 each and so the average of marks came down to 45. The total number of candidates, who appeared at the examination, was:
Let total number of candidates be x.
∴ 50x  30 × 100 = 45x
⇒ 5x = 3000
⇒ x = 3000/5 = 600
The series is given, with one term missing. Choose amongst the given responses and complete the series.
ABZ, CDY, EFX, GHW, __.
Z is the last letter as per alphabetical order.
C and D are 3rd and 4th letter respectively as per alphabetical order.
Y is the 2nd last letter as per alphabetical order.
Following the similar pattern, we get IJV.
Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in which of the statements are sufficient to answer the question. Choose your answer from the options based on this.
What can be the code for '12'?
I. If 'For your sake' is written as '13 12 21'.
II. If 'Don't leave for tomorrow' is written as '31 13 14 11'.
If ANIMAL is coded as 321435 and ELEPHANT is coded as 65609328, then METAL is coded as
M is coded as 4, E is coded as 6, T is coded as 8, A is coded as 3, L is coded as 5.
T is to the northeast of D and east of S. How is D related to H, if H is to the east of T?
In the following question, which one set of letters when sequentially placed at the gaps in the given letter series shall complete it?
a _ b d _ b _ c a b _ _ a b b _
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.
Arrange the given words in a meaningful sequence.
1. Kilogram
2. Gram
3. Ton
4. Quintal
Ton (1000 kgs) > Quintal (100 Kgs) > Kilogram (1000 grams) > Gram
Pointing to a photograph, Prakash said "Her father's only son is the father of my brother". How is that person in the photograph related to Prakash's father?
The person in the photograph is the sister of Parkash’s father.
In a certain code language, " play your good game" is coded as " ad pd cd md" , "play game run fast" is coded as " zd cd md td" , "run speed end game" is coded as " fd zd ld md". Find out what will be the code for " your good"?
" play your good game" is coded as " ad pd cd md"..(I)
"play game run fast" is coded as " zd cd md td"..(II)
"run speed end game" is coded as " fd zd ld md"..(III)
From I, and III, we get: game= md
Then, from II and I we get: play= cd
So, "your /good" = "ad/ pd" in any order.
Each question below is followed by two arguments numbered I and II. You have to decide which of the argument is a 'strong' argument and which is a 'weak' argument. 'Strong' arguments are those which are both important and directly related to the question. 'Weak' arguments are those which are of minor importance and also may not be directly related to the question.
Statement: Should young entrepreneurs be encouraged?
Arguments: I. Yes. They will help in the industrial development of the country.
II. Yes. They will reduce the burden on the employment market.
In each of the questions below are given some statements followed by some conclusions. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements:
All knots are ships.
No ship is a lip.
All lips are hips.
Conclusions:
I. Some hips are lips
II. No lip is the knot.
The statement can be represented as:
Both conclusions I and II follow
In the following question, select the number which can be placed at the sign of question mark (?) from the given alternatives.
We have,
In fig (i) → 7*8 + 3*2 = 56+6 = 62 → 6+2 = 8
In fig (ii) → 5*9 + 1*4 = 45+4 = 49→ 4+9 = 13
Similarly,
In fig (iii) → 6*7 + 3*5 = 42+15= 57 → 5+7= 12
In each of the questions below, one statement is given, followed by two conclusions which may or may not follow. From the options below, choose the one that reflects the correct choice of conclusion(s) that follows/follow.
National curriculums don't always work for rural and regional schools.
I. Curriculums should be tailormade for rural and regional schools as per their requirements and specifications.
II. While formulating national curriculums, authorities don't always take diversity of rural and regional schools into consideration.
Each of the questions below consists of a question and two statements given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.
Among M, P, K, J, T and W, who is lighter than only the heaviest?
I. P is heavier than M and T.
II. W is heavier than P but lighter than J who is not the heaviest.
from statement II, J>W>P
From both the statements, J>W>P> M, T. Therefore K is the heaviest. So J is lighter than only the heaviest.
The average of the position values is taken
SIT= (19+9+20)/2 =24
Select the suitable figure from the Answer figures that would replace the question mark (?).
