KAI.

RAJARAM MARATHE HIGHER SECONDARY SCHOOL

TERMINAL EXAM-2024-25
STD:- 11TH SUBJECT:- MATHS MARKS:- 50 TIME:- 2:30 HRS

Section A
Q.1. Select and write the correct answer for the following multiple choice type of questions:[07]

( )
c
22 π
1) is equal to
15
a) 2460 b) 2640 c) 2240 d) 4260
2) The common ratio for the G. P. 0.12, 0.24, 0.48, is ____.
a) 0.12 b) 0.2 c) 0.02 d) 2

( )
4
x − 16
3) lim 2 =
x →2 x −5 x +6
a) 23 b) 32 c) - 32 d) - 16
4) If A = [ α2 α2 ] , then α = _______.
a) ± 3 b) ± 2 c) ± 5 d) 0
5) 1560 is equal to

( ) ( ) ( ) ( )
c c c c
17 π 13 π 11π 7π
a) b) c) d)
5 15 15 15
592 590 588 586 584
i +i +i +i +i
6) 582 580 578 576 574
i +i +i +i +i
a) - 2 b) 1 c) 0 d) - 1
7) √ −3 √ −6 is equal to
a) - 3√ 2 b) 3√ 2 c) 3√ 2i d) -3√ 2i
Q.2. Answer the following questions : [07]
0
i) Find the length of an arc of a circle which subtends an angle of 108 at the centre, if the radius
of the circle is 15 cm.
ii) Determine which of the following pairs of angles are co - terminal 2100, - 1500.
iii) Find the value of determinant :-
−4
−15
. |27 |
iv) Verify whether the following sequence is H. P.
1 1 1 1
, , , ,…
3 5 7 9
v) Evaluate the following limit : -
lim
z →− 3 z√
z +6

vi) Evaluate the following limit : -

5
y + 243
lim 3 .
y →− 3 y + 27

vii) Evaluate the following limit : -

lim √
2 x+6
.
x →3 x
Section B
Attempt any EIGHT questions of the following : [16]
Q.3. Find the modulus and amplitude of the following complex numbers.
7 - 5 i.
Q.4. Simplify : - √ −16+3 √ −25+ √ − 36 − √ −625 .
Q.5. Check whether the following sequence is G. P. If so, write tn.
 2, 6, 18, 54, ….
Q.6. For the following G. P. s, find Sn 3, 6, 12, 24, ….
Q.7. Evaluate the following limit : -

lim
z→2 [
z 2 −5 z+ 6
z2 − 4 ]
Q.8. Evaluate the following limit : -
x +3
lim 2
x→ −3 x + 4 x +3

Q.9. Find the value of determinant :- |24i −i3 | .

[ ]
3 −4 5
Q.10. Find the value of determinant :- 1 1 −2 .
2 3 1

[ ]
2 −1 3
Q.11. Find the value of determinant :- 1 2 −1 .
5 7 2

[ ]
−1 1 2
Q.12. Find the value of determinant :- −2 3 −4 .
−3 4 0

[ ]
2 7 65
Q.13. Find the value of determinant :- 3 8 75 .
5 9 86
Section C
Attempt any FOUR questions of the following : [12]
Q.14. Find the square root of the following complex number : -
- 8 - 6 i.
Q.15. Evaluate the following limit : -

lim
x →0
[ √6+ x+ x 2 − √ 6
x
. ]
Q.16. Evaluate the following limit : -
2
x +2 x −15
lim 2 .
x →3 x − 5 x +6

Q.17. Evaluate the following limit : -

lim
∆ x→ 0
[
( x +∆ x )2 − 2(x +∆ x )+1 −(x 2 − 2 x +1)
∆x ]
Q.18. Find the value of determinant : -

[ ]
a ℎ g
ℎ b f
g f c
Q.19. Find the value of x if

| x 2 − x+ 1 x +1
x +1 x +1 |
= 0.
 Section D
Attempt any TWO questions of the following : [08]
Q.20 Solve the following linear equations by using Cramer’s Rule:
x + y + z = 6, x - y + z = 2, x + 2 y - z =2.
Q.21. Evaluate the following : -
lim √ 2
x 2 +9 − √2 x 2+ 9
.
x →0 √ 3 x + 4 − √ 2 x + 4
2

Q.22. Solve the following equation : -

[ ]
x +2 x +6 x − 1
x +6 x − 1 x +2 =0.
x −1 x +2 x +6
Q.23. The sum of three numbers is 15. If the second number is subtracted from the sum of first
and third numbers then we get 5. When the third number is subtracted from the sum of
twice the first number and the second number, we get 4. Find the three numbers.