Wednesday 18 September 2019

DAILY TEN WORDS HIGH-FREQUENCY WORDS IN ENGLISH - Z - LIST - COMPILED BY - ZENMURALI

11. zero-based (adj) according to present needs only, without reference to previous practice [v zero-base]
தற்கால தேவைகளை கொண்ட மற்றும் முன்னரே உள்ள நடைமுறையின்படி அல்லாமல்
# Finance Minister presented the zero-based budget in the parliament.

12. zero hour (n) time fixed for the operations to begin; the time set for the start of an action or operation
ஒரு செயலையோ மற்றும் நடவடிக்கைகளையோ தொடங்க ஒதுக்கப்படும் காலம்
# The opposition party raised questions in the parliament during zero hour.

13. zero rated (adj) on which no VAT (Value Added Tax) charged [v – zero rated]
மதிப்புக்கூட்டு வரியில்லாமல் நேரடியாக விளையும் இடங்களில் கொள்முதல் செய்திடும் விலை
# Zero rated cost of the tea leafs have gone drastically low because of good rains in the areas of cultivation.

14. zero-sum (n) denoting a game or situation in which whatever is gained by one side is lost by other
விளையாட்டில் அல்லது சந்தர்ப்பத்தில் ஒருவருக்கு ஆதயமாகவும் மற்றவருக்கு நஷ்டமாகவும் இருப்பதை குறித்தல்
# It is a zero-sum game that the employees getting pay rise after their prolonged strike is a loss of profit to the employer.

15. zero tolerance (n) extreme intolerance of antisocial behavior (usually by an uncompromising application of the law)
சகித்துக்கொள்ளமுடியாத சமுகவிரோத நடவடிக்கை
# Ragging will be dealt with zero tolerance in educational
institutions.

16. zest (n) eagerness, excitement, satisfaction [adj zestful, adv – zestfully]
ஆர்வம், மன எழுச்சி, மனநிறைவு
# Youngsters celebrated Valentine’s Day with great zest.
Ant. dullness, distaste, displeasure

17. zeugma (n) figure of speech using a verb or adjective with two nouns [adj – zeugmatic]
இரண்டு பெயர்சொற்களை உடைய வினைச்சொல் அல்லது அடைமொழி சொல் கொண்ட வாக்கியம்
# She celebrated her birthday by giving sweets and saying sweet words to her boyfriend is an example of zeugma.

18. zigzag (n) a line or pattern which looks like a Z [adj – zigzag, v – zigzag, adv – zigzag]
வளைந்து வளைந்து செல்தல், கோணல் மாணல்
# Snakes always move in a zigzag manner.
Ant. straight

19. zilch (n) zero, nil, nothing
பூஜ்ஜியம், ஒன்றும் இன்மை, ஒன்றுமில்லாத நிலை
# My grandmother has zilch knowledge about computers.
Ant. some

20. zillion (n) indefinite large number [adj – zillion]
அறுதியற்ற பெரிய எண்
# Our brain has over a zillion neurons.

Monday 2 September 2019

DAILY TEN WORDS HIGH-FREQUENCY WORDS IN ENGLISH - Z - LIST - COMPILED BY - ZENMURALI

1. zany (adj) strange, surprising or uncontrolled in a humorous way [n zany, zaniness, adv – zanily]
வித்தியாசமாக, ஆச்சரியம் அல்லது அடக்கமுடியாத நகைச்சுவைகொண்ட
# Charlie Chaplin acted in zany movies.
Ant. serious

2. zap (v) to attack or destroy something in a fast and powerful way; cook or heat in a microwave oven [n zap, zapper]
அதிவேகமாக சக்தியுடன் தாக்கி அழி; மைக்ரோ ஓவனில் சமை அல்லது சூடுபடுத்து
# I zapped the snake with big log.
Ant. create, start, begin

3. zeal (n) great enthusiasm or eagerness [adj zealous, adv zealously]
அதீத உற்சாகம் அல்லது பேராவல், பெரும் ஆர்வம்
# In any venture If you have zeal and enthusiasm you are sure to win.
Ant. indifference, apathy, disinterest

4. zealot (n) a fanatic and uncompromising follower of religion or policy
வெறித்தனமாக மற்றும் சமரசத்திற்கு இடமில்லாதபடி மதத்தையோ அல்லது கொள்கையையோ பின்பற்றுபவர்
# Zealots are experts in brain washing the common people to follow them.
Ant. indifference, dispassion 

5. zebrine (adj) resembling a zebra
வரிக்குதிரை தோற்றமுடைய
# The zebrine T-shirts are available in the shopping mall.
Ant. plain, simple

6. zebra crossing (n) a street crossing marked with white stripes
பாதசாரிகள் கடக்கும் இடம்
# To prevent accidents, walk through the zebra crossing to cross the road.

