JEE Exam > JEE Notes > Additional Study Material for JEE > Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths
Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths | Additional Study Material for JEE PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
65/1/2 1 [P.T.O.
¸üÖê»Ö ®ÖÓ.
Roll No.
ÝÖ×ÞÖŸÖ
MATHEMATICS
×®Ö¬ÖÖÔ׸üŸÖ ÃÖ´ÖµÖ : 3 ‘ÖÞ™êüü] [†×¬ÖÛúŸÖ´Ö †ÓÛú : 100
Time allowed : 3 hours ] [ Maximum Marks : 100
ÃÖÖ´ÖÖ®µÖ ×®Ö¤ìü¿Ö :
(i) ÃÖ³Öß ¯ÖÏ¿®Ö †×®Ö¾ÖÖµÖÔ Æïü …
(ii) Ûéú¯ÖµÖÖ •ÖÖÑ“Ö Ûú¸ü »Öë ×Ûú ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë 26 ¯ÖÏ¿®Ö Æïü …
(iii) ÜÖÞ›ü-† Ûêú ¯ÖÏ¿®Ö ÃÖÓ. 1–6 ŸÖÛú †×ŸÖ »Ö‘Öã-ˆ¢Ö¸ü ¾ÖÖ»Öê ¯ÖÏ¿®Ö Æïü †Öî¸ü ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö Ûêú ×»Ö‹ 1 †ÓÛú ×®Ö¬ÖÖÔ׸üŸÖ Æîü …
(iv) ÜÖÞ›ü-²Ö Ûêú ¯ÖÏ¿®Ö ÃÖÓ. 7–19 ŸÖÛú ¤üß‘ÖÔ-ˆ¢Ö¸ü I ¯ÖÏÛúÖ¸ü Ûêú ¯ÖÏ¿®Ö Æïü †Öî¸ü ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö Ûêú ×»Ö‹ 4 †ÓÛú ×®Ö¬ÖÖÔ׸üŸÖ Æïü …
(v) ÜÖÞ›ü-ÃÖ Ûêú ¯ÖÏ¿®Ö ÃÖÓ. 20–26 ŸÖÛú ¤üß‘ÖÔ-ˆ¢Ö¸ü II ¯ÖÏÛúÖ¸ü Ûêú ¯ÖÏ¿®Ö Æïü †Öî¸ü ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö Ûêú ×»Ö‹ 6 †ÓÛú ×®Ö¬ÖÖÔ׸üŸÖ
Æïü …
(vi) ˆ¢Ö¸ü ×»ÖÜÖ®ÖÖ ¯ÖÏÖ¸Óü³Ö Ûú¸ü®Öê ÃÖê ¯ÖÆü»Öê Ûéú¯ÖµÖÖ ¯ÖÏ¿®Ö ÛúÖ ÛÎú´ÖÖÓÛú †¾Ö¿µÖ ×»Ö×ÜÖ‹ …
Series : SSO/1/C
ÛúÖê›ü ®ÖÓ.
Code No.
65/1/2
• Ûéú¯ÖµÖÖ •ÖÖÑ“Ö Ûú¸ü »Öë ×Ûú ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë ´ÖãצüŸÖ ¯Öéšü 8 Æïü …
• ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë ¤üÖ×Æü®Öê ÆüÖ£Ö Ûúß †Öê¸ü פü‹ ÝÖ‹ ÛúÖê›ü ®Ö´²Ö¸ü ÛúÖê ”ûÖ¡Ö ˆ¢Ö¸ü-¯Öã×ßÖÛúÖ Ûêú ´ÖãÜÖ-¯Öéšü ¯Ö¸ü ×»ÖÜÖë …
• Ûéú¯ÖµÖÖ •ÖÖÑ“Ö Ûú¸ü »Öë ×Ûú ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë 26 ¯ÖÏ¿®Ö Æïü …
• Ûéú¯ÖµÖÖ ¯ÖÏ¿®Ö ÛúÖ ˆ¢Ö¸ü ×»ÖÜÖ®ÖÖ ¿Öãºþ Ûú¸ü®Öê ÃÖê ¯ÖÆü»Öê, ¯ÖÏ¿®Ö ÛúÖ ÛÎú´ÖÖÓÛú †¾Ö¿µÖ ×»ÖÜÖë …
• ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ÛúÖê ¯ÖœÌü®Öê Ûêú ×»Ö‹ 15 ×´Ö®Ö™ü ÛúÖ ÃÖ´ÖµÖ ×¤üµÖÖ ÝÖµÖÖ Æîü … ¯ÖÏ¿®Ö-¯Ö¡Ö ÛúÖ ×¾ÖŸÖ¸üÞÖ ¯Öæ¾ÖÖÔÆËü®Ö ´Öë 10.15 ²Ö•Öê
×ÛúµÖÖ •ÖÖµÖêÝÖÖ … 10.15 ²Ö•Öê ÃÖê 10.30 ²Ö•Öê ŸÖÛú ”ûÖ¡Ö Ûêú¾Ö»Ö ¯ÖÏ¿®Ö-¯Ö¡Ö ÛúÖê ¯ÖœÌëüÝÖê †Öî¸ü ‡ÃÖ †¾Ö×¬Ö Ûêú ¤üÖî¸üÖ®Ö ¾Öê
ˆ¢Ö¸ü-¯Öã×ßÖÛúÖ ¯Ö¸ü ÛúÖê‡Ô ˆ¢Ö¸ü ®ÖÆüà ×»ÖÜÖëÝÖê …
• Please check that this question paper contains 8 printed pages.
• Code number given on the right hand side of the question paper should be written on the
title page of the answer-book by the candidate.
• Please check that this question paper contains 26 questions.
• Please write down the Serial Number of the question before attempting it.
• 15 minutes time has been allotted to read this question paper. The question paper will be
distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the
question paper only and will not write any answer on the answer-book during this period.
¯Ö¸üßõÖÖ£Öá ÛúÖê›ü ÛúÖê ˆ¢Ö¸ü-¯Öã×ßÖÛúÖ Ûêú ´ÖãÜÖ-¯Öéšü
¯Ö¸ü †¾Ö¿µÖ ×»ÖÜÖë …
Candidates must write the Code on
the title page of the answer-book.
SET – 2
Page 2
65/1/2 1 [P.T.O.
¸üÖê»Ö ®ÖÓ.
Roll No.
ÝÖ×ÞÖŸÖ
MATHEMATICS
×®Ö¬ÖÖÔ׸üŸÖ ÃÖ´ÖµÖ : 3 ‘ÖÞ™êüü] [†×¬ÖÛúŸÖ´Ö †ÓÛú : 100
Time allowed : 3 hours ] [ Maximum Marks : 100
ÃÖÖ´ÖÖ®µÖ ×®Ö¤ìü¿Ö :
(i) ÃÖ³Öß ¯ÖÏ¿®Ö †×®Ö¾ÖÖµÖÔ Æïü …
(ii) Ûéú¯ÖµÖÖ •ÖÖÑ“Ö Ûú¸ü »Öë ×Ûú ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë 26 ¯ÖÏ¿®Ö Æïü …
(iii) ÜÖÞ›ü-† Ûêú ¯ÖÏ¿®Ö ÃÖÓ. 1–6 ŸÖÛú †×ŸÖ »Ö‘Öã-ˆ¢Ö¸ü ¾ÖÖ»Öê ¯ÖÏ¿®Ö Æïü †Öî¸ü ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö Ûêú ×»Ö‹ 1 †ÓÛú ×®Ö¬ÖÖÔ׸üŸÖ Æîü …
(iv) ÜÖÞ›ü-²Ö Ûêú ¯ÖÏ¿®Ö ÃÖÓ. 7–19 ŸÖÛú ¤üß‘ÖÔ-ˆ¢Ö¸ü I ¯ÖÏÛúÖ¸ü Ûêú ¯ÖÏ¿®Ö Æïü †Öî¸ü ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö Ûêú ×»Ö‹ 4 †ÓÛú ×®Ö¬ÖÖÔ׸üŸÖ Æïü …
(v) ÜÖÞ›ü-ÃÖ Ûêú ¯ÖÏ¿®Ö ÃÖÓ. 20–26 ŸÖÛú ¤üß‘ÖÔ-ˆ¢Ö¸ü II ¯ÖÏÛúÖ¸ü Ûêú ¯ÖÏ¿®Ö Æïü †Öî¸ü ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö Ûêú ×»Ö‹ 6 †ÓÛú ×®Ö¬ÖÖÔ׸üŸÖ
Æïü …
(vi) ˆ¢Ö¸ü ×»ÖÜÖ®ÖÖ ¯ÖÏÖ¸Óü³Ö Ûú¸ü®Öê ÃÖê ¯ÖÆü»Öê Ûéú¯ÖµÖÖ ¯ÖÏ¿®Ö ÛúÖ ÛÎú´ÖÖÓÛú †¾Ö¿µÖ ×»Ö×ÜÖ‹ …
Series : SSO/1/C
ÛúÖê›ü ®ÖÓ.
