1. The question asks to find the measure of angle PCA given that angle CAB is 53°08' and PQ is a tangent to a circle with centre O touching it at point C.
2. It asks to find the value of k if k19, 2k21 and 2k17 are consecutive terms of an AP.
3. It provides information that the angle of elevation of the top of a ladder leaning against a wall is 60° and the foot of the ladder is 2.5 m away from the wall, and asks to find the length of the ladder.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
2. 230/1
âæ×æ‹Ø çÙÎðüàæ Ñ
(i) âÖè ÂýàÙ ¥çÙßæØü ãñ´Ð
(ii) §â ÂýàÙ-˜æ ×ð´ 31 ÂýàÙ ãñ´ Áæð ¿æÚU ¹‡ÇUæð´ - ¥, Õ, â ¥æñÚU Î ×ð´ çßÖæçÁÌ ãñ´Ð
(iii) ¹‡ÇU ¥ ×ð´ °·¤-°·¤ ¥´·¤ ßæÜð 4 ÂýàÙ ãñ´Ð ¹‡ÇU Õ ×ð´ 6 ÂýàÙ ãñ´ çÁâ×ð´ âð ÂýˆØð·¤ 2 ¥´·¤ ·¤æ
ãñÐ ¹‡ÇU â ×ð´ 10 ÂýàÙ ÌèÙ-ÌèÙ ¥´·¤æð´ ·ð¤ ãñ´Ð ¹‡ÇU Î ×ð´ 11 ÂýàÙ ãñ´ çÁÙ×ð´ âð ÂýˆØð·¤ 4 ¥´·¤
·¤æ ãñÐ
(iv) ·ñ¤Ü·é¤ÜðÅUÚU ·¤æ ÂýØæð» ßçÁüÌ ãñÐ
General Instructions :
(i) All questions are compulsory.
(ii) The question paper consists of 31 questions divided into four sections – A, B, C
and D.
(iii) Section A contains 4 questions of 1 mark each. Section B contains 6 questions of
2 marks each, Section C contains 10 questions of 3 marks each and Section D
contains 11 questions of 4 marks each.
(iv) Use of calculators is not permitted.
3. 330/1 P.T.O.
¹‡ÇU - ¥
SECTION - A
ÂýàÙ â´Øæ 1 âð 4 Ì·¤ ÂýˆØð·¤ ÂýàÙ 1 ¥´·¤ ·¤æ ãñÐ
Question numbers 1 to 4 carry 1 mark each.
1. ¥æ·ë¤çÌ 1 ×ð´ O ·ð¤‹Îý ßæÜð ßëžæ ·ð¤ çÕ´Îé C ÂÚU PQ °·¤ SÂàæü ÚðU¹æ ãñÐ ØçÎ AB °·¤ ÃØæâ
ãñ ÌÍæ ÐCAB5308 ãñ, Ìæð ÐPCA ™ææÌ ·¤èçÁ°Ð
¥æ·ë¤çÌ 1
In fig.1, PQ is a tangent at a point C to a circle with centre O. If AB is a
diameter and ÐCAB5308, find ÐPCA.
Figure 1
2. k ·ð¤ ç·¤â ×æÙ ·ð¤ çÜ° k19, 2k21 ÌÍæ 2k17 °·¤ â×æ´ÌÚU ŸæðÉ¸è ·ð¤ ·ý¤×æ»Ì ÂÎ ãñ´?
For what value of k will k19, 2k21 and 2k17 are the consecutive terms of
an A.P. ?
3. °·¤ ÎèßæÚU ·ð¤ âæÍ Ü»è âèɸè ÿæñçÌÁ ·ð¤ âæÍ 608 ·¤æ ·¤æð‡æ ÕÙæÌè ãñÐ ØçÎ âèÉ¸è ·¤æ ÂæÎ
ÎèßæÚU âð 2.5 ×è. ·¤è ÎêÚUè ÂÚU ãñ, Ìæð âèÉ¸è ·¤è ÜÕæ§ü ™ææÌ ·¤èçÁ°Ð
A ladder, leaning against a wall, makes an angle of 608 with the horizontal.
If the foot of the ladder is 2.5 m away from the wall, find the length of the
ladder.
4. 430/1
4. 52 žææð´ ·¤è ¥‘ÀUè Âý·¤æÚU Èð´¤ÅUè »§ü Ìæàæ ·¤è »aè ×ð´ âð ØæÎë‘ÀUØæ °·¤ žææ çÙ·¤æÜæ »ØæÐ
ÂýæçØ·¤Ìæ ™ææÌ ·¤èçÁ° ç·¤ çÙ·¤æÜæ »Øæ žææ Ù Ìæð ÜæÜ Ú´U» ·¤æ ãñ ¥æñÚU Ù ãè °·¤ Õð$»× ãñÐ
A card is drawn at random from a well shuffled pack of 52 playing cards. Find
the probability of getting neither a red card nor a queen.
¹‡ÇU - Õ
SECTION - B
ÂýàÙ â´Øæ 5 âð 10 Ì·¤ ÂýˆØð·¤ ÂýàÙ 2 ¥´·¤ ·¤æ ãñÐ
Question numbers 5 to 10 carry 2 marks each.
5. ØçÎ çmƒææÌè â×è·¤ÚU‡æ 2x21px21550 ·¤æ °·¤ ×êÜ 25 ãñ ÌÍæ çmƒææÌè â×è·¤ÚU‡æ
p(x21x)1k50 ·ð¤ ×êÜ â×æÙ ãñ´, Ìæð k ·¤æ ×æÙ ™ææÌ ·¤èçÁ°Ð
If 25 is a root of the quadratic equation 2x21px21550 and the quadratic
equation p(x21x)1k50 has equal roots, find the value of k.
