Euclid's Division Lemma states that if a and b are any two positive integers, then there exist unique whole numbers q and r such that

A.	a = bq + r, 0 < r ≤ b
B.	a = bq + r, 0 < q ≤ b
C.	a = bq + r, 0 ≤ r < b
D.	a = bq + r, 0 ≤ q < b

If two zeros of polynomial x³ + bx² + cx + d are 4+√3 and 4-√3, find its third zero.

A.	-b - 8
B.	c - 8
C.	8 - b
D.	b - 8

Draw the graphs of the equations ^@x + y = 1^@ and ^@4x + 2y = 8^@ and find the the area of the quadrilateral so formed.

A.	^@ -3.5 \text{ sq. units. } ^@
B.	^@ -7.5 \text{ sq. units. } ^@
C.	^@ 7.5 \text{ sq. units. } ^@
D.	^@ 3.5 \text{ sq. units. } ^@

Find the values of ^@ k ^@ for which ^@ 4 c^2 + k c + 30 ^@ ^@ = 0 ^@ has real roots.

A.	^@ k \geq \sqrt{ 480 } ^@
B.	^@k \geq \dfrac { 841 } { 120 }^@
C.	^@k \leq 16 ^@
D.	None of these

If the sum of first ^@ n, \space 2n ^@, and ^@ 3n ^@ terms of an AP is ^@ S_1, \space S_2 ^@, and ^@ S_3 ^@ respectively, then ^@ S_3 ^@ is equal to:

A.	^@ (S_2 - S_1) ^@
B.	^@ 2(S_2 - S_1) ^@
C.	^@ 3(S_2 - S_1) ^@
D.	^@ \text { None of these } ^@

A vertical stick which is ^@ 36 \space cm^@ long casts a ^@33 \space cm^@ long shadow on the ground. At the same time, a vertical tower casts a ^@70 \space m^@ long shadow on the ground. Find the height of the tower.

A.	^@ 71.36 \space m ^@
B.	^@ 76.36 \space m ^@
C.	^@ 81.36 \space m ^@
D.	^@ 86.36 \space m ^@

Find the coordinates of the point which divides the line segment joining the points ^@A(-13, 13)^@ and ^@B(-39, -26)^@ in the ratio ^@5 : 8^@.

A.	^@(5, 8)^@
B.	^@(-3, -34)^@
C.	^@(-1, -3)^@
D.	None of these

^@ \dfrac{ ( 1 + \cot \theta + \tan \theta) (\sin \theta - \cos \theta) } { \sec^3 \theta - \mathrm{cosec}^3 \theta } = ? ^@

A.	^@ sin\theta \space cos\theta ^@
B.	^@ sin\theta - cos\theta ^@
C.	^@ 1 ^@
D.	^@ sin^2\theta \space cos^2\theta ^@

A circle is touching the side ^@ BC ^@ of ^@ \triangle ABC ^@ at ^@ P ^@ and touching ^@ AB ^@ and ^@ AC ^@ produced at ^@ Q ^@ and ^@ R ^@ respectively. Which of the following hold true?

A.	^@ AQ = \dfrac { 1 }{ 2 } \text{(Perimeter of } \triangle ABC)^@
B.	^@AQ = \text{ Perimeter of } \triangle ABC ^@
C.	^@ AQ = \dfrac { 1 } { 4 } \text{(Perimeter of } \triangle ABC) ^@
D.	^@ \text{ None of these } ^@

A.
B.
C.
D.

A chord of a circle of radius ^@ 12 \space cm ^@ subtends a right angle at the center. Find the area of the corresponding minor segment.^@ \bigg[\pi = \dfrac { 22 } { 7 } \bigg] ^@

A.	^@ 141.14 \space cm^2 ^@
B.	^@ 41.14 \space cm^2^@
C.	^@ 291.14 \space cm^2^@
D.	^@ \text { None of these } ^@

The perimeters of the ends of the frustum of a cone are ^@7.48 \space cm^@ and ^@9.24 \space cm^@. If the height of the frustum is ^@28 \space cm^@, find its curved surface area. (Take ^@\pi = \dfrac { 22 } { 7 }^@).

A.	^@ 234.08 \space cm^2 ^@
B.	^@ 74.48 \space cm^2 ^@
C.	^@ 8.36 \space cm^2 ^@
D.	^@ \text { None of these } ^@

If the median value of the data below is 45. What is the value of x?

Class interval	30-36	36-42	42-48	48-54	54-60
Frequency	11	x	12	10	18

A.	16
B.	19
C.	18
D.	17

A bag contains 6 red balls, 4 blue balls and 5 green balls. Richard draws 2 balls out of the bag. What is the probability that he gets a red ball and a blue ball?

A.	105 22
B.	105 25
C.	25 105
D.	24 105

The HCF of 374 and 374 is

A.	379
B.	373
C.	374
D.	None of above

Faces of a cube are marked with 1,2,3,4,5 and 6. If two views of cube are as shown below, what will be there on the face opposite to face 6?

A.	3
B.	5
C.	1
D.	Cannot be determined

In this diagram, the triangle represents men, the square represents teachers and the circle represents tall. Find the number of men who are tall but not teachers.

A.	3
B.	1
C.	2
D.	7

Find the missing number

19	48	114
93	122	?

A.	181
B.	188
C.	195
D.	262

Which is the odd one out in this set
lqva, glqv, hmsr, bglq

A.	glqv
B.	bglq
C.	lqva
D.	hmsr

Which is the odd one out in this set

^@PAR, MXH, OZO, SDA^@

A.	^@PAR^@
B.	^@OZO^@
C.	^@SDA^@
D.	^@ MXH ^@