Code No.
65/1/2
• Ûéú¯ÖµÖÖ •ÖÖÑ“Ö Ûú¸ü »Öë ×Ûú ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë ´ÖãצüŸÖ ¯Öéšü 8 Æïü …
• ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë ¤üÖ×Æü®Öê ÆüÖ£Ö Ûúß †Öê¸ü פü‹ ÝÖ‹ ÛúÖê›ü ®Ö´²Ö¸ü ÛúÖê ”ûÖ¡Ö ˆ¢Ö¸ü-¯Öã×ßÖÛúÖ Ûêú ´ÖãÜÖ-¯Öéšü ¯Ö¸ü ×»ÖÜÖë …
• Ûéú¯ÖµÖÖ •ÖÖÑ“Ö Ûú¸ü »Öë ×Ûú ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë 26 ¯ÖÏ¿®Ö Æïü …
• Ûéú¯ÖµÖÖ ¯ÖÏ¿®Ö ÛúÖ ˆ¢Ö¸ü ×»ÖÜÖ®ÖÖ ¿Öãºþ Ûú¸ü®Öê ÃÖê ¯ÖÆü»Öê, ¯ÖÏ¿®Ö ÛúÖ ÛÎú´ÖÖÓÛú †¾Ö¿µÖ ×»ÖÜÖë …
• ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ÛúÖê ¯ÖœÌü®Öê Ûêú ×»Ö‹ 15 ×´Ö®Ö™ü ÛúÖ ÃÖ´ÖµÖ ×¤üµÖÖ ÝÖµÖÖ Æîü … ¯ÖÏ¿®Ö-¯Ö¡Ö ÛúÖ ×¾ÖŸÖ¸üÞÖ ¯Öæ¾ÖÖÔÆËü®Ö ´Öë 10.15 ²Ö•Öê
×ÛúµÖÖ •ÖÖµÖêÝÖÖ … 10.15 ²Ö•Öê ÃÖê 10.30 ²Ö•Öê ŸÖÛú ”ûÖ¡Ö Ûêú¾Ö»Ö ¯ÖÏ¿®Ö-¯Ö¡Ö ÛúÖê ¯ÖœÌëüÝÖê †Öî¸ü ‡ÃÖ †¾Ö×¬Ö Ûêú ¤üÖî¸üÖ®Ö ¾Öê
ˆ¢Ö¸ü-¯Öã×ßÖÛúÖ ¯Ö¸ü ÛúÖê‡Ô ˆ¢Ö¸ü ®ÖÆüà ×»ÖÜÖëÝÖê …
• Please check that this question paper contains 8 printed pages.
• Code number given on the right hand side of the question paper should be written on the
title page of the answer-book by the candidate.
• Please check that this question paper contains 26 questions.
• Please write down the Serial Number of the question before attempting it.
• 15 minutes time has been allotted to read this question paper. The question paper will be
distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the
question paper only and will not write any answer on the answer-book during this period.
¯Ö¸üßõÖÖ£Öá ÛúÖê›ü ÛúÖê ˆ¢Ö¸ü-¯Öã×ßÖÛúÖ Ûêú ´ÖãÜÖ-¯Öéšü
¯Ö¸ü †¾Ö¿µÖ ×»ÖÜÖë …
Candidates must write the Code on
the title page of the answer-book.
SET – 2
65/1/2 2
General Instructions :
(i) All questions are compulsory.
(ii) Please check that this Question Paper contains 26 Questions.
(iii) Questions 1 – 6 in Section-A are Very Short Answer Type Questions carrying 1 mark
each.
(iv) Questions 7 – 19 in Section-B are Long Answer I Type Questions carrying 4 marks
each.
(v) Questions 20 – 26 in Section-C are Long Answer II Type Questions carrying
6 marks each
(vi) Please write down the serial number of the Question before attempting it.
ÜÖÞ›ü – †
SECTION – A
¯ÖÏ¿®Ö ÃÖÓܵÖÖ 1 ÃÖê 6 ŸÖÛú ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö 1 †ÓÛú ÛúÖ Æîü …
Question numbers 1 to 6 carry 1 mark each.
1. µÖפü ‹Ûú ¸êüÜÖÖ ×®Ö¤ìü¿ÖÖÓÛú †õÖÖë Ûúß ¬Ö®ÖÖŸ´ÖÛú פü¿ÖÖ†Öë Ûêú ÃÖÖ£Ö ÛúÖêÞÖ a, ß, ? ²Ö®ÖÖŸÖß Æîü, ŸÖÖê sin
2
a + sin
2
ß +
sin
2
? ÛúÖ ´ÖÖ®Ö ×»Ö×ÜÖ‹ … 1
If a line makes angles a, ß, ? with the positive direction of coordinate axes, then write
the value of sin
2
a + sin
2
ß + sin
2
?.
2. µÖפü A =
?
?
?
?
?
?
1 2
3 –1
, B =
?
?
?
?
?
?
1 3
–1 1
Æïü, ŸÖÖê AB ÛúÖ ´ÖÖ®Ö ×»Ö×ÜÖ‹ … 1
If A =
?
?
?
?
?
?
1 2
3 –1
and B =
?
?
?
?
?
?
1 3
–1 1
, write the value of AB .
3. C ÛúÖ ×¾Ö»ÖÖê¯Ö®Ö Ûú¸üÛêú ¾ÖÛÎúÖë Ûêú Ûãú»Ö xy = C cos x ÛúÖê ×®Öºþ×¯ÖŸÖ Ûú¸ü®Öê ¾ÖÖ»ÖÖ †¾ÖÛú»Ö ÃÖ´ÖßÛú¸üÞÖ ×»Ö×ÜÖ‹ … 1
Write the differential equation obtained by eliminating the arbitrary constant C in the
equation representing the family of curves xy = C cos x.
4. †¾ÖÛú»Ö ÃÖ´ÖßÛú¸üÞÖ 1 +
?
?
?
?
?
?
dy
dx
4
= 7
?
?
?
?
?
? d
2
y
dx
2
3
Ûúß ÛúÖê×™ü ŸÖ£ÖÖ ‘ÖÖŸÖ ÛúÖ µÖÖêÝÖ ×»Ö×ÜÖ‹ … 1
Write the sum of the order and degree of the differential equation
1 +
?
?
?
?
?
?
dy
dx
4
= 7
?
?
?
?
?
? d
2
y
dx
2
3
Page 3
65/1/2 1 [P.T.O.
¸üÖê»Ö ®ÖÓ.
Roll No.
ÝÖ×ÞÖŸÖ
MATHEMATICS
×®Ö¬ÖÖÔ׸üŸÖ ÃÖ´ÖµÖ : 3 ‘ÖÞ™êüü] [†×¬ÖÛúŸÖ´Ö †ÓÛú : 100
Time allowed : 3 hours ] [ Maximum Marks : 100
ÃÖÖ´ÖÖ®µÖ ×®Ö¤ìü¿Ö :
(i) ÃÖ³Öß ¯ÖÏ¿®Ö †×®Ö¾ÖÖµÖÔ Æïü …
(ii) Ûéú¯ÖµÖÖ •ÖÖÑ“Ö Ûú¸ü »Öë ×Ûú ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë 26 ¯ÖÏ¿®Ö Æïü …
(iii) ÜÖÞ›ü-† Ûêú ¯ÖÏ¿®Ö ÃÖÓ. 1–6 ŸÖÛú †×ŸÖ »Ö‘Öã-ˆ¢Ö¸ü ¾ÖÖ»Öê ¯ÖÏ¿®Ö Æïü †Öî¸ü ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö Ûêú ×»Ö‹ 1 †ÓÛú ×®Ö¬ÖÖÔ׸üŸÖ Æîü …
(iv) ÜÖÞ›ü-²Ö Ûêú ¯ÖÏ¿®Ö ÃÖÓ. 7–19 ŸÖÛú ¤üß‘ÖÔ-ˆ¢Ö¸ü I ¯ÖÏÛúÖ¸ü Ûêú ¯ÖÏ¿®Ö Æïü †Öî¸ü ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö Ûêú ×»Ö‹ 4 †ÓÛú ×®Ö¬ÖÖÔ׸üŸÖ Æïü …
(v) ÜÖÞ›ü-ÃÖ Ûêú ¯ÖÏ¿®Ö ÃÖÓ. 20–26 ŸÖÛú ¤üß‘ÖÔ-ˆ¢Ö¸ü II ¯ÖÏÛúÖ¸ü Ûêú ¯ÖÏ¿®Ö Æïü †Öî¸ü ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö Ûêú ×»Ö‹ 6 †ÓÛú ×®Ö¬ÖÖÔ׸üŸÖ
Æïü …
(vi) ˆ¢Ö¸ü ×»ÖÜÖ®ÖÖ ¯ÖÏÖ¸Óü³Ö Ûú¸ü®Öê ÃÖê ¯ÖÆü»Öê Ûéú¯ÖµÖÖ ¯ÖÏ¿®Ö ÛúÖ ÛÎú´ÖÖÓÛú †¾Ö¿µÖ ×»Ö×ÜÖ‹ …
Series : SSO/1/C
ÛúÖê›ü ®ÖÓ.
