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00:00We have all the questions in the test, like 185, 141, 97, we are saying that the middle number is
00:09left and right, so 185, 97, plus 282, and 2 divided by 2, 141, so this is 96, so I
00:21will have a number in 89,
00:23plus 9, when I divide by 2, it will be 96, so we can multiply two by 2, how much?
00:32192, so in 89, what will we do?
00:35We can multiply it by 1, 0, 3, because in both sum of sum, it will be 192, 2 divided
00:41by 96, 5, 6, 15, 4, 9, 8, 7, 4, 14, then 2, 4, 5, 6, 30,
00:49OTAO 15
00:50Ngherde porne naisa 36
00:52OTAO 18
00:53Ngherde ya seven forza 28
00:55OTAO 14
00:56Ngherde ya two forza eight
00:58OTAO
00:58Qaf kardenge
00:59Or answer h gha bachyo
01:004 ho chayeg
01:02Chene shopkeeper
01:04Sold a fan at 10 percent profit
01:08Had he sold a fan at 20 percent profit
01:11He would have gained 50 more
01:13The cost price
01:14Dora see this is a trick
01:16Lagau do no profit
01:1720 bho or ten
01:19can be
01:20If you have two profits, you will have a difference.
01:24What do you mean?
01:24Difference
01:25More how much?
01:2750
01:2850
01:2810
01:29100
01:310
01:32Answer
01:33500
01:35Universal
01:3511
01:3612
01:3713
01:3714
01:3715
01:38C
01:40C
01:4114
01:4115
01:42Universal
01:4211
01:4512
01:4613
01:5120
01:5311
01:5610
02:0214
02:0415
02:0420
02:0515
02:0616
02:0816
02:0816
02:1018
02:1220
02:1315
02:1520
02:15minus four j and v2 equal to three i minus j are collinear if y equal to collinear
02:22کی شرط کیا ہوتی ہے دیکھو پہلے آئی کا coefficient لکھ دیا three
02:27j کا coefficient minus y نیچے والے آئی کا coefficient three j کا minus one
02:32اور اس کا determinant کس کے equal لیں گے ہم zero کے یہ multiply گیا
02:37minus three آگیا یہ multiply کریں plus three y آجائے گا three y
02:41three کے برابر ہوگا تو بچو y کس کے برابر آجائے گا one کے آجائے گا
02:46تو اس کا ملہب ہے vector collinear کے لئے ہیں شرط کیا ہے y کس کے
02:49برابر ہوگا بیٹا one کے برابر ہوگا کہہ رہے ہیں کہ x plus three
02:54coma minus five minus y برابر ہے three x plus two minus y plus five کے تو x y
03:00کے value نکالیں یار اگر x plus three برابر ہے three x plus two کے
03:06تو بہت آسان ہو گیا ہے یہاں سے two x برابر one کے ہو جائے گا x
03:11کی value ہو جائے گی half اب x کی value half کا ایک ہی option ہے تو
03:15لازمی بات ہے y بھی zero ہوگا بیسے کیسے نکالتے ہیں minus five
03:20plus y کو minus five minus y کے equal put کرتے ہیں لیکن صاف دیکھ رہے ہیں
03:26یہ کس کے برابر آئے گا zero کے اور zero ہی آئے گا پھر کہہ رہے ہیں
03:29if the shadow of four feet tall girl is four feet then angle of elevation
03:36ایک trick ہمیشہ ذہن میں رکھو اگر shadow اور person کی height سے
03:41ایسا ایک ہی angle پہ ہوتا ہے 45 degree یعنی pi by four
03:46if magnitude of mi plus m plus one j plus m minus one k is two
03:53تو m کی value چاہیے اب بچو اس کا مطلب کیا ہوتا ہے
03:57i کی اکوشن کی سکوئیر پلاس j کی اکوشن کی سکوئیر پلاس g کی اکوشن کی سکوئیر
04:02equal to two
04:04اب یہاں m سکوئر ہے
04:07اس کو a plus pOOl سک وئر کے فارمولے سے کھولیں گے
04:10اس کو a minus pOOl سکوئر کی
04:12جس میں یہاں سے minus two m اور plus two m کٹ جائے گا
04:15یہاں سے plus one plus one two اور three m سکوئیر
04:19اس کے بعد بچوئے سکوئریں بہت سائد کریں گے
04:21جس سے three m سکوئر plus two equal to four آ جائے گا
04:25Now, if you take this plus 2, then 3m squared is 2.
04:30If you take this plus 3m squared, then divide it.
04:34Then, this will be plus minus 2 root 3.
04:39The answer will be option D.
04:42That's great.
04:43This is the main concept of the main concept.
04:47This is minus 2m plus 2m.
04:50This is the solution.
04:51This is the solution.
