UP Board 2018: Class 12th Mathematics (II) Solved Guess Paper

This is that time of the year again when Board exams are approaching and all students are preparing for the Board Exams. Therefore in this article, we present you UP Board Class 12th Mathematics (second) solved guess paper to prepare for the upcoming mathematics board exam scheduled to be conducted on 12^th February 2018.

There is always a sense of anxiety and nervousness regarding exams. In these circumstances either you get stressed and stop giving your best performance or take a few planned steps in the right direction to get desire result.

If you are thorough with the topics and every concept and searching some important mathematics question with solution then you are on right path. Here we present you the UP Board Class 12th Mathematics (second) solved guess paper to prepare for the upcoming Mathematics board exam 2018. While practicing this guess paper, you should realize about all topics you are confident and also the week topics.

Mathematics is one such subject in which students can score maximum marks by following the right preparation techniques and question solving skills. You cannot learn Mathematics by just memorizing a set of formulae given in the book. You need to understand how to use those formulae, for which you would require more and more practice. So, it’s very important to solve practice papers, guess papers and sample papers. This will help you track your preparedness and also letting you know your weak areas which you may improve later. 

UP Board Class 12th Mathematics (second) solved guess paper 2018 has been specially prepared by the subject experts after the brief analysis of previous year question papers and the latest examination format. The paper consists entirely fresh questions picked from the most important topics of class 12th Mathematics (second).

Board exam is the part of life but not the LIFE: Attempt your exam papers without stress

Salient features of this Solved Guess Paper are:

• Strictly follows latest UP Board Class 12th Mathematics (second) syllabus

• Based on latest examination pattern

• Focuses upon topics, from which questions are likely to be asked

• Offers detailed solutions for each and every question

• Perfect for practice & revision.

Some questions from the solved guess paper are given below:

प्रश्न:  यदि रेखाएं 3x + 4y - 7 = a तथा px + qy + 10 = a  एक दुसरे के समान्तर हो, तब सिद्ध कीजिए कि 3q = 4p

उत्तर: रेखा 3x + 4y - 7 = 0 की प्रवणता m₁ = - [x/y]  ⇒ m₁ = -3/4

तथा रेखा px +qy + 10 =0 की प्रवणता m₂ = - [x/y] =  -p/q

रेखाएं एक दुसरे के समान्तर हे तब m₁ = m₂

-3/4 = -p/q

3q = 4p

UP Board 2018: Class 12th Mathematics(I) Solved Guess Paper

प्रश्न : एक गतिमान कण 1 सेकेण्ड में S = (3t² + 2t +1) सेमी दुरी तय करता है | 4 से. बाद कण का वेग ज्ञात  कीजिए |

उत्तर: t सेकेण्ड में कण की दुरी S = (3t² + 2t +1)

t के सापेक्ष अवकलन करने पर

ds / dt = d / dt (3t² + 2t +1)

V = 6t + 2

प्रश्न : उस वृत का समीकरण ज्ञात किजिए जिसके दो व्यासो के समीकरण 2x + y + 4 = 0 और x –y – 1 = 0 और वृत्त बिंदु (1,1) से गुजरता है |

उत्तर :

दिये गये व्यास

2x + y + 4 = 0         …………… (i)

x – y – 1 = 0           ……………(ii)

समी. (i) व  (ii) को जोड़ने पर

3x + 3 = 0 ⇒ 3x = - 3 ⇒ x = - 1

X का मान समी. (2) में रखने पर

- 1 – y – 1 = 0 ⇒ - y – 2  = 0 ⇒ y = - 2

अत; व्रत का केन्द्र (-1, -2)

व्रत के केन्द्र (-1, -2) से बिन्दु (1,1) के बीच की दूरी = √(1-1)² + (-2 – 1)²

√(-2)² + (-3)²

√4+9  =√13

अत: व्रत की त्रिज्या √13

अब व्रत का समी. : ( x – h )² + ( y – k ) ² = a²

( x – 1 )² + ( y + 2 ) ² = (√13)²

X² + 1 + 2x + y² + 4 + 2y = 13

X² = y² + 2x + 4y = 13 – 5

x² + y² + 2x + 4y = 8

प्रश्न :  यदि अतिपरवलय x² / a² – y² / b² = 1 तथा x² / a² – y² / b² = - 1 की उत्केन्द्रता क्रमश e₁ और e₂ है तो सिद्ध कीजिए कि : 1 / e₁² + 1 / e₂² = 1

उत्तर : अतिपरवलय x² / a² – y² / b² = 1 की उत्केन्द्रता का समी. e1 = √1 + b² / a²

e₁² = 1 + b² / a²

e₁² = a² + b² / a²

1 / e₁² = a² / a² + b²         ………………. (i)

इसी प्रकार अतिपरवलय x² / a² – y² / b² = - 1 की उत्केन्द्रता का समी. e² = √1 + a² / b²

e₂² = 1 +a² / b²

e₂² = b² + a² / b²

1/e₂² = b² / b² + a²           …………….. (ii)

समी. (i) व (ii) को जोड़ने पर

1 / e₁² + 1 / e₂² = a² / a² + b² + b² / b² + a²

= a²  + b² / a² + b²

अत: 1 / e₁² + 1 / e₂² =1

Practicing this paper will help the students in understanding the depth with which a topic should be studied in order to prepare effectively to get the desired results.

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