Code No.
65/1/2
• Ûéú¯ÖµÖÖ •ÖÖÑ“Ö Ûú¸ü »Öë ×Ûú ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë ´ÖãצüŸÖ ¯Öéšü 8 Æïü …
• ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë ¤üÖ×Æü®Öê ÆüÖ£Ö Ûúß †Öê¸ü פü‹ ÝÖ‹ ÛúÖê›ü ®Ö´²Ö¸ü ÛúÖê ”ûÖ¡Ö ˆ¢Ö¸ü-¯Öã×ßÖÛúÖ Ûêú ´ÖãÜÖ-¯Öéšü ¯Ö¸ü ×»ÖÜÖë …
• Ûéú¯ÖµÖÖ •ÖÖÑ“Ö Ûú¸ü »Öë ×Ûú ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë 26 ¯ÖÏ¿®Ö Æïü …
• Ûéú¯ÖµÖÖ ¯ÖÏ¿®Ö ÛúÖ ˆ¢Ö¸ü ×»ÖÜÖ®ÖÖ ¿Öãºþ Ûú¸ü®Öê ÃÖê ¯ÖÆü»Öê, ¯ÖÏ¿®Ö ÛúÖ ÛÎú´ÖÖÓÛú †¾Ö¿µÖ ×»ÖÜÖë …
• ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ÛúÖê ¯ÖœÌü®Öê Ûêú ×»Ö‹ 15 ×´Ö®Ö™ü ÛúÖ ÃÖ´ÖµÖ ×¤üµÖÖ ÝÖµÖÖ Æîü … ¯ÖÏ¿®Ö-¯Ö¡Ö ÛúÖ ×¾ÖŸÖ¸üÞÖ ¯Öæ¾ÖÖÔÆËü®Ö ´Öë 10.15 ²Ö•Öê
×ÛúµÖÖ •ÖÖµÖêÝÖÖ … 10.15 ²Ö•Öê ÃÖê 10.30 ²Ö•Öê ŸÖÛú ”ûÖ¡Ö Ûêú¾Ö»Ö ¯ÖÏ¿®Ö-¯Ö¡Ö ÛúÖê ¯ÖœÌëüÝÖê †Öî¸ü ‡ÃÖ †¾Ö×¬Ö Ûêú ¤üÖî¸üÖ®Ö ¾Öê
ˆ¢Ö¸ü-¯Öã×ßÖÛúÖ ¯Ö¸ü ÛúÖê‡Ô ˆ¢Ö¸ü ®ÖÆüà ×»ÖÜÖëÝÖê …
• Please check that this question paper contains 8 printed pages.
• Code number given on the right hand side of the question paper should be written on the
title page of the answer-book by the candidate.
• Please check that this question paper contains 26 questions.
• Please write down the Serial Number of the question before attempting it.
• 15 minutes time has been allotted to read this question paper. The question paper will be
distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the
question paper only and will not write any answer on the answer-book during this period.
¯Ö¸üßõÖÖ£Öá ÛúÖê›ü ÛúÖê ˆ¢Ö¸ü-¯Öã×ßÖÛúÖ Ûêú ´ÖãÜÖ-¯Öéšü
¯Ö¸ü †¾Ö¿µÖ ×»ÖÜÖë …
Candidates must write the Code on
the title page of the answer-book.
SET – 2
65/1/2 2
General Instructions :
(i) All questions are compulsory.
(ii) Please check that this Question Paper contains 26 Questions.
(iii) Questions 1 – 6 in Section-A are Very Short Answer Type Questions carrying 1 mark
each.
(iv) Questions 7 – 19 in Section-B are Long Answer I Type Questions carrying 4 marks
each.
(v) Questions 20 – 26 in Section-C are Long Answer II Type Questions carrying
6 marks each
(vi) Please write down the serial number of the Question before attempting it.
ÜÖÞ›ü – †
SECTION – A
¯ÖÏ¿®Ö ÃÖÓܵÖÖ 1 ÃÖê 6 ŸÖÛú ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö 1 †ÓÛú ÛúÖ Æîü …
Question numbers 1 to 6 carry 1 mark each.
1. µÖפü ‹Ûú ¸êüÜÖÖ ×®Ö¤ìü¿ÖÖÓÛú †õÖÖë Ûúß ¬Ö®ÖÖŸ´ÖÛú פü¿ÖÖ†Öë Ûêú ÃÖÖ£Ö ÛúÖêÞÖ a, ß, ? ²Ö®ÖÖŸÖß Æîü, ŸÖÖê sin
2
a + sin
2
ß +
sin
2
? ÛúÖ ´ÖÖ®Ö ×»Ö×ÜÖ‹ … 1
If a line makes angles a, ß, ? with the positive direction of coordinate axes, then write
the value of sin
2
a + sin
2
ß + sin
2
?.
2. µÖפü A =
?
?
?
?
?
?
1 2
3 –1
, B =
?
?
?
?
?
?
1 3
–1 1
Æïü, ŸÖÖê AB ÛúÖ ´ÖÖ®Ö ×»Ö×ÜÖ‹ … 1
If A =
?
?
?
?
?
?
1 2
3 –1
and B =
?
?
?
?
?
?
1 3
–1 1
, write the value of AB .
3. C ÛúÖ ×¾Ö»ÖÖê¯Ö®Ö Ûú¸üÛêú ¾ÖÛÎúÖë Ûêú Ûãú»Ö xy = C cos x ÛúÖê ×®Öºþ×¯ÖŸÖ Ûú¸ü®Öê ¾ÖÖ»ÖÖ †¾ÖÛú»Ö ÃÖ´ÖßÛú¸üÞÖ ×»Ö×ÜÖ‹ … 1
Write the differential equation obtained by eliminating the arbitrary constant C in the
equation representing the family of curves xy = C cos x.
4. †¾ÖÛú»Ö ÃÖ´ÖßÛú¸üÞÖ 1 +
?
?
?
?
?
?
dy
dx
4
= 7
?
?
?
?
?
? d
2
y
dx
2
3
Ûúß ÛúÖê×™ü ŸÖ£ÖÖ ‘ÖÖŸÖ ÛúÖ µÖÖêÝÖ ×»Ö×ÜÖ‹ … 1
Write the sum of the order and degree of the differential equation
1 +
?
?
?
?
?
?
dy
dx
4
= 7
?
?
?
?
?
? d
2
y
dx
2
3
65/1/2 3 [P.T.O.
5. ÃÖפü¿Ö
?
a =
^
i – 2
^
j Ûúß ×¤ü¿ÖÖ ´Öë ‹Ûú ÃÖפü¿Ö –ÖÖŸÖ Ûúßו֋ וÖÃÖÛúÖ ¯Ö׸ü´ÖÖÞÖ 7 ‡ÛúÖ‡Ô Æîü … 1
Find a Vector in the direction of
?
a =
^
i – 2
^
j that has magnitude 7 units.
6. µÖפü
?
a ŸÖ£ÖÖ
?
b ´ÖÖ¡ÖÛú ÃÖפü¿Ö Æïü, ŸÖÖê
?
a ŸÖ£ÖÖ
?
b Ûêú ²Öß“Ö ÛúÖ ÛúÖêÞÖ ŒµÖÖ Æîü, •Ö²Ö×Ûú 2
?
a –
?
b ‹Ûú ´ÖÖ¡ÖÛú
ÃÖפü¿Ö Æîü ? 1
If
?
a and
?
b are unit Vectors, then what is the angle between
?
a and
?
b so that 2
?
a –
?
b
is a unit vector ?
ÜÖÞ›ü – ²Ö
SECTION – B
¯ÖÏ¿®Ö ÃÖÓܵÖÖ 7 ÃÖê 19 ŸÖÛú ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö 4 †ÓÛú ÛúÖ Æîü …
Question numbers 7 to 19 carry 4 marks each.
7. –ÖÖŸÖ Ûúßו֋ :
)
?
(
x
(x – 1)
2
(x + 2)
dx 4
†£Ö¾ÖÖ
–ÖÖŸÖ Ûúßו֋ :
)
?
(
x + 2
2x
2
+ 6x + 5
dx
Find :
)
?