04:52If you take this plus 2m, then you will find the solution.
04:55Find the equation of the normal to the ellipse.
04:583x squared plus y squared equal to 57 at point 2,3.
05:02So, look at this point, which equation will satisfy?
05:05It will be possible.
05:07Then, length of r cut off of a circle of radius 6 cm by a central angle of.
05:19c is minus 3x.
05:21Let's not do this.
05:22Let's go back to this point 2p upon 3 radian.
05:24S is equal to r theta.
05:26x is 6 cm.
05:28Here we will have 2pi.
05:29Now, we will add 2pi.
05:31into 245
05:33and we can do this
05:35trick
05:35equation of
05:37the hyperbola
05:413x square minus
05:434y square equal to 12
05:44so this point
05:46if you can do this formula
05:49x is 4y minus 3
05:51then this one will satisfy
05:53okay
05:54definition
05:55and here
05:57the question of the straight line
05:59passing through origin
06:01perpendicular to y axis
06:03perpendicular to y axis
06:05parallel to x axis
06:06in two words
06:09if perpendicular to x axis
06:12then y equal to 0
06:13because passing through origin
06:14if theta
06:18between 90 and 360
06:20theta equal to cos inverse 2
06:22then theta
06:22here cos
06:242 upon 3
06:28which means
06:29sine value
06:29root 3 upon 2
06:31reciprocal
06:31when it is 60 and 120 degree
06:35here
06:3690 to 360
06:37so of course
06:4060
06:40120
06:42because sine
06:44root 3 by 2
06:46then
06:46cos
06:471
06:4720
06:472 upon root 3
06:50answer
06:50120
06:52now
06:53a, d, i, i, 40
06:54b, 20, c, 20
06:56so of course
06:58divide
06:59two
06:5940
07:00area
07:01formula
07:0340
07:05minus
07:0630
07:06cancel
07:07answer
07:080
07:09then
07:10a, 3
07:12b, 4
07:12c, 5
07:13mid
07:13right
07:162
07:17middle
07:18x
07:180
07:24term
07:25also
07:25here
07:26here
07:26dot
07:30to find
07:31that answer
07:32is
07:32and
07:34the right
07:35trick
07:36this is a short cut which is a formula because it is very important.
07:42minus 2 cos x upon 2 minus 2 sin x upon 2.
07:46In this paper, sometimes we have to take minus 2 common.
07:50cos x upon 2 plus sin x upon 2.
07:53Last time this form came out.
07:55This one plus sin x upon 2,
07:58minus 2 cos x,
08:00but minus 2 sin x upon 2,
08:02plus 2 sin x upon 2.
08:04This is a good idea.
08:06So, that is the sequence.
08:08k minus 1, k plus 3,
08:103, minus 1, form and arithmetic progression.
08:13Arithmetic progression is an answer.
08:15Second term minus first term is equal.
08:18Third term minus second term.
08:20Second term is k plus 3.
08:23First term is k minus 1.
08:26Then, third term minus 2.
08:30Well, bachos,
08:31so,
08:31k minus k cancel.
08:33Plus 3, minus 1.
08:344 bachos.
08:353 ke minus k,
08:372 ke bachos.
08:37And this minus minus 2.
08:39This minus 2 is true.
08:41Then, plus 2 is true.
08:43If it is true,
08:44then, k ke ke ajaega,
08:453 ke ajaega.
08:46And this is my answer.
08:47The answer is value of limit 2.
08:50Here is 0.
08:514 e ki power 2t, dt.
08:55So,
08:56pyaare bachos.
08:57First,
08:58when we take limits,
09:00it will be integration.
09:02It will be 4,
09:03e ki power 2t,
09:042t,
09:052t,
09:062t,
09:074 upon 2,
09:092,
09:092,
09:092,
09:092,
09:092,
09:102,
09:12e ki power 4,
09:14e ki power 0.
09:16e ki power 0,
09:18e ki power 0,
09:19o ande ki power 0,
09:19one bu Planet 0 0.
09:20powerful.
09:21Pop auspion and point 0 to 8.
09:24It will be powerful.