Option a, c are incorrect as the object on top is wrongly drawn.
Option d is incorrect as object at the bottom is wrongly drawn.
Find out the odd term in the given series.
21,24, 81, 36, 6, 4
In the following question select the related word from the given alternatives.
Tuberculosis:Lungs ∷ Jaundice: ?
Z is older than only two persons. T is younger to both W and V. Y is younger to neither Z nor T, who is older than both S and Z. U is younger to at least three persons, none of whom is S. Who among the given persons is older than as many persons as is younger to?
We get,
___ < ___ < Z
Then,
T is younger to both W and V.
We get,
T < W, V
Since,
Y is younger to neither Z nor T, who is older than both S and Z.
We get,
___ < ___ < Z < T < W, V, Y
Only S and U are left and, we know,
U is younger to at least three persons, none of whom is S.
So, we get,
S < U < Z < T < W, V, Y
Hence, T is the one who is younger to as well as elder to same number of persons i.e. 3 persons.
In the following question, select the related numbers from the given alternatives.
7834 : 499 ∷ 5271 : ?
3*(41) = 9
We get, 499.
Similarly,
5*(21) = 5
7*(11) =0
We get, 50.
In each of the questions given below, there are two statements followed by an inference. Mark the correct option accordingly.
(a) Collection of frequent flyer miles is not useful at all.
(b) All the airlines have their respective frequent flyer programmes.
Inference: It's okay not to enrol under frequent flyer programmes of any airline.
Identify the diagram that best represents the relationship among the given classes.
Children, naughty, energetic
(1)
(2)
(3)
(4)
A series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series.
EHF, ILJ, MPN, ?
H+4 L +4 P +4 T
F+4 J +4 N +4 R
Which one set letters when sequentially placed at the gaps in the given letter series shall complete it?
MNO_MMN_OO_MM_NNN_OOO
BANKER is coded as SFLOBC, how CLERK will be coded?
Anantapur district in Andhra Pradesh is famous for
Highly specialized form of agriculture in which crops like coffee, tea and rubber are cultivated refer to:
Wrester Vinesh Phogat has become first Indian women athlete to win gold medal at the Asian Games 2018 held in Jakarta, Indonesia. She hails from:
Which state Government has signed a Memorandum of Understanding (MoU) with the All India Football Federation (AIFF)?
Tughlaqabad, a ruined fort situated in Delhi was built by Ghiyasuddin Tughlaq, the founder of the Tughlaq dynasty of the Delhi Sultanate.
Which from the following was authored by Mulk Raj Anand?
The sultans of which dynasty ruled for the largest time?
Ghujasuddin Tughlaq and ended with the last ruler Nasiruddin Mahmud in 1412 A.D. One of the most controversial ruler of Delhi belongs to this dynasty Mohammed bin Tughlaq, who had brought the idea of introducing token currency for the first time in India
Who had saved the Delhi Sultanate from Chengiz Khan?
Which of the following is located in Fatehpur Sikri?
Which of the following cities was not built by Firoz Shah Tughlaq?
The two elements that are frequently used for making transistors are ___ and ___.
What is the orbital speed of a satellite rotating near the surface of earth?
Which of the following has the smallest atomic radius?
What should be the Mach number of a body for being hypersonic?
Which of the following gases is lighter than air ?
The element required for Solar energy conversion is ____.
A moving body of mass 20 kg has 40 joules of kinetic energy Calculate its speed?
The behaviour of a perfect gas, undergoing any change in the variables which control physical properties, is governed by
Which of the following belongs to the 18th group of the Periodic Table?
In screw jack, effort required to lift a load is given by:
Which of the following is used for removing air bubbles from glass during its manufacture ?
Which one of the following is the reason for small liquid drops assuming spherical stage?
What changes will happen to a bowl of ice water kept at exactly zero degree Celsius?
If an object is placed at between F and 2F in front of a Convex Lens, then the image formed will be
Which one of the following denotes inertial mass?
A machine having an efficiency less than 50%, is known as:
L.P.G. is a hydrocarbon consisting of a mixture of:
In an atomic nucleus, neutrons and protons are held together by —
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