(
x
(x – 1)
2
(x + 2)
dx
OR
Find :
)
?
(
x + 2
2x
2
+ 6x + 5
dx
8. 15 ²Ö»²ÖÖë Ûêú œÌêü¸ü ÃÖê, וÖÃÖ´Öë 5 ²Ö»²Ö ÜÖ¸üÖ²Ö Æïü, 2 ²Ö»²ÖÖë ÛúÖ ‹Ûú ®Ö´Öæ®ÖÖ µÖÖ¥ü“”ûµÖÖ, ײ֮ÖÖ ¯ÖÏןÖãÖÖ¯Ö®ÖÖ Ûêú ×®ÖÛúÖ»ÖÖ
•ÖÖŸÖÖ Æîü … ÜÖ¸üÖ²Ö ²Ö»²ÖÖë Ûúß ÃÖÓܵÖÖ ÛúÖ ¯ÖÏÖ×µÖÛúŸÖÖ ²ÖÓ™ü®Ö –ÖÖŸÖ Ûúßו֋ … 4
†£Ö¾ÖÖ
‹Ûú ×¾Ö¿ÖêÂÖ ÃÖ´ÖõÖÖ ÛúÖê A ŸÖ£ÖÖ B «üÖ¸üÖ Ã¾ÖŸÖÓ¡Ö ºþ¯Ö ÃÖê Æü»Ö Ûú¸ü®Öê Ûúß ¯ÖÏÖ×µÖÛúŸÖÖ‹Ñ ÛÎú´Ö¿Ö:
1
2
ŸÖ£ÖÖ
1
3
Æïü … µÖפü
¤üÖê®ÖÖë þ֟ÖÓ¡Ö ºþ¯Ö ÃÖê ÃÖ´ÖõÖÖ ÛúÖê Æü»Ö Ûú¸ü®Öê ÛúÖ ¯ÖϵÖÖÃÖ Ûú¸üŸÖê Æïü, ŸÖÖê ¯ÖÏÖ×µÖÛúŸÖÖ –ÖÖŸÖ Ûúßו֋ ×Ûú
(i) ÃÖ´ÖõÖÖ Æü»Ö ÆüÖê •ÖÖŸÖß Æîü …
(ii) ˆ®Ö´Öë ÃÖê ŸÖ£µÖŸÖÖ ÛúÖê‡Ô ‹Ûú ÃÖ´ÖõÖÖ Æü»Ö Ûú¸ü »ÖêŸÖÖ Æîü …
Page 4
65/1/2 1 [P.T.O.
¸üÖê»Ö ®ÖÓ.
Roll No.
ÝÖ×ÞÖŸÖ
MATHEMATICS
×®Ö¬ÖÖÔ׸üŸÖ ÃÖ´ÖµÖ : 3 ‘ÖÞ™êüü] [†×¬ÖÛúŸÖ´Ö †ÓÛú : 100
Time allowed : 3 hours ] [ Maximum Marks : 100
ÃÖÖ´ÖÖ®µÖ ×®Ö¤ìü¿Ö :
(i) ÃÖ³Öß ¯ÖÏ¿®Ö †×®Ö¾ÖÖµÖÔ Æïü …
(ii) Ûéú¯ÖµÖÖ •ÖÖÑ“Ö Ûú¸ü »Öë ×Ûú ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë 26 ¯ÖÏ¿®Ö Æïü …
(iii) ÜÖÞ›ü-† Ûêú ¯ÖÏ¿®Ö ÃÖÓ. 1–6 ŸÖÛú †×ŸÖ »Ö‘Öã-ˆ¢Ö¸ü ¾ÖÖ»Öê ¯ÖÏ¿®Ö Æïü †Öî¸ü ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö Ûêú ×»Ö‹ 1 †ÓÛú ×®Ö¬ÖÖÔ׸üŸÖ Æîü …
(iv) ÜÖÞ›ü-²Ö Ûêú ¯ÖÏ¿®Ö ÃÖÓ. 7–19 ŸÖÛú ¤üß‘ÖÔ-ˆ¢Ö¸ü I ¯ÖÏÛúÖ¸ü Ûêú ¯ÖÏ¿®Ö Æïü †Öî¸ü ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö Ûêú ×»Ö‹ 4 †ÓÛú ×®Ö¬ÖÖÔ׸üŸÖ Æïü …
(v) ÜÖÞ›ü-ÃÖ Ûêú ¯ÖÏ¿®Ö ÃÖÓ. 20–26 ŸÖÛú ¤üß‘ÖÔ-ˆ¢Ö¸ü II ¯ÖÏÛúÖ¸ü Ûêú ¯ÖÏ¿®Ö Æïü †Öî¸ü ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö Ûêú ×»Ö‹ 6 †ÓÛú ×®Ö¬ÖÖÔ׸üŸÖ
Æïü …
(vi) ˆ¢Ö¸ü ×»ÖÜÖ®ÖÖ ¯ÖÏÖ¸Óü³Ö Ûú¸ü®Öê ÃÖê ¯ÖÆü»Öê Ûéú¯ÖµÖÖ ¯ÖÏ¿®Ö ÛúÖ ÛÎú´ÖÖÓÛú †¾Ö¿µÖ ×»Ö×ÜÖ‹ …
Series : SSO/1/C
ÛúÖê›ü ®ÖÓ.
Code No.
65/1/2
• Ûéú¯ÖµÖÖ •ÖÖÑ“Ö Ûú¸ü »Öë ×Ûú ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë ´ÖãצüŸÖ ¯Öéšü 8 Æïü …
• ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë ¤üÖ×Æü®Öê ÆüÖ£Ö Ûúß †Öê¸ü פü‹ ÝÖ‹ ÛúÖê›ü ®Ö´²Ö¸ü ÛúÖê ”ûÖ¡Ö ˆ¢Ö¸ü-¯Öã×ßÖÛúÖ Ûêú ´ÖãÜÖ-¯Öéšü ¯Ö¸ü ×»ÖÜÖë …
• Ûéú¯ÖµÖÖ •ÖÖÑ“Ö Ûú¸ü »Öë ×Ûú ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë 26 ¯ÖÏ¿®Ö Æïü …
• Ûéú¯ÖµÖÖ ¯ÖÏ¿®Ö ÛúÖ ˆ¢Ö¸ü ×»ÖÜÖ®ÖÖ ¿Öãºþ Ûú¸ü®Öê ÃÖê ¯ÖÆü»Öê, ¯ÖÏ¿®Ö ÛúÖ ÛÎú´ÖÖÓÛú †¾Ö¿µÖ ×»ÖÜÖë …
• ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ÛúÖê ¯ÖœÌü®Öê Ûêú ×»Ö‹ 15 ×´Ö®Ö™ü ÛúÖ ÃÖ´ÖµÖ ×¤üµÖÖ ÝÖµÖÖ Æîü … ¯ÖÏ¿®Ö-¯Ö¡Ö ÛúÖ ×¾ÖŸÖ¸üÞÖ ¯Öæ¾ÖÖÔÆËü®Ö ´Öë 10.15 ²Ö•Öê
×ÛúµÖÖ •ÖÖµÖêÝÖÖ … 10.15 ²Ö•Öê ÃÖê 10.30 ²Ö•Öê ŸÖÛú ”ûÖ¡Ö Ûêú¾Ö»Ö ¯ÖÏ¿®Ö-¯Ö¡Ö ÛúÖê ¯ÖœÌëüÝÖê †Öî¸ü ‡ÃÖ †¾Ö×¬Ö Ûêú ¤üÖî¸üÖ®Ö ¾Öê
ˆ¢Ö¸ü-¯Öã×ßÖÛúÖ ¯Ö¸ü ÛúÖê‡Ô ˆ¢Ö¸ü ®ÖÆüà ×»ÖÜÖëÝÖê …
• Please check that this question paper contains 8 printed pages.
• Code number given on the right hand side of the question paper should be written on the
title page of the answer-book by the candidate.
• Please check that this question paper contains 26 questions.
• Please write down the Serial Number of the question before attempting it.
• 15 minutes time has been allotted to read this question paper. The question paper will be
distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the
question paper only and will not write any answer on the answer-book during this period.
¯Ö¸üßõÖÖ£Öá ÛúÖê›ü ÛúÖê ˆ¢Ö¸ü-¯Öã×ßÖÛúÖ Ûêú ´ÖãÜÖ-¯Öéšü
¯Ö¸ü †¾Ö¿µÖ ×»ÖÜÖë …
Candidates must write the Code on
the title page of the answer-book.
SET – 2
65/1/2 2
General Instructions :
(i) All questions are compulsory.
(ii) Please check that this Question Paper contains 26 Questions.
(iii) Questions 1 – 6 in Section-A are Very Short Answer Type Questions carrying 1 mark
each.
(iv) Questions 7 – 19 in Section-B are Long Answer I Type Questions carrying 4 marks
each.