6. ×æÙæ P ÌÍæ Q, A(2, 22) ÌÍæ B(27, 4) ·¤æð ç×ÜæÙð ßæÜð ÚðU¹æ¹´ÇU ·¤æð §â Âý·¤æÚU â×ç˜æÖæçÁÌ
·¤ÚUÌð ãñ´ ç·¤ P, çÕ´Îé A ·ð¤ Âæâ ãñÐ P ÌÍæ Q ·ð¤ çÙÎðüàææ´·¤ ™ææÌ ·¤èçÁ°Ð
Let P and Q be the points of trisection of the line segment joining the points
A(2, 22) and B(27, 4) such that P is nearer to A. Find the coordinates of
P and Q.
7. ¥æ·ë¤çÌ 2 ×ð´ °·¤ ¿ÌéÖüéÁ ABCD, O ·ð´¤Îý ßæÜð ßëžæ ·ð¤ ÂçÚU»Ì §â Âý·¤æÚU ÕÙæ§ü »§ü ãñ ç·¤
ÖéÁæ°¡ AB, BC, CD ÌÍæ DA ßëžæ ·¤æð ·ý¤×àæÑ çÕ´Îé¥æð´ P, Q, R ÌÍæ S ÂÚU SÂàæü ·¤ÚUÌè ãñ´Ð
çâh ·¤èçÁ° ç·¤ AB1CD5BC1DA Ð
¥æ·ë¤çÌ 2
6. 630/1
In Fig. 3, from an external point P, two tangents PT and PS are drawn to a
circle with centre O and radius r. If OP52r, show that ÐOTS5ÐOST5308.
Figure 3
¹‡ÇU - â
SECTION - C
ÂýàÙ â´Øæ 11 âð 20 Ì·¤ ÂýˆØð·¤ ÂýàÙ ·ð¤ 3 ¥´·¤ ãñ´Ð
Question numbers 11 to 20 carry 3 marks each.
11. ¥æ·ë¤çÌ 4 ×ð´ O ·ð¤‹Îý ßæÜð ßëžæ ·¤æ ÃØæâ AB513 âð×è ãñ ÌÍæ AC512 âð×è ãñÐ BC ·¤æð
ç×ÜæØæ »Øæ ãñÐ ÀUæØæ´ç·¤Ì ÿæð˜æ ·¤æ ÿæð˜æÈ¤Ü ™ææÌ ·¤èçÁ°Ð ( p53.14 ÜèçÁ° )
¥æ·ë¤çÌ 4
In fig.4, O is the centre of a circle such that diameter AB513 cm and
AC512 cm. BC is joined. Find the area of the shaded region. (Take p53.14)
Figure 4
14. 1430/1
29. â´Øæ¥æð´ 1, 2, 3 ÌÍæ 4 ×ð´ âð ·¤æð§ü â´Øæ x ØæÎë‘ÀUØæ ¿éÙè »§ü ÌÍæ â´Øæ¥æð´ 1, 4, 9 ÌÍæ 16
×ð´ âð ·¤æð§ü â´Øæ y ØæÎë‘ÀUØæ ¿éÙè »§ü ÂýæçØ·¤Ìæ ™ææÌ ·¤èçÁ° x ÌÍæ y ·¤æ »é‡æÙÈ¤Ü 16 âð ·¤×
ãñÐ
A number x is selected at random from the numbers 1, 2, 3 and 4. Another
number y is selected at random from the numbers 1, 4, 9 and 16. Find the
probability that product of x and y is less than 16.
30. ¥æ·ë¤çÌ 9 ×ð´, O ·ð´¤Îý ßæÜð ßëžæ ·¤æ °·¤ ç˜æ’ع´ÇU OAP ÎàææüØæ »Øæ ãñ çÁâ·¤æ ·ð¤‹Îý ÂÚU
¥Ì´çÚUÌ ·¤æð‡æ u ãñÐ AB ßëžæ ·¤è ç˜æ’Øæ OA ÂÚU Ü´Õ ãñ Áæð OP ·ð¤ ÕɸæÙð ÂÚU çÕ´Îé B ÂÚU
·¤æÅUÌæ ãñÐ çâh ·¤èçÁ° ç·¤ ÚðU¹æ´ç·¤Ì Öæ» ·¤æ ÂçÚU×æ r
pu
u 1 u 1 2tan sec 1
180
ãñÐ
¥æ·ë¤çÌ 9
In Fig. 9, is shown a sector OAP of a circle with centre O, containing ∠ u. AB
is perpendicular to the radius OA and meets OP produced at B. Prove that
the perimeter of shaded region is r
pu
u 1 u 1 2tan sec 1
180
Figure 9
15. 1530/1 P.T.O.
31. °·¤ ×æðÅÚU ÕæðÅU, çÁâ·¤è çSÍÚU ÁÜ ×ð´ ¿æÜ 24 ç·¤×è/ƒæ´ÅUæ ãñ, ÏæÚUæ ·ð¤ ÂýçÌ·ê¤Ü 32 ç·¤×è ÁæÙð
×ð´, ßãè ÎêÚUè ÏæÚUæ ·ð¤ ¥Ùé·ê¤Ü ÁæÙð ·¤è ¥Âðÿææ 1 ƒæ´ÅUæ ¥çÏ·¤ â×Ø ÜðÌè ãñÐ ÏæÚUæ ·¤è ¿æÜ
™ææÌ ·¤èçÁ°Ð
A motor boat whose speed is 24 km/h in still water takes 1 hour more to go
32 km upstream than to return downstream to the same spot. Find the speed
of the stream.