09:285S where 3 is 3 Symmel
09:30function
09:32now
09:34here
09:35multiply
09:36divide
09:36root
09:37here
09:45here
09:46here
09:59multiply
10:00here
10:02here
10:02the figure
10:05a b equal to a c and b c greater than a b
10:08this is great
10:10state which of the following is true
10:13x greater than 60
10:15y less than x
10:17y greater than 60
10:19this diagram
10:21this diagram
10:22and this y
10:24if this side b c
10:26is a b
10:27and this is where
10:29one it is
10:30distance
10:31is
10:34about
10:35quantity
10:36because
10:41this angle
10:42is
10:45is
10:48greater
10:49since
10:51this
10:51circle
10:51is
10:51bigger
10:52to
10:52so this angle will be bigger
10:54so this will be correct
10:57which option will be correct
10:58x greater than 60 statement
11:01this structure
11:02what name is
11:04this one
11:06any salt
11:07any salt
11:12and this one
11:14benzo nitrile
11:16benzo nitrile
11:17pass paper
11:18find equation of straight line
11:21passing therow origin
11:23and perpendicular to y axis
11:25when passing therow origin
11:27this one can be
11:29perpendicular to y axis
11:31this one
11:34this one
11:34this one
11:38a
11:39answer
11:40x equal to 0
11:41find equation of circle whose center is at
11:452,0
11:45and radius 3 unit
11:48center 2,0
11:50x minus h square plus y minus k square equal to r square
11:55this one can solve
11:56h2
11:56r3
11:58final answer
12:00equation of ellipse
12:04relate to
12:07its center
12:08at origin
12:10and foci
12:10foci
12:11are 2
12:11foci
12:13c
12:13a
12:14multiply by e
12:15e
12:16e
12:17e
12:17e
12:17e
12:18e
12:18e
12:18e
12:18e
12:18e
12:19e
12:19e
12:19e
12:19e
12:19e
12:21e
12:27and
12:28of
12:29e
12:44eご
12:46the
12:462020
12:47s
12:47s
12:49of the parabola answer option
12:51then point dividing
12:53a,2
12:54then point ratio
12:57formulae so answer
12:583,0
13:00then equation of tangent to the
13:04hyperbola
13:05at
13:05equation of
13:07LS
13:08tangent
13:11x1
13:12y1
13:124
13:14minus 3
13:15then divide
13:16divide
13:16then x2
13:18which is a2
13:20and this is b2
13:21a2
13:22b2
13:23and x1
13:23y1
13:24here
13:24then answer
13:26this option
13:28x2
13:29plus yx2
13:30equal to x
13:30then
13:31dy upon dx
13:32add 1,3
13:34first
13:34this is the same term
13:35so a plus a 2a
13:37this is 2x2
13:38y
13:392
13:39divided
13:40x2
13:41y equal to 3
13:42derivative
13:55x2
13:56y
13:57x2
13:58y
13:58y
14:00constant
14:01y
14:01y
14:01y
14:01y
14:01y
14:01y
14:01y
14:01y
14:01y
14:01y
14:02y
14:03y
14:03y
14:03y
14:03y
14:04y
14:07y
14:13y
14:15y
14:17y
14:17y
14:21y
14:22positive and negative
14:23this is the previous angle
14:24so the answer is minus sign
14:28then the term
14:30is independent of x
14:32in the expansion of
14:33x square minus 2x upon 6
14:36this is the situation
14:38here is n combination r
14:39a power n
14:41b power r
14:43minus 2x upon power r
14:46this is the answer
14:47here is the numerator
14:49denominator
14:50denominator
14:51denominator
14:513
14:52overall power 6
14:53r 4
14:54r ki value of 4
14:57आपने put
14:57की
14:57तो हम power
14:59का combination
15:00r से लेते हैं
15:01तो 6
15:02combination 4
15:02जोके 15
15:03आचाएगा
15:03और 2 गी वार
15:054 16
15:0516 को 15 से
15:07multiply करते हैं
15:08final answer
15:08बच्चो
15:09240
15:10चालेस
15:12कह रहे हैं
15:12the sum of the
15:13present ages of father
15:15in sunny 50 years
15:18also 5 years ago
15:19the father age was seven times
15:21the age
15:23present age
15:25of the father
15:26I mean, now the father and son
15:29is 50 years
15:30and 5 years ago
15:33the father's age was seven times
15:35now
15:375 years ago
15:38that means
15:39that both of them
15:41have 5-5 years
15:42now
15:43if both of them have 50
15:45so now
15:465 years ago
15:47both of them have 40
15:48why is this technical part
15:505 father and son
15:525 years ago
15:54father son
15:56how many times
15:56are the seven times
15:58so understood
15:59if you think
16:00if you think
16:02father 35
16:03and
16:03beta 5
16:0435 and 5
16:06how many times
16:07are the 40
16:07and 35
16:09are the 5
16:10and if you think
16:115 years ago
16:12if father 35
16:13then