(v) Questions 20 – 26 in Section-C are Long Answer II Type Questions carrying
6 marks each
(vi) Please write down the serial number of the Question before attempting it.
ÜÖÞ›ü – †
SECTION – A
¯ÖÏ¿®Ö ÃÖÓܵÖÖ 1 ÃÖê 6 ŸÖÛú ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö 1 †ÓÛú ÛúÖ Æîü …
Question numbers 1 to 6 carry 1 mark each.
1. µÖפü ‹Ûú ¸êüÜÖÖ ×®Ö¤ìü¿ÖÖÓÛú †õÖÖë Ûúß ¬Ö®ÖÖŸ´ÖÛú פü¿ÖÖ†Öë Ûêú ÃÖÖ£Ö ÛúÖêÞÖ a, ß, ? ²Ö®ÖÖŸÖß Æîü, ŸÖÖê sin
2
a + sin
2
ß +
sin
2
? ÛúÖ ´ÖÖ®Ö ×»Ö×ÜÖ‹ … 1
If a line makes angles a, ß, ? with the positive direction of coordinate axes, then write
the value of sin
2
a + sin
2
ß + sin
2
?.
2. µÖפü A =
?
?
?
?
?
?
1 2
3 –1
, B =
?
?
?
?
?
?
1 3
–1 1
Æïü, ŸÖÖê AB ÛúÖ ´ÖÖ®Ö ×»Ö×ÜÖ‹ … 1
If A =
?
?
?
?
?
?
1 2
3 –1
and B =
?
?
?
?
?
?
1 3
–1 1
, write the value of AB .
3. C ÛúÖ ×¾Ö»ÖÖê¯Ö®Ö Ûú¸üÛêú ¾ÖÛÎúÖë Ûêú Ûãú»Ö xy = C cos x ÛúÖê ×®Öºþ×¯ÖŸÖ Ûú¸ü®Öê ¾ÖÖ»ÖÖ †¾ÖÛú»Ö ÃÖ´ÖßÛú¸üÞÖ ×»Ö×ÜÖ‹ … 1
Write the differential equation obtained by eliminating the arbitrary constant C in the
equation representing the family of curves xy = C cos x.
4. †¾ÖÛú»Ö ÃÖ´ÖßÛú¸üÞÖ 1 +
?
?
?
?
?
?
dy
dx
4
= 7
?
?
?
?
?
? d
2
y
dx
2
3
Ûúß ÛúÖê×™ü ŸÖ£ÖÖ ‘ÖÖŸÖ ÛúÖ µÖÖêÝÖ ×»Ö×ÜÖ‹ … 1
Write the sum of the order and degree of the differential equation
1 +
?
?
?
?
?
?
dy
dx
4
= 7
?
?
?
?
?
? d
2
y
dx
2
3
65/1/2 3 [P.T.O.
5. ÃÖפü¿Ö
?
a =
^
i – 2
^
j Ûúß ×¤ü¿ÖÖ ´Öë ‹Ûú ÃÖפü¿Ö –ÖÖŸÖ Ûúßו֋ וÖÃÖÛúÖ ¯Ö׸ü´ÖÖÞÖ 7 ‡ÛúÖ‡Ô Æîü … 1
Find a Vector in the direction of
?
a =
^
i – 2
^
j that has magnitude 7 units.
6. µÖפü
?
a ŸÖ£ÖÖ
?
b ´ÖÖ¡ÖÛú ÃÖפü¿Ö Æïü, ŸÖÖê
?
a ŸÖ£ÖÖ
?
b Ûêú ²Öß“Ö ÛúÖ ÛúÖêÞÖ ŒµÖÖ Æîü, •Ö²Ö×Ûú 2
?
a –
?
b ‹Ûú ´ÖÖ¡ÖÛú
ÃÖפü¿Ö Æîü ? 1
If
?
a and
?
b are unit Vectors, then what is the angle between
?
a and
?
b so that 2
?
a –
?
b
is a unit vector ?
ÜÖÞ›ü – ²Ö
SECTION – B
¯ÖÏ¿®Ö ÃÖÓܵÖÖ 7 ÃÖê 19 ŸÖÛú ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö 4 †ÓÛú ÛúÖ Æîü …
Question numbers 7 to 19 carry 4 marks each.
7. –ÖÖŸÖ Ûúßו֋ :
)
?
(
x
(x – 1)
2
(x + 2)
dx 4
†£Ö¾ÖÖ
–ÖÖŸÖ Ûúßו֋ :
)
?
(
x + 2
2x
2
+ 6x + 5
dx
Find :
)
?
(
x
(x – 1)
2
(x + 2)
dx
OR
Find :
)
?
(
x + 2
2x
2
+ 6x + 5
dx
8. 15 ²Ö»²ÖÖë Ûêú œÌêü¸ü ÃÖê, וÖÃÖ´Öë 5 ²Ö»²Ö ÜÖ¸üÖ²Ö Æïü, 2 ²Ö»²ÖÖë ÛúÖ ‹Ûú ®Ö´Öæ®ÖÖ µÖÖ¥ü“”ûµÖÖ, ײ֮ÖÖ ¯ÖÏןÖãÖÖ¯Ö®ÖÖ Ûêú ×®ÖÛúÖ»ÖÖ
•ÖÖŸÖÖ Æîü … ÜÖ¸üÖ²Ö ²Ö»²ÖÖë Ûúß ÃÖÓܵÖÖ ÛúÖ ¯ÖÏÖ×µÖÛúŸÖÖ ²ÖÓ™ü®Ö –ÖÖŸÖ Ûúßו֋ … 4
†£Ö¾ÖÖ
‹Ûú ×¾Ö¿ÖêÂÖ ÃÖ´ÖõÖÖ ÛúÖê A ŸÖ£ÖÖ B «üÖ¸üÖ Ã¾ÖŸÖÓ¡Ö ºþ¯Ö ÃÖê Æü»Ö Ûú¸ü®Öê Ûúß ¯ÖÏÖ×µÖÛúŸÖÖ‹Ñ ÛÎú´Ö¿Ö:
1
2
ŸÖ£ÖÖ
1
3
Æïü … µÖפü
¤üÖê®ÖÖë þ֟ÖÓ¡Ö ºþ¯Ö ÃÖê ÃÖ´ÖõÖÖ ÛúÖê Æü»Ö Ûú¸ü®Öê ÛúÖ ¯ÖϵÖÖÃÖ Ûú¸üŸÖê Æïü, ŸÖÖê ¯ÖÏÖ×µÖÛúŸÖÖ –ÖÖŸÖ Ûúßו֋ ×Ûú
(i) ÃÖ´ÖõÖÖ Æü»Ö ÆüÖê •ÖÖŸÖß Æîü …
(ii) ˆ®Ö´Öë ÃÖê ŸÖ£µÖŸÖÖ ÛúÖê‡Ô ‹Ûú ÃÖ´ÖõÖÖ Æü»Ö Ûú¸ü »ÖêŸÖÖ Æîü …
65/1/2 4
From a lot of 15 bulbs which include 5 defectives, a sample of 2 bulbs is drawn at
random (without replacement). Find the probability distribution of the number of
defective bulbs.
OR
Probability of solving specific problem independently by A and B are
1
2
and
1
3
respectively. If both try to solve the problem independently, find the probability that
(i) the problem is solved
(ii) exactly one of them solves the problem.
9. ? ÛúÖ ´ÖÖ®Ö –ÖÖŸÖ Ûúßו֋ ŸÖÖ×Ûú “ÖÖ¸ü ز֤ãü A, B, C ŸÖ£ÖÖ D ו֮ÖÛêú ×ãÖ×ŸÖ ÃÖפü¿Ö ÛÎú´Ö¿Ö: 4
^
i + 5
^
j +
^
k,
–
^
j –
^
k, 3
^
i + ?
^
j + 4
^
k ŸÖ£ÖÖ –4
^
i + 4
^
j + 4
^
k Æïü, ÃÖ´ÖŸÖ»ÖßµÖ Æïü … 4
Find the value of ? so that the four points A, B, C and D with position vectors
4
^
i + 5
^
j +
^
k, –
^
j –
^
k, 3
^
i + ?
^
j + 4
^
k and –4
^
i + 4
^
j + 4
^
k respectively are coplanar.
