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IIPUlatha

This document is a model question paper for the First Test in Mathematics for Class II PU at Government PU College, Yelahanka, Bangalore North, for the academic year 2025-26. It consists of multiple-choice questions, short answer questions, and detailed problems covering various mathematical concepts. The total marks for the paper are 40, with a time limit of 1 hour and 30 minutes.

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haku91139
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16 views2 pages

IIPUlatha

This document is a model question paper for the First Test in Mathematics for Class II PU at Government PU College, Yelahanka, Bangalore North, for the academic year 2025-26. It consists of multiple-choice questions, short answer questions, and detailed problems covering various mathematical concepts. The total marks for the paper are 40, with a time limit of 1 hour and 30 minutes.

Uploaded by

haku91139
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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GOVERNMENT PU COLLEGE (AN0089) , Yelahanka Bangalore North

FIRST TEST MODEL PAPAR 1

CLASS: II PU SUBJECT : MATHEMATICS MAX MARKS : 40

TIME : 1 hour 30 min Academic year : 2025-26

I Answer all FIVE Multiple Choice Questions 5x1=5

1. The relation R in the set { 1, 2 , 3 } given by R = { ( 1 , 1 ) , ( 1 , 2 ) } is


(A) Reflexive but not symmetric (B) symmetric but not transitive
(B) Transitive but not symmetric (D) equivalence relation
2. Let f : R → R be defined by f(x) =
𝟏
𝐱
, x ∈ R . Then f is

(A) One – one (B) onto (C) bijective (D) not defined

3. tan -1 √3 + sec-1 ( - 2 ) is equal to

(A) 𝜋 (B) - (C) (D)

4. If A be a non singular matrix of order 3 with | adj A | = 25 then |A| is


equal to

(A) 5 (B) 25 (C) 125 (D) 3

5. The number of points where f(x) = |x + 2|+|x – 3| is not differentiable is


(A) 2 (B) 3 (C) 0 (D) 0

II Answer any FIVE Questions 5 x 2 = 10

6. Verify the function f: R → R given by f(x) = x2 is one-one or onto .

7.
𝟏
Prove that sin -1 ( 2x √1 − 𝑥 ) = 2 cos-1 x , ≤ 𝒙 ≤𝟏.
√𝟐

8.
𝟏
Write the simplest form of cot -1 ( ) , |x|>1.
𝒙𝟐 𝟏

𝟐 −1 10
9. If x +y = , find the values of x and y .
𝟑 1 5
10. If A , B are symmetric matrices of same order, then show that

(AB – BA ) is a Skew symmetric matrix.

11. Find the equation of the line joining ( 1 , 3 ) and ( 0 , 0 ) using


determinants.

12. Find if 2x + 3y = sin y .


III Answer any FIVE Questions 5 x 3 = 15

13. Determine whether the relation R in the set A = {1,2,3,… 14 } defined

by R = { ( x , y ) : 3x – y = 0 } is reflexive , symmetric and transitive .

14. Show that the relation R in the set Z of integers given by

R = { ( a , b ) : 2 divides a – b } is an equivalence relation .

𝟏𝟐 𝟑 𝟓𝟔
15. Prove that cos -1 ( ) + sin -1 ( )= sin -1 ( )
𝟏𝟑 𝟓 𝟔𝟓

𝟏 𝐱 𝟏
16. Solve : tan-1 ( )= tan-1 x ,x>0.
𝟏 𝐱 𝟐

17. Express the matrix 1 2 as the sum of a symmetric and


3 4

Skew - symmetric matrix.

2 3
18. For A= , verify that A ( adj A) = (adj A ) A = | A| I .
−4 −6

19. Find the value of k so that the function f defined by

𝐤 𝐱 𝟐 𝒊𝒇 𝒙 ≤𝟐
f(x) = is continuous at x = 2 .
𝟑 𝒊𝒇 𝒙 >𝟐

VI Answer any TWO Questions 2 x 5 = 10

20. Let A = R – { 2 } and B = R – { 1 } . Consider the function f : A →B


𝐱 𝟏
defined by f ( x ) = 𝐱 𝟐
. Is f one-one and onto ? Justify your answer.

1 2 3
21. If A = 3 −2 1 , then show that A3 – 23 A – 40 I = 0 .
4 2 1
22. Solve the system of equations by matrix method
x – y + 2z = 1

2y – 3z = 1

3x –2y + 4z = 2

𝒅𝟐 𝒚 𝐝𝐲
23. If y = 3 e2x + 2 e3x Prove that -5 +6y=0.
𝒅𝒙𝟐 𝐝𝐱

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