16:14how many years ago
16:1640 years
16:17how many times
16:18are the 35
16:19and 5
16:19plus
16:20I think
16:21now
16:22I mean, 50
16:22are the 5
16:245
16:25three five years ago
16:27father
16:27father
16:28father
16:31seven times
16:33so
16:3435
16:36five
16:37five
16:39eleven
16:40whole
16:42number
16:46eleven
16:47eleven plus three
16:49fourteen
16:49fourteen plus two sixteen
16:52one by three
16:54one by two
16:55four by five
16:57five
17:00three
17:01five
17:02five
17:05three
17:11five
17:14five
17:14five
17:15five
17:16five
17:16five
17:16six
17:19four
17:19four
17:19four
17:19four
17:19five
17:19four
17:20four
17:20five
17:20six
17:22six
17:23six
17:24six
17:24six
17:24six
17:25six
17:25four
17:27five
17:27six
17:28six
17:30six
17:30six
17:31six
17:31six
17:31four
17:32seven
17:32two
17:33twelve
17:33five
17:33six
17:33five
17:34five
17:34five
17:34five
17:35six
17:41nine
17:4249
17:4419
17:4519
17:4630
17:4719
17:4830
17:4917
17:5129
17:5439
17:5919
18:0019
18:0230
18:0430
18:0530
18:0530
18:0630
18:0639
18:0630
18:0730
18:0830
18:0830
18:0830
18:0829
18:0930
18:0930
18:1030
18:10your crack limit x tends to zero is sine square x upon four then here x square
18:15is so bacho
18:17a few days ago use
18:20a sign x upon four
18:23i can do whole square
18:24i can do it
18:25i can do it
18:26i can do it
18:27i can do it
18:28i can do it
18:28i can do it
18:29i can do it
18:29i can do it
18:31i can do it
18:32i can do it
18:34if you want to do it
18:34then obviously it is 4 square x16
18:36and in math rule
18:38the last thing that will be the most superior
18:40so you can balance it
18:41we can balance it
18:41this will be 1 upon 16
18:43this will be 1 so final answer will be 1 upon 16
18:47then we ask the period
18:48we forget everything
18:49in the period
18:50we forget the first one
18:52in the next one
18:54in the sign
18:54the x is 2
18:56the x is 2
18:56the sign of period is 2
18:57the actual period is 2
18:59the period is 2
19:00to divide by x
19:01x की कोफिशियन से डिवाइट करते हैं तो आंसर पाई हो चाहिए का
19:05फिर्स थी टंग पूछ रहे हैं 1-x² की तो वेसी बात है पहली तो 1 आईगी यार
19:11फिर अगली alternate sign के तहत माइनस nx होती है जो कि ऑफकोर्स माइनस 2x होनी चाहिए
19:18तो इनमें minus 2x का एकी option है जिसमें 1-2x है तो understood सी बाते answer यही होगा
19:26आगे चेक करने की जरूरत भी नहीं है बच्छो
19:30square root में 1-sinx dx तो बच्छो इस result को याद रखो क्योंकि हर साल आता है यह हर
19:37test में
19:38यह होता है minus 2 cos x minus 2 sin x plus c
19:42मेरे जो direct shot trick results हैं उनमें से एक हैं
19:45अगर minus common ले लो तो देखो 2 cos x plus sin x upon 2 हो जाएगा
19:50इसी तरह 1 plus sin x
19:53if market is equal to 368917 then m80 तो देखो
20:01m की जगा 3 a की जगा इन्होंने 6 दिया है
20:06तो obvious से बात है शुरू में 36 तो होगा होगा
20:10फिर उसके बाद t की बात हो रही है ती की जगा क्या है 7
20:14देखे ना t आखरी letter है 7
20:16तो answer होना चाहिए 367
20:19फिर कहरें if 1,2,4,3,5,1 stand for newton
20:23तो 3512 क्या होगा अब देखो 33 third last है
20:27यहां third last क्या है टी शुरू में टी होगा
20:31और उसके बाद five की बात हो रही है
20:34five second last है यानी o
20:36t o
20:38उसके बाद फिर क्या है one
20:40one है या किसके बराबर n के बराबर
20:43तो t o n तक क्या जा रहा है
20:46tone जा रहा है आगे देखने की सोथ नहीं है
20:49which describes something from other
20:51या इसको odd man out भी कहते है
20:53gain profit interest फाइदा मन चीज़ है
20:56सर्फ आर में जो नुकसान में
20:57तो answer आर मोचाएगा
21:00फिर कहरें three two
21:02double one four six five seven
21:04stand for possible
21:06then two one six seven
21:09two
21:10का मतब है यहां पे
21:12start होना चाहिए उसे
21:14अरे एक ही option उसे start है
21:16भई खतम होगया मसला है
21:18फिर seven six eight
21:20one two three stand for prince
21:22यह देखो ना one eight two three
21:25one third last
21:26यहनी start होगा end से
21:28अरे end से भी यह की है
21:30तो यह यह भी answer है
21:32तो यह जो यह trick में नहीं देखते जो
21:34which word describes something different
21:36from other
21:38truck blue south देख रहा है भई यह truck की बाद है
21:40बागी सारे खलें
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