10. ¸êüÜÖÖ†Öë
?
r = (
^
i + 2
^
j +
^
k) + ?(
^
i –
^
j +
^
k) ŸÖ£ÖÖ
?
r = (2
^
i –
^
j –
^
k) + µ(2
^
i +
^
j + 2
^
k) Ûêú ²Öß“Ö Ûúß
®µÖæ®ÖŸÖ´Ö ¤æü¸üß –ÖÖŸÖ Ûúßו֋ … 4
Find the shortest distance between the lines
?
r = (
^
i + 2
^
j +
^
k) + ?(
^
i –
^
j +
^
k) and
?
r = (2
^
i –
^
j –
^
k) + µ(2
^
i +
^
j + 2
^
k)
11. Æü»Ö Ûúßו֋ : tan
–1
2x + tan
–1
3x =
p
4
4
†£Ö¾ÖÖ
×ÃÖ¨ü Ûúßו֋ ×Ûú : tan
–1
63
16
= sin
–1
5
13
+ cos
–1
3
5
Solve : tan
–1
2x + tan
–1
3x =
p
4
OR
Prove that : tan
–1
63
16
= sin
–1
5
13
+ cos
–1
3
5
Page 5
65/1/2 1 [P.T.O.
¸üÖê»Ö ®ÖÓ.
Roll No.
ÝÖ×ÞÖŸÖ
MATHEMATICS
×®Ö¬ÖÖÔ׸üŸÖ ÃÖ´ÖµÖ : 3 ‘ÖÞ™êüü] [†×¬ÖÛúŸÖ´Ö †ÓÛú : 100
Time allowed : 3 hours ] [ Maximum Marks : 100
ÃÖÖ´ÖÖ®µÖ ×®Ö¤ìü¿Ö :
(i) ÃÖ³Öß ¯ÖÏ¿®Ö †×®Ö¾ÖÖµÖÔ Æïü …
(ii) Ûéú¯ÖµÖÖ •ÖÖÑ“Ö Ûú¸ü »Öë ×Ûú ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë 26 ¯ÖÏ¿®Ö Æïü …
(iii) ÜÖÞ›ü-† Ûêú ¯ÖÏ¿®Ö ÃÖÓ. 1–6 ŸÖÛú †×ŸÖ »Ö‘Öã-ˆ¢Ö¸ü ¾ÖÖ»Öê ¯ÖÏ¿®Ö Æïü †Öî¸ü ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö Ûêú ×»Ö‹ 1 †ÓÛú ×®Ö¬ÖÖÔ׸üŸÖ Æîü …
(iv) ÜÖÞ›ü-²Ö Ûêú ¯ÖÏ¿®Ö ÃÖÓ. 7–19 ŸÖÛú ¤üß‘ÖÔ-ˆ¢Ö¸ü I ¯ÖÏÛúÖ¸ü Ûêú ¯ÖÏ¿®Ö Æïü †Öî¸ü ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö Ûêú ×»Ö‹ 4 †ÓÛú ×®Ö¬ÖÖÔ׸üŸÖ Æïü …
(v) ÜÖÞ›ü-ÃÖ Ûêú ¯ÖÏ¿®Ö ÃÖÓ. 20–26 ŸÖÛú ¤üß‘ÖÔ-ˆ¢Ö¸ü II ¯ÖÏÛúÖ¸ü Ûêú ¯ÖÏ¿®Ö Æïü †Öî¸ü ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö Ûêú ×»Ö‹ 6 †ÓÛú ×®Ö¬ÖÖÔ׸üŸÖ
Æïü …
(vi) ˆ¢Ö¸ü ×»ÖÜÖ®ÖÖ ¯ÖÏÖ¸Óü³Ö Ûú¸ü®Öê ÃÖê ¯ÖÆü»Öê Ûéú¯ÖµÖÖ ¯ÖÏ¿®Ö ÛúÖ ÛÎú´ÖÖÓÛú †¾Ö¿µÖ ×»Ö×ÜÖ‹ …
Series : SSO/1/C
ÛúÖê›ü ®ÖÓ.
Code No.
65/1/2
• Ûéú¯ÖµÖÖ •ÖÖÑ“Ö Ûú¸ü »Öë ×Ûú ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë ´ÖãצüŸÖ ¯Öéšü 8 Æïü …
• ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë ¤üÖ×Æü®Öê ÆüÖ£Ö Ûúß †Öê¸ü פü‹ ÝÖ‹ ÛúÖê›ü ®Ö´²Ö¸ü ÛúÖê ”ûÖ¡Ö ˆ¢Ö¸ü-¯Öã×ßÖÛúÖ Ûêú ´ÖãÜÖ-¯Öéšü ¯Ö¸ü ×»ÖÜÖë …
• Ûéú¯ÖµÖÖ •ÖÖÑ“Ö Ûú¸ü »Öë ×Ûú ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ´Öë 26 ¯ÖÏ¿®Ö Æïü …
• Ûéú¯ÖµÖÖ ¯ÖÏ¿®Ö ÛúÖ ˆ¢Ö¸ü ×»ÖÜÖ®ÖÖ ¿Öãºþ Ûú¸ü®Öê ÃÖê ¯ÖÆü»Öê, ¯ÖÏ¿®Ö ÛúÖ ÛÎú´ÖÖÓÛú †¾Ö¿µÖ ×»ÖÜÖë …
• ‡ÃÖ ¯ÖÏ¿®Ö-¯Ö¡Ö ÛúÖê ¯ÖœÌü®Öê Ûêú ×»Ö‹ 15 ×´Ö®Ö™ü ÛúÖ ÃÖ´ÖµÖ ×¤üµÖÖ ÝÖµÖÖ Æîü … ¯ÖÏ¿®Ö-¯Ö¡Ö ÛúÖ ×¾ÖŸÖ¸üÞÖ ¯Öæ¾ÖÖÔÆËü®Ö ´Öë 10.15 ²Ö•Öê
×ÛúµÖÖ •ÖÖµÖêÝÖÖ … 10.15 ²Ö•Öê ÃÖê 10.30 ²Ö•Öê ŸÖÛú ”ûÖ¡Ö Ûêú¾Ö»Ö ¯ÖÏ¿®Ö-¯Ö¡Ö ÛúÖê ¯ÖœÌëüÝÖê †Öî¸ü ‡ÃÖ †¾Ö×¬Ö Ûêú ¤üÖî¸üÖ®Ö ¾Öê
ˆ¢Ö¸ü-¯Öã×ßÖÛúÖ ¯Ö¸ü ÛúÖê‡Ô ˆ¢Ö¸ü ®ÖÆüà ×»ÖÜÖëÝÖê …
• Please check that this question paper contains 8 printed pages.
• Code number given on the right hand side of the question paper should be written on the
title page of the answer-book by the candidate.
• Please check that this question paper contains 26 questions.
• Please write down the Serial Number of the question before attempting it.
• 15 minutes time has been allotted to read this question paper. The question paper will be
distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the
question paper only and will not write any answer on the answer-book during this period.
¯Ö¸üßõÖÖ£Öá ÛúÖê›ü ÛúÖê ˆ¢Ö¸ü-¯Öã×ßÖÛúÖ Ûêú ´ÖãÜÖ-¯Öéšü
¯Ö¸ü †¾Ö¿µÖ ×»ÖÜÖë …
Candidates must write the Code on
the title page of the answer-book.
SET – 2
65/1/2 2
General Instructions :
(i) All questions are compulsory.
(ii) Please check that this Question Paper contains 26 Questions.
(iii) Questions 1 – 6 in Section-A are Very Short Answer Type Questions carrying 1 mark
each.
(iv) Questions 7 – 19 in Section-B are Long Answer I Type Questions carrying 4 marks
each.
(v) Questions 20 – 26 in Section-C are Long Answer II Type Questions carrying
6 marks each
(vi) Please write down the serial number of the Question before attempting it.
ÜÖÞ›ü – †
SECTION – A
¯ÖÏ¿®Ö ÃÖÓܵÖÖ 1 ÃÖê 6 ŸÖÛú ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö 1 †ÓÛú ÛúÖ Æîü …
Question numbers 1 to 6 carry 1 mark each.
1. µÖפü ‹Ûú ¸êüÜÖÖ ×®Ö¤ìü¿ÖÖÓÛú †õÖÖë Ûúß ¬Ö®ÖÖŸ´ÖÛú פü¿ÖÖ†Öë Ûêú ÃÖÖ£Ö ÛúÖêÞÖ a, ß, ? ²Ö®ÖÖŸÖß Æîü, ŸÖÖê sin
2
a + sin
2
ß +
sin
2
? ÛúÖ ´ÖÖ®Ö ×»Ö×ÜÖ‹ … 1
If a line makes angles a, ß, ? with the positive direction of coordinate axes, then write
the value of sin
2
a + sin
2
ß + sin
2
?.
2. µÖפü A =
?
?
?
?
?
?
1 2
3 –1
, B =
?
?
?
?
?
?
1 3
–1 1
Æïü, ŸÖÖê AB ÛúÖ ´ÖÖ®Ö ×»Ö×ÜÖ‹ … 1
If A =
?
?
?
?
?
?
1 2
3 –1
and B =
?
?
?
?
?
?
1 3
–1 1
, write the value of AB .
