Examinations: COMMUNITY MODEL Class:
Annual Term 2025 Inter(1)
Subject: GIRLS COLLEGE DOBERAN Total Marks: Obtained marks
Mathematics KALAN 20
Time Allowed Roll no:
30 mnts ……………………………………..
Note: Follow proper paper presentation method, draw proper margins and ending lines, use markers for headings, write clear and neat.
OBJECTIVE TYPE
Q1) Note: choose the correct option.
1. If then in which quad angle lies
st
(A) 1 (B) 2nd (C) 3rd (D) 4th
2. Three cube roots of 27 are;
(A) (B) (C) (D)
3. Multiplicative inverse of (1, 0) is;
(A) (-1, 0) (B) (0, 1) (C) (0, -1) (D) (1, 0)
4. If are the roots of equation 3x²-2x+4=0hen is equal to
(A)-2/3 B)4/3 (C) 4/2 (D) 4/5
5. belongs to set of
(A) Real numbers (B) Complex numbers (C) Prime numbers (D) Even numbers
6. If A & B are any two singular matrices such that is equal to:
(A) (B) (C) (D) AB
7. The power set of the empty set is
(A)Empty set (B) Power set (C) Non empty set (D) Improper set
8. Tabular form of the set
(A){-2, 2} (B) (C) {} (D)
9. Transpose of diagonal matrix is;
(A)Row matrix (B) Scalar matrix (C) Null matrix (D) Diagonal matrix
10. 21st term of 2+4+6+……. Is
(A) 40 (B) 42 (C) 44 (D) 46
11. Range of cosine function is:
(A) (-1, 1) (B) (C) (D)
12. 8.7.6 =
(A) (B) (C) (D)
13. In how many ways can 4-keys be arranged on a circular key ring:
(A)1 (B) 3 (C) 4 (D) 2
14. n!>n² for integral values of n≥4._______
(A) 1 (B)2 (C) 3 (D) 4
15. The period of is;
(A) (B) (C) (D)
16. _____
(B) (C) (D) 1
(A)
17. The angle lies in quadrant;
(A) I (B) II (C) III (D) IV
18. The radius of inscribed circle is :
(A) (B) (C) (D)
19. is valid only if;
(A) r < n (B) r > n (C) (D)
20.
(A) (B) (C) (D) None of these
Examinations COMMUNITY MODEL Class:
Annual term: 2025 Inter(1)
Subject: GIRLS COLLEGE DOBERAN Total Marks: Obtained marks
Mathematics KALAN 80
Time Allowed Name:
2:30 Hours ……………………………………..
Note: Follow proper paper presentation method, draw proper margins and ending lines, use markers for headings, write clear and neat.
SUBJECTIVE TYPE
SELETION : I
2- Write short answer of any eight parts from the following
i. Define complex number. Is 0 is a complex number?
ii. Whether the set {0, 1} is closed or not w.r.t addition and multiplication?
iii. Factorize : 3x²+3y²
iv. Find multiplicative inverse of : -3-5i.
v. Determine whether the statement is tautology or not?
vi. Define monoid.
vii. Give the table for addition elements of the set of residue classes modulo 5.
viii. [−25 21] [−112 53]
If X = then find the value of X
ix. If A=[ 1i 1+i
−1 ]
find A+(
A¿¿
t
2 α β
x. x . If α β are t h e roots of 3 x −2 x+ 4=0 find +
β a
xi. Find fourth root of 81 xii. Show that
3- Write short answer of any eight parts from the following
i. Define conditional equation
1
ii. Solve: 2
x −1
n
iii. Write 1st four terms; a n=
2n+ 1
iv. Determine whether -19 is a term of 17,13,9,….
v. Find the 5th term of G.P. 3,6,12,….
vi. are in G.P. Show that common ratio is
vii. Find the value of n, when
viii. A die is rolled, what is the probability that dots on the top are greater than 5?
ix. Evaluate: (1+2x)⁻¹ up to 4 terms. xii. Calculate (2.02)⁴ by binomial theorem.
4-Write short answers of any nine parts from the following
1+cos θ
i. Define trigonometry. ii. Prove that = (cosθ +cotθ )2
1−cosθ
α α
+cos sin
iii. Find iv. Show that
1+ sinα
√ 2
= α
1−sinα sin −cos α
2
2
2
° °
180 + α 90 −α α α
v Prove that; vi. Prove that :sin( )sin( )= -sin cos
sin 3θ cos 3θ
vii Show that; − =2 viii. Find the period of sin3/x
sinθ cosθ
ix Find x if r = (s-b) tanβ/2 x. Write any two half angle formula.
xi Show that cos(sin⁻¹x)= √ 1−x 2 .
xii Show that; xiii. Solve equation 4cos²x-3=0
SECTION: II
Note: Attempt any three questions from the following
( )
2
m +1 π
5 (a) If cosecθ = ∧ 0<θ< . Find the remaining trigonometric functions.
2m 2
Prove that:
(b)
6. (a) Show that; Prove that: (b) Show that;
7. (a) If α and β are the roots of from the equation whose roots are .
(b) The sides of a triangle are . Prove that the greatest angle of the
triangle is 120.
8. (a) Prove that :
(b) Prove that;
9. (a):find solution set of the following equation
Cosθ+Cos3θ+Cos5θ+cos7θ=0
(b).Show that .2tan⁻¹ 1/3+ tan⁻¹1/7=π/4
Best of Luck
