UNIT-1: MATRICES AND DETERMINANTS
3 MARK QUESTIONS
1.
]
IfA
= [ 3 −9 , find A
+ A′.
−4 7
5 −2
2.
If A = [2 −1 3] and
B = [3 1 ] , find AB matrix.
2 4
2 −1 3
|
3. If
matrix A=[5 |
1 |
0] is a singular matrix, then find
the value of x. |
|
1 |
0 |
x |
4. Find the adjoint of the matrix
4 −5 .
A = [ ]
5.
If
3 −1
3 −2
find the characteristic equation.
A = [ ]
0 −2
5 MARK QUESTIONS
1.
Solve the equations x + y =
3, 2x +
3y = 8 by Cramer’s rule.
2.
Solve for x, if
3.
Verify Cayley-Hamilton
theorem if A = [1 3
].
2 −4
4.
VerifyA(AdjA) = |A|. I. if
5 −2 .
A = [ ]
3 1
|
3 |
−1 |
2 |
|
5. Find the
adjoint of the
matrix A = [2 |
−3 |
1] |
|
0 |
4 |
2 |
6
MARK QUESTIONS
1. Solve for x &y from the equations
4x + y =
7,
3y + 4z = 5, 5x + 3z = 2by Cramer’s rule.
|
1 |
2 |
2 |
|
2. Find the inverse of the matrix
[−1 |
3 |
0] |
|
0 |
−2 |
1 |
3. Prove
that adj(AB)=(adjB).(adjA) if A = [−1 0 3 5
5 ] and B = [ ]
3 2 4
4. Find the characteristic roots of a matrix[ 1 −1].
−6 −2
5.
Solve the equations
by Gauss elimination method 3x − y +
z = 0, x + 2y −
2z =
3, 3x + z = 4. UNIT-2:
VECTORS 3 MARK QUESTIONS
1. Find the magnitude of vector 2i +3j – 6k
2. If a⃗ = i + 2j − 3k, b¯⃗ = 3i − 5j + 2k find magnitude of ¯3¯¯¯a⃗ −
¯2¯¯¯b⃗
3.
Show that cos 8i −
sin 8j is unit vector
4.
Show that
the vectors 2i + 5j − 6k,and 7i + 2j + 4k orthogonal vectors.
5.
If a⃗ = 5i + 2j − 4k, and b¯⃗ = 2i − 5j + 3kfind a⃗Xb¯⃗ .
5 MARK QUESTIONS
1.
Find cosine of the angle
between the vectors
4i − 2j − 3kand 2i − 3j +
4k.
2.
Find the
projection of b¯⃗ on
a⃗ if a⃗ = 5i + 2j − 4kand b¯⃗ = 2i − 5j + 6k.
3.
If a⃗ = 3i + 2j − 4k and b¯⃗ = i − 2j + 5k are two sides of
a triangle, find its area. 4. Simplify
(a⃗ + b¯⃗). (a⃗ − b¯⃗)and (a⃗ + b¯⃗)X(a⃗ − b¯⃗).
5. Find the magnitude of moment of force 4i − 2j + 5k about (2,5,-7)
acting at (4,7,0) 6 MARK QUESTIONS
1.
If A=(2,5,7), B=(3,9,4) and C=(-2,5,7) are three vertices of
parallelogram find its area.
2.
If a force 4i + 6j +
2k acting on a body displaces it from (2,7,-8)
to (3,9,4). Find the
work done by the force.
3.
Find the sine of the angle between
the vectors 4i − 2j −
3kand 2i − 3j +
4k.
4.
Find the unit vector in the direction perpendicular to both
vector 2i − 5j + kand
5i + j + 7k.
5.
Show that the points whose position vectors are i − 3j − 5k, 2i − j + k and 3i − 4j − 4k form a right angled triangle.
UNIT-3: PROBABILITY AND LOGARITHMS
3 MARK QUESTIONS
1.
Define equally likely events, Independent event, and mutually exclusive event.
2.
Define probability of an event.
3.
A coin is tossed twice. What is the probability that at least one head occurs.
4.
A die is thrown once, what is the probability an odd number appears.
5.
If E and F are events such that P(E)=0.6, P(F)=0.3 and P(E∩F)= 0.2.
Find P(E/F).
5
MARK QUESTIONS
1.
Prove that 1
1+logc ab
+ 1
1+loga bc
+ 1 = 1
1+logb ca
2.
If x = logc ab , y = logb bc , z = loga ca , Prove
that xyz = x + y + z + 2
3.
If x = log2a a , y = log3a 2a , z = log4a 3a , prove that xyz + 1 = 2yz
4.
If a2 + b2 = 7ab, prove that log (a+b) = 1
3 2
(log a + log b)
5.
Solve for x given that (log2 x)2 + (log2 x) −
20 =
0
6
MARK QUESTIONS
1.