3. C ÛúÖ ×¾Ö»ÖÖê¯Ö®Ö Ûú¸üÛêú ¾ÖÛÎúÖë Ûêú Ûãú»Ö xy = C cos x ÛúÖê ×®Öºþ×¯ÖŸÖ Ûú¸ü®Öê ¾ÖÖ»ÖÖ †¾ÖÛú»Ö ÃÖ´ÖßÛú¸üÞÖ ×»Ö×ÜÖ‹ … 1
Write the differential equation obtained by eliminating the arbitrary constant C in the
equation representing the family of curves xy = C cos x.
4. †¾ÖÛú»Ö ÃÖ´ÖßÛú¸üÞÖ 1 +
?
?
?
?
?
?
dy
dx
4
= 7
?
?
?
?
?
? d
2
y
dx
2
3
Ûúß ÛúÖê×™ü ŸÖ£ÖÖ ‘ÖÖŸÖ ÛúÖ µÖÖêÝÖ ×»Ö×ÜÖ‹ … 1
Write the sum of the order and degree of the differential equation
1 +
?
?
?
?
?
?
dy
dx
4
= 7
?
?
?
?
?
? d
2
y
dx
2
3
65/1/2 3 [P.T.O.
5. ÃÖפü¿Ö
?
a =
^
i – 2
^
j Ûúß ×¤ü¿ÖÖ ´Öë ‹Ûú ÃÖפü¿Ö –ÖÖŸÖ Ûúßו֋ וÖÃÖÛúÖ ¯Ö׸ü´ÖÖÞÖ 7 ‡ÛúÖ‡Ô Æîü … 1
Find a Vector in the direction of
?
a =
^
i – 2
^
j that has magnitude 7 units.
6. µÖפü
?
a ŸÖ£ÖÖ
?
b ´ÖÖ¡ÖÛú ÃÖפü¿Ö Æïü, ŸÖÖê
?
a ŸÖ£ÖÖ
?
b Ûêú ²Öß“Ö ÛúÖ ÛúÖêÞÖ ŒµÖÖ Æîü, •Ö²Ö×Ûú 2
?
a –
?
b ‹Ûú ´ÖÖ¡ÖÛú
ÃÖפü¿Ö Æîü ? 1
If
?
a and
?
b are unit Vectors, then what is the angle between
?
a and
?
b so that 2
?
a –
?
b
is a unit vector ?
ÜÖÞ›ü – ²Ö
SECTION – B
¯ÖÏ¿®Ö ÃÖÓܵÖÖ 7 ÃÖê 19 ŸÖÛú ¯ÖÏŸµÖêÛú ¯ÖÏ¿®Ö 4 †ÓÛú ÛúÖ Æîü …
Question numbers 7 to 19 carry 4 marks each.
7. –ÖÖŸÖ Ûúßו֋ :
)
?
(
x
(x – 1)
2
(x + 2)
dx 4
†£Ö¾ÖÖ
–ÖÖŸÖ Ûúßו֋ :
)
?
(
x + 2
2x
2
+ 6x + 5
dx
Find :
)
?
(
x
(x – 1)
2
(x + 2)
dx
OR
Find :
)
?
(
x + 2
2x
2
+ 6x + 5
dx
8. 15 ²Ö»²ÖÖë Ûêú œÌêü¸ü ÃÖê, וÖÃÖ´Öë 5 ²Ö»²Ö ÜÖ¸üÖ²Ö Æïü, 2 ²Ö»²ÖÖë ÛúÖ ‹Ûú ®Ö´Öæ®ÖÖ µÖÖ¥ü“”ûµÖÖ, ײ֮ÖÖ ¯ÖÏןÖãÖÖ¯Ö®ÖÖ Ûêú ×®ÖÛúÖ»ÖÖ
•ÖÖŸÖÖ Æîü … ÜÖ¸üÖ²Ö ²Ö»²ÖÖë Ûúß ÃÖÓܵÖÖ ÛúÖ ¯ÖÏÖ×µÖÛúŸÖÖ ²ÖÓ™ü®Ö –ÖÖŸÖ Ûúßו֋ … 4
†£Ö¾ÖÖ
‹Ûú ×¾Ö¿ÖêÂÖ ÃÖ´ÖõÖÖ ÛúÖê A ŸÖ£ÖÖ B «üÖ¸üÖ Ã¾ÖŸÖÓ¡Ö ºþ¯Ö ÃÖê Æü»Ö Ûú¸ü®Öê Ûúß ¯ÖÏÖ×µÖÛúŸÖÖ‹Ñ ÛÎú´Ö¿Ö:
1
2
ŸÖ£ÖÖ
1
3
Æïü … µÖפü
¤üÖê®ÖÖë þ֟ÖÓ¡Ö ºþ¯Ö ÃÖê ÃÖ´ÖõÖÖ ÛúÖê Æü»Ö Ûú¸ü®Öê ÛúÖ ¯ÖϵÖÖÃÖ Ûú¸üŸÖê Æïü, ŸÖÖê ¯ÖÏÖ×µÖÛúŸÖÖ –ÖÖŸÖ Ûúßו֋ ×Ûú
(i) ÃÖ´ÖõÖÖ Æü»Ö ÆüÖê •ÖÖŸÖß Æîü …
(ii) ˆ®Ö´Öë ÃÖê ŸÖ£µÖŸÖÖ ÛúÖê‡Ô ‹Ûú ÃÖ´ÖõÖÖ Æü»Ö Ûú¸ü »ÖêŸÖÖ Æîü …
65/1/2 4
From a lot of 15 bulbs which include 5 defectives, a sample of 2 bulbs is drawn at
random (without replacement). Find the probability distribution of the number of
defective bulbs.
OR
Probability of solving specific problem independently by A and B are
1
2
and
1
3
respectively. If both try to solve the problem independently, find the probability that
(i) the problem is solved
(ii) exactly one of them solves the problem.
9. ? ÛúÖ ´ÖÖ®Ö –ÖÖŸÖ Ûúßו֋ ŸÖÖ×Ûú “ÖÖ¸ü ز֤ãü A, B, C ŸÖ£ÖÖ D ו֮ÖÛêú ×ãÖ×ŸÖ ÃÖפü¿Ö ÛÎú´Ö¿Ö: 4
^
i + 5
^
j +
^
k,
–
^
j –
^
k, 3
^
i + ?
^
j + 4
^
k ŸÖ£ÖÖ –4
^
i + 4
^
j + 4
^
k Æïü, ÃÖ´ÖŸÖ»ÖßµÖ Æïü … 4
Find the value of ? so that the four points A, B, C and D with position vectors
4
^
i + 5
^
j +
^
k, –
^
j –
^
k, 3
^
i + ?
^
j + 4
^
k and –4
^
i + 4
^
j + 4
^
k respectively are coplanar.
10. ¸êüÜÖÖ†Öë
?
r = (
^
i + 2
^
j +
^
k) + ?(
^
i –
^
j +
^
k) ŸÖ£ÖÖ
?
r = (2
^
i –
^
j –
^
k) + µ(2
^
i +
^
j + 2
^
k) Ûêú ²Öß“Ö Ûúß
®µÖæ®ÖŸÖ´Ö ¤æü¸üß –ÖÖŸÖ Ûúßו֋ … 4
Find the shortest distance between the lines
?
r = (
^
i + 2
^
j +
^
k) + ?(
^
i –
^
j +
^
k) and
?
r = (2
^
i –
^
j –
^
k) + µ(2
^
i +
^
j + 2
^
k)
11. Æü»Ö Ûúßו֋ : tan
–1
2x + tan
–1
3x =
p
4
4
†£Ö¾ÖÖ
×ÃÖ¨ü Ûúßו֋ ×Ûú : tan
–1
63
16
= sin
–1
5
13
+ cos
–1
3
5
Solve : tan
–1
2x + tan
–1
3x =
p
4
OR
Prove that : tan
–1
63
16
= sin
–1
5
13
+ cos
–1
3
5
65/1/2 5 [P.T.O.
12. µÖפü y =
x cos
–1
x
1 – x
2
– log 1 – x
2
Æîü, ŸÖÖê ×ÃÖ¨ü Ûúßו֋ ×Ûú
dy
dx
=
cos
–1
x
(1 – x
2
)
3/2
4
If y =
x cos
–1
x
1 – x
2
– log 1 – x
2
, then prove that
dy
dx
=
cos
–1
x
(1 – x
2
)
3/2
13. x Ûêú ÃÖÖ¯ÖêõÖ (sin x)
x
+ sin
–1
x ÛúÖ †¾ÖÛú»Ö•Ö –ÖÖŸÖ Ûúßו֋ … 4
Find the derivative of (sin x)
x
+ sin
–1
x w.r.t. x
14. µÖפü x = a sec
3
?, y = a tan
3
? Æîü, ŸÖÖê
d
2
y
dx
2
ÛúÖ ´ÖÖ®Ö ? =
p
4
¯Ö¸ü –ÖÖŸÖ Ûúßו֋ … 4
If x = a sec
3
?, y = a tan
3
?, find
d
2
y
dx
2
at ? =
p
4
15. –ÖÖŸÖ Ûúßו֋ :
)
?
