Karnataka 1st PUC Second Test Question Paper 2025 Mathematics

Government of Karnataka
Karnataka Secondary Education Examination Board

Question Papers
Quarterly Exam

SECOND QUARTERLY TEST DECEMBER 2025
CLASS:IPUC SUBJECT: MATHEMATICS (35) Max. Marks : 40
Time: 1 Hr. 30 Mins

PART-A
Answer all the multiple choice questions: 7x1=7
1) The sum of all the binomial coefficients in the expansion of (a + b is
A) 2n B) 2n-1 C) n D) 2+1
n?
2) The 7th term of the sequence defined by a
49 7 14 49
A) 64 B) 128 C D) 128
128
3) The centre and radius of the circle (x+ 5) + (y-3) = 36.
A) (5,3) and 6 B) (-5, 3) and 6 C) (5,-3) and 36 D) (-5, 3) and 36
4) The eccentricity of the hyperbola -y=6is
A) 2 B) /2 C) 3 D) 1
5) Statement 1:The perpendicular distance from the point (6, 7, 8) to Zx - plane is 7
Statement 2: The perpendicular distance of the point (a, b, c) from the x-axis is +
A) Statement 1is true and Statement 2 is false
B Statement 1is false and Statement 2 is false
C) Staterment 1istrue and Statement 2 is true, Statement 2 is not correct explanation for
statement 1
D) Statement 1 is true and Statement 2 is true, Statement 2 is a correct explanation for
statement 1
6) The octant in which the points (-3, 1, 2) lie.
A) VIoctant B) Voctant C) VIIoctant D) VIII octant
7) Match the List Iwith List II
List I List II
sin 2x
Ja) lim i) 12
I’0 3x

1
|b)The derivative ofx'-27 with respect to x at x =-2 ii)
COS X
c) lim
X’0 TU X

Choose the correct answer from the options given below
A)a-i, b-ii, c-ii B) a-ii, b-i, c-i C) a-ii, b-i, c-ii D) a-ii, b-i, c-ii
II For question numbers 8 to 10 choose appropriate answer from the given answer
below: 3x1=3
(10, -2, 6, 2)
8) The geometric mean of the numbers 4 and 9 is

(PTO)

-2

9) The length of the major axis of the Ellipse 25 16

x-2 if x <0
10) If f(x) = x+2 if x>0 then im f(x) is
X’0

PART-B
III Answer any THREE of the following : 3x2=6
11) Using binomial theorem evaluate (101.
12) Find the co-ordinates of the focus and equation of the directrix of the parabola y = 12x.
3x*-x-10
13) Evaluate : lim
’2 x'-4

14) Evaluate : lim
X’1

15) In the GP. 3, 32, 33 ....... n terms. If S = 120, find the value of 'n'.

PART-C
IV Answer any THREE of the following: 3x3=9

16) Find the 3 numbers to be inserted between land 256 such that resulting sequence is in GP.
17) Differentiate cosx w.r.t. x from first principle.

18) Find (2+1)+(2-1).
19) Find the equation of the circle with radius 5 whose centre lie on X-axis and passes through
the point (2, 3).
20) Showthat the points (-2, 3, 5)(1, 2, 3) &(7, 0, -1) are collinear.
PART-D
Answer any THREE of the following : 3x5=15
21) IfA.M and GM of thetwo positive numbers 'a' and 'b' are 10 and 8 respectively. Find the
numbers.

22) Find the sumn of the series 8 + 88 + 888 + 8888 + +n terms.
Sin x
23) Prove that lim 1, where 'x' is in radian.
X’0| X

24) Find the derivative of f(x) = X+1 3x-1 W.r.t. x.

25) Define Ellipse and derive the equation of an elipse a? =1 (a > b).
**** *

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