An integer is chosen at random from the numbers
ranging from 1 to 50 . What is the probability that the integer chosen is a
multiple of 3 or 10 ?
2.
Two unbiased dice are thrown once . Find the
probability of getting the sum of the numbers obtained on the two dice is
neither a multiple of 2 nor a multiple of 4
.
3.
One card is drawn from a well shuffled pack of 52
cards. If E is the event “the card drawn is a king or an ace” and F is the
event “ the card drawn is an ace or a jack “
then find the conditional probability of the event E, when the event F
has already occurred .
4.
A pair of dice is thrown once. If the two numbers
appearing on them are different, find the probability that the sum of the
numbers is 6.
5.
A family has two children. What is the probability that
both the children are boys given that (i) the youngest is a boy. (ii) at least
one is a boy ?
UNIT-4: ALLIED ANGLES AND COMPOUND ANGLES
ALLIED ANGLES
3
MARKS QUESTIONS
1.
Find the value of
2.
Find the value of
3. 
3.If sin and ,
find cos
4.
4. If A+B+C =1800
Prove that cot
5.
5.find the value of tan
5 MARKS QUESTIONS
1.
Prove that =1
2. 
If secx = 13/5 and 2700 , Find the value of 
3.
Find the value of
4.
Evaluate
5.
Show that tan2250xcot4050+tan7650xcot6750+cosec1350xsec3150
= 0 6 MARK QUESTIONS
1 .Evaluate tan3150xcot4050+tan7650xcot6750+cosec1350xsec3150
2.
Find x if 
3.
If sin 
, find the value of 
4. Evaluate
5.
Show that
COMPOUND ANGLES
3 MARKS QUESTIONS
1.
Find the value of
sin150
2.
Show that
3.
Prove that
4.
Using tan(A+B), prove that
cot(A+B)= 
5.
Prove that
5 MARKS QUESTIONS
1.
Prove that cos(A-B) cos(A+B)= cos2A-sin2B
2.
Show that 
3.
If sinA=
4.
Prove that tan3
5.
If A+B =
TRASFORMATION FORMULAE
3 MARKS QUESTIONS
1
P.T 
2
P.T 
3
Show that
4
Show that
5
Show that
MARKS QUESTIONS
1
P.T 
2
In and triangle ABC prove that tanA + tanB +tanC = tanA tanB tanC
3
Show that 
4
Prove that
5
Prove that 
MARKS QUESTIONS
1
Prove that cos200xcos400xcos800xcos600= 1/16
2
In any triangle ABC prove that sinA + sinB + sinC=4Cos(A/2)cos(B/2)cos(C/2)
3
Show that
4
If A+B+C = 1800
prove that
5
If A+B+C = 1800 prove that
sin2A-sin2B+sin2C=4cosAcosCsinB
UNIT-5: COMPLEX NUMBERS
3 MARK QUESTIONS
1.
Evaluate i–999
2.
Find the complex
conjugate of (1 + 2i)(3i −
4)
3.
Express (3 +
4i)–1 in the form a+ib
4.
Find the real part and imaginary part of 1
√2 + i
5.
ifx + iy = cos 8 + i sin 8 show that
x + 1
s
= 2 cos 8
5 MARK QUESTIONS
1 25 2
1. 
Evaluate (i19 + ( ) )
i
2. Find the modulus and amplitude of(1 − i√3)
3. 
Express in a + ib form: (2+3i)
(1+3i).(2+i)
4.
Express the complex
number 1 + i in the polar form.
5. Find the amplitude of √3 + i and
represent in Argand diagram.
UNIT-6: INTRODUCTION TO CALCULUS
3 MARK QUESTIONS
1.
Evaluate: lim
s2–9
2.
Evaluate:
s→–3 s+3
tan mθ
lim (
8→0
)
sin n8
3.
Evaluate:
n+1 n
lim ( ) .
4.
Evaluate:
n→∞ n
3s2–2s+1
lim ( 2 )
5.
Evaluate:
s→∞
2s +5s–1
1–cos 2s)
lim (
s→0 x2
5
MARK QUESTIONS
1.
Evaluate:lim s2+s–2.
s→1
s2–1
2.
Evaluate: lim (√a+s–√a–s)
s→0 3s
3.
Evaluate: lim (xm–1)
x→1
xn–1
4.
Evaluate:
1–cosx+ tan2 x
lim ( )
8→0
scins
5.
Evaluate: lim (eax–ebx).
s→0 x
6
MARK QUESTIONS
1. 
Prove that lim
sin8 =
1, if θ is in "radian".
8→0 8
2.
Evaluate: lim (sin πx)
s→0
s–1
3.
Evaluate: lim ( (5–n2)(n–2) ).
n→∞
4.
Evaluate: lim
(2n–3)(n+3)(5–n)
s2–5s+4 .
s→1
s2–12s+11
5.
Evaluate: lim ( s2–4 )
s→2 √s+2–√3s–2