(
(x
2
+ 1)e
x
(x + 1)
2
dx 4
Find
)
?
(
(x
2
+ 1)e
x
(x + 1)
2
dx
16. ¤üÖê ×¾ÖªÖ»ÖµÖ A ŸÖ£ÖÖ B †¯Ö®Öê ×¾ÖªÖÙ£ÖµÖÖë ÛúÖê ÃÖÆüµÖÖêÝÖ Ûúß ³ÖÖ¾Ö®ÖÖ, ÃÖŸµÖ¾ÖÖפüŸÖÖ ŸÖ£ÖÖ ÃÖÆü®Ö¿Ö߻֟ÖÖ Ûêú ´Ö滵ÖÖë Ûêú
×»Ö‹ ¯ÖÏ×ŸÖ ×¾ÖªÖ£Öá ÛÎú´Ö¿Ö: ` x, ` y ŸÖ£ÖÖ ` z ÛúÖ ¯Öã¸üÃÛúÖ¸ü ¤êü®ÖÖ “ÖÖÆüŸÖê Æïü … ×¾ÖªÖ»ÖµÖ A †¯Ö®Öê ÛÎú´Ö¿Ö: 3, 1, 2
×¾ÖªÖÙ£ÖµÖÖë ÛúÖê ‡®Ö ´Ö滵ÖÖë Ûêú ×»Ö‹ Ûãú»Ö ` 1,100 ¯Öã¸üÃÛúÖ¸ü þֺþ¯Ö ¤êü®ÖÖ “ÖÖÆüŸÖÖ Æîü … ×¾ÖªÖ»ÖµÖ B †¯Ö®Öê ÛÎú´Ö¿Ö: 1,
2, 3 ×¾ÖªÖÙ£ÖµÖÖë ÛúÖê ` 1,400 ¯Öã¸üÃÛúÖ¸ü þֺþ¯Ö ¤êü®ÖÖ “ÖÖÆüŸÖÖ Æîü … µÖפü ‡®Ö ŸÖß®ÖÖë ´Ö滵ÖÖë ¯Ö¸ü פü‹ ÝÖ‹ ‹Ûú-‹Ûú
¯Öã¸üÃÛúÖ¸ü Ûúß Ûãú»Ö ¸üÖ×¿Ö ` 600 Æîü, ŸÖÖê
(i) ˆ¯Ö¸üÖêŒŸÖ ×ãÖ×ŸÖ ÛúÖê ¸îü×ÜÖÛú ÃÖ´ÖßÛú¸üÞÖ ²Ö®ÖÖÛú¸ü ‹Ûú †Ö¾µÖæÆü ÃÖ´ÖßÛú¸üÞÖ Ûêú ºþ¯Ö ´Öë ¾µÖŒŸÖ Ûúßו֋ …
(ii) ŒµÖÖ ÃÖ´ÖßÛú¸üÞÖ ×®ÖÛúÖµÖ ÛúÖê †Ö¾µÖæÆüÖë Ûêú ¯ÖϵÖÖêÝÖ ÃÖê Æü»Ö ×ÛúµÖÖ •ÖÖ ÃÖÛúŸÖÖ Æîü ?
(iii) †Ö¯Ö ×ÛúÃÖ ´Öæ»µÖ ¯Ö¸ü †×¬ÖÛúŸÖ´Ö ¯Öã¸üÃÛúÖ¸ü ¤êü®ÖÖ “ÖÖÆüŸÖê Æïü †Öî¸ü ŒµÖÖë ? 4
Two schools A and B decided to award prizes to their students for three values, team
spirit, truthfulness and tolerance at the rate of ` x, ` y and ` z per student respectively.
School A, decided to award a total of ` 1,100 for the three values to 3, 1 and 2 students
respectively while school B decided to award ` 1,400 for the three values to 1, 2 and 3
students respectively. If one prize for all the three values together amount to ` 600
then
(i) Represent the above situation by a matrix equation after forming linear
equations.
(ii) Is it possible to solve the system of equations so obtained using matrices ?
(iii) Which value you prefer to be rewarded most and why ?
Read More
|
22 videos|162 docs|17 tests
|
FAQs on Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths - Additional Study Material for JEE
| 1. What is the exam pattern of JEE Mathematics paper for Class 12? |  |
Ans. The JEE Mathematics paper for Class 12 consists of 30 questions in total. The paper is divided into two sections - Section A and Section B. Section A consists of 20 multiple-choice questions (MCQs) with four options, out of which only one is correct. Section B consists of 10 questions with a single-digit integer answer ranging from 0 to 9.
| 2. How should I prepare for the JEE Mathematics paper for Class 12? | |
Ans. To prepare for the JEE Mathematics paper for Class 12, it is essential to have a thorough understanding of the concepts covered in the syllabus. Start by reviewing the textbooks and class notes, and make sure to practice solving a variety of problems. It is also helpful to solve past year papers and take mock tests to familiarize yourself with the exam pattern and improve time management skills.
| 3. What are some important topics to focus on for the JEE Mathematics paper for Class 12? | |
Ans. Some important topics to focus on for the JEE Mathematics paper for Class 12 include calculus, algebra, coordinate geometry, vectors and 3D geometry, and probability. These topics carry significant weightage in the exam and mastering them will help you score well. However, it is important to have a balanced preparation and not neglect other topics as well.
| 4. Are calculators allowed in the JEE Mathematics paper for Class 12? | |
Ans. No, calculators or any electronic devices are not allowed in the JEE Mathematics paper for Class 12. The exam is designed to test your problem-solving abilities and mathematical skills without the aid of calculators. It is important to practice solving problems manually to build speed and accuracy.
| 5. How can I manage time effectively during the JEE Mathematics paper for Class 12? | |
Ans. Time management is crucial during the JEE Mathematics paper for Class 12. Start by allocating a specific amount of time to each section based on the number of questions. Prioritize solving the questions you are confident about first and then move on to the more challenging ones. If you encounter a difficult question, it is better to skip it and come back to it later if time permits. Regular practice and mock tests will help you improve your speed and efficiency.
Related Exams
About this Document
|
4.83/5 Rating |
|
Nov 22, 2024 Last updated |
Document Description: Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths for JEE 2024 is part of Additional Study Material for JEE preparation.
The notes and questions for Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths have been prepared according to the JEE exam syllabus. Information about Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths covers topics
like and Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths Example, for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths.
Introduction of Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths in English is available as part of our Additional Study Material for JEE
for JEE & Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths in Hindi for Additional Study Material for JEE course.
Download more important topics related with notes, lectures and mock test series for JEE
Exam by signing up for free. JEE: Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths | Additional Study Material for JEE
Description
Full syllabus notes, lecture & questions for Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths | Additional Study Material for JEE - JEE | Plus excerises question with solution to help you revise complete syllabus for Additional Study Material for JEE | Best notes, free PDF download
Information about Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths
In this doc you can find the meaning of Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths defined & explained in the simplest way possible. Besides explaining types of
Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths theory, EduRev gives you an ample number of questions to practice Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths tests, examples and also practice JEE
tests
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Mathematics (Set - 2)
,2015
,Viva Questions
,Extra Questions
,Maths | Additional Study Material for JEE
,mock tests for examination
,past year papers
,Summary
,Exam
,Past Year Paper
,video lectures
,Maths | Additional Study Material for JEE
,2015
,Class 12
,2015
,Free
,Objective type Questions
,Semester Notes
,MCQs
,Previous Year Questions with Solutions
,Maths | Additional Study Material for JEE
,Past Year Paper
,Sample Paper
,Mathematics (Set - 2)
,Past Year Paper
,Delhi
,Class 12
,Class 12
,study material
,practice quizzes
,Delhi
,Important questions
,Delhi
,shortcuts and tricks
,ppt
,Mathematics (Set - 2)
;
Additional Information about Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths for JEE Preparation
Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths Free PDF Download
The Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths is an invaluable resource that delves deep into the core of the JEE exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths now and kickstart your journey towards success in the JEE exam.
Importance of Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths
The importance of Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths cannot be overstated, especially for JEE aspirants.
This document holds the key to success in the JEE exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths Notes
Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths Notes on EduRev are your ultimate resource for success.
Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths JEE Questions
The "Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths JEE Questions" guide is a valuable resource for all aspiring students preparing for the
JEE exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths on the App
Students of JEE can study Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Past Year Paper, Mathematics (Set - 2), Delhi, 2015, Class 12, Maths is prepared as per the latest JEE syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup