Download Test - 1 - Aniket Mathematics

Mathematics – XI
PUSH – UP
TEST – 1
Max Marks – 100
Time – 3 hr
4 – Marks
(1) Show that , cot x . cot 2x – cot 2x . cot 3x – cot 3x . cot x = 1
(2) Find the value of tan
.
(3) Show that , cos2 x + cos2 x +
+ cos2 x –
=
(4) Find the general solution of the equation ; sin 2x – sin 4x + sin 6x = 0.
(5) In a triangle ABC prove that : tan
(6) Show that :
=
cot
=
(7) Using Principle of Mathematical Induction prove that,
for all n ≥ 1 , 12 + 22 + 32 + - - - + n2 >
(8) Using Principle of Mathematical Induction prove that :
for all n ≥ 1 ,
. .
+
+
. .
. .
+--- +
(
)(
)
=
(
(
)
)(
)
(9) Using Principle of Mathematical Induction prove that :
for all n ≥ 1 , 1.3 + 3.5 + 5.7 + - - - + (2n – 1)(2n + 1) =
(
)
(10) Using Principle of Mathematical Induction prove that :
for all n ≥ 1 , n3 + (n + 1)3 + (n + 2)3 is divisible by 9.
(11) Using Principle of Mathematical Induction prove that :
for all n ≥ 1 , 1 +
.
+
.
+
.
+--- +
(
)(
)
=
(
)
(12) Using Principle of Mathematical Induction prove that,
n
n
for all n ≥ 1 , 2.7 + 3.5 – 5 is divisible by 24.
(13) If ‘α’ and ‘β’ are two different complex numbers with | β | = 1 , then find
(14) If x – i y =
, then prove that (
+
) =
(15) Find the real numbers ‘x’ & ‘y’ if ( x – i y )( 3 + 5 i ) is the conjugate of – 6 – 24 i .
(16) If (x + i y )3 = u + i v , then show that
+
= 4( x2 – y2 )
P.T.O
pg.1 of 1
6 – Marks
(17) In a triangle ABC prove that : (
–
(18) Convert the complex number ,
) cot A + (
–
i–1
cos
) cot B + (
–
) cot C = 0
, into polar form
+ i sin
(19) Solve for ‘x’ : x2 – 5x + i x – i + 18 = 0.
(20) Find the square root of the complex number 8 – 15i
(21) Using Principle of Mathematical Induction prove that :
for all n ≥ 1 , cos x + cos 2x + cos 3x + - - - + cos nx = sin
(22) Find the value of sin
, cos
and tan
if sin x = –
******
pg.1 of 2
.cosec
. cos
; with π < x <
(
)