7. zeitgeist (n) the trend of thought and feeling in a period, the spirit of the time; the spirit characteristic of an age or generation
தற்காலய தலைமுறைகளின் உணர்வுகளை பிரதிபலிக்கும் போக்கு 
# Sci-Fi movies are the zeitgeist in recent times.

8. zenith (n) peak, highest point, culmination [adj zenithal]
உச்சி
# A politician may reach either zenith of fame or a fall in career during the different phases of his life.
Ant. lowest point

9. zenana (n) apartments in which women are secluded
உயர்குடிப் பெண்களின் அந்தப்புரம், பெண்களை மற்றவரிடமிருந்து தனிமைப்படுத்திவைக்கும் அறைகள்
# In olden days, there is a custom in India that women were kept in the zenana after their widowhood.

10. zephyr (n) gentle wind, light breeze
இதமான காற்று, இதமான தென்றல்
# The old age people prefer places where they can feel and enjoy the zephyr.
Ant. gust, windstorm, tornado

Friday 23 August 2019

TRIGONOMETRICAL IDENTITIES - PART – 100

134. sin A cos A – 
[sin A cos (  – A) cos A / sec (  – A)] - 
[cos A sin (  – A) sin A / cosec (  – A)] = 0

TRIGONOMETRICAL IDENTITIES - PART – 99

133. cosec Ꝋ - sin Ꝋ = m, sec Ꝋ - cos Ꝋ = n
Show that (m2n)2/3 + (mn2)2/3 = 1

TRIGONOMETRICAL IDENTITIES - PART – 98

132. Prove that :
sin A / sin (90 – A) + cos / cos (90 – A)
=
sec A cosec A

TRIGONOMETRICAL IDENTITIES - PART – 97

131. Solve for x, 0 ≤ x ≤ 90
(i) 3 tan2 2x = 1
(ii) tan2 x = 3 (sec x – 1)

TRIGONOMETRICAL IDENTITIES - PART – 96

130. Solve for x, 0 ≤ x ≤ 90
(i) 4 cos22x – 3  = 0
(ii) 2 sin2x – sin x  = 0

Thursday 22 August 2019

TRIGONOMETRICAL IDENTITIES - PART – 95

129. If cos A = 9/ 41; find the value of
(1 / sin2 A) –  (1 / tan2 A)


TRIGONOMETRICAL IDENTITIES - PART – 94

128. If (2 cos 2 A – 1) (tan 3 A – 1) = 0; find the  values of A.   

TRIGONOMETRICAL IDENTITIES - PART – 93

127. If tan A = 1 and tan B = √3; evaluate
(i) cos A cos B – sin A sin B
(ii) sin A cos B + cos A sin B

TRIGONOMETRICAL IDENTITIES - PART – 92

126. Find   ; find A, if :
(i) sin A / (sec A – 1) + sin A / (sec A – 1) = 2      

TRIGONOMETRICAL IDENTITIES - PART – 91

125. Find   ; find A, if :
(i) cos A / (1 – sin A) + cos A / (1 + sin A) = 4

Friday 2 August 2019

TRIGONOMETRICAL IDENTITIES - PART – 90

Find A, if A is less than zero and A is less than 90 degrees.
(1) cos2 A – cos A = 0
(2) 2 cos2 A + cos A – 1 = 0

TRIGONOMETRICAL IDENTITIES - PART – 89

Find A, if A is less then are equal to zero and A is greater than are equal to zero.
(1) 2 cos2 A – 1 = 0 , (2) sin 3 A – 1 = 0 and 
(3) 4 sin2 A – 3 = 0

Wednesday 31 July 2019

TRIGONOMETRICAL IDENTITIES - PART – 88

122. If 4 cos2 A – 3 = 0 then prove that
(i) sin 3 A = 3 sin A – 4 sin3 A.
(ii) cos 3 A = 4 cos3 A – 3 cos A

TRIGONOMETRICAL IDENTITIES - PART – 87

121. (i) If 2 sin A – 1 = 0, 
show that sin 3A = 3 sin A – 4 sin3 A.
(ii) If 4 cos2 A – 3 = 0, 
show that cos 3A = 4 cos3 A – 3 cos A.


TRIGONOMETRICAL IDENTITIES - PART – 86

120. If tan A = n tan B and 
sin A = m sin B, 
prove that: cos2 A = (m2 – 1) / (m2 + 1).

Tuesday 30 July 2019

Monday 29 July 2019

TRIGONOMETRICAL IDENTITIES - PART – 82

116. If x = r cos A  cos B, 
y = cos A sin B and then 
z = r sin A, then prove that 
x2 + y2 + z2 = r2

TRIGONOMETRICAL IDENTITIES - PART – 81

115. If sin A + cos A  = m and
sec A + cosec A = n show that 
n (m2 – 1) = 2 m

TRIGONOMETRICAL IDENTITIES - PART – 80

114. If x = r sin A  cos B, 
y = sin A sin B and then 
z = r cos A, then prove that 
x2 + y2 + z2 = r2

TRIGONOMETRICAL IDENTITIES - PART – 79

113. If m = a sec A + b tan A and 
n = a tan A + b sec A, then prove that 
m2 – n2 = a2 – b2

TRIGONOMETRICAL IDENTITIES - PART – 78

112. If p = sin A + cos A and 
q = sec A + cosec A, then prove that 
q (p2 – 1) = 2 p

Saturday 27 July 2019

TRIGONOMETRICAL IDENTITIES - PART – 77

111. If x cos A + y sin A = m and 
            x sin A – y cos A = n, then prove that: 
            x2 + y2 = m2 + n2


TRIGONOMETRICAL IDENTITIES - PART – 76

110. If x = a sec A cos B, 
y = b sec A sin B and z = c tan A 
show that
x2/a2 + y2/b2 + z2/c2 = 1


TRIGONOMETRICAL IDENTITIES - PART – 75

109. If tan A + sin A = m and tan A – sin A = n; 
prove that
 m2 – n2 = 4 (mn)1/2

Friday 26 July 2019

TRIGONOMETRICAL IDENTITIES - PART – 74

108. [(cos A) / (cosec A + 1)]
+
[(cos A )/ (cosec A –  1)]
= 2 tan A

TRIGONOMETRICAL IDENTITIES - PART – 73

107. [cot A – tan A]  [(2 cos^2 A – 1) / (sin A cos A)]


TRIGONOMETRICAL IDENTITIES - PART – 72

106. (cosec A + 1) / (cosec A – 1)
=
(sec A + tan A)2

TRIGONOMETRICAL IDENTITIES - PART – 71

105. (sin Ꝋ + 2sec Ꝋ)2 + (cos Ꝋ + cosec Ꝋ)2
=
(1 + sec Ꝋ cosec Ꝋ)2


TRIGONOMETRICAL IDENTITIES - PART – 70

104. (sin Ꝋ – 2sin3 Ꝋ) / (2cos3 Ꝋ – cos Ꝋ)
=
      tanꝊ   
                         

TRIGONOMETRICAL IDENTITIES - PART – 69

103. (cosec A – sin A) (sec A – cos A)
=
1 / tan A + cot A


TRIGONOMETRICAL IDENTITIES - PART – 68


TRIGONOMETRICAL IDENTITIES - PART – 67


TRIGONOMETRICAL IDENTITIES - PART – 66


TRIGONOMETRICAL IDENTITIES - PART – 65


TRIGONOMETRICAL IDENTITIES - PART – 64


TRIGONOMETRICAL IDENTITIES - PART – 63


TRIGONOMETRICAL IDENTITIES - PART – 62




TRIGONOMETRICAL IDENTITIES - PART – 61

95. (sinꝊ – cosꝊ + 1) / (sinꝊ + cosꝊ – 1)
=
(1/ (secꝊ – tanꝊ)  

TRIGONOMETRICAL IDENTITIES - PART – 60

94. (cos2 A + tan2 A – 1) / sin2 A = tan2

TRIGONOMETRICAL IDENTITIES - PART – 59

93. [(1 + cot A) / cos A] + [(1 + tan A) / sin A]
=
2 (sec A + cosec A)