If the HCF of two numbers, a & b, is 12 and their LCM is 307, then what will be the value of a × b ?

A.	4003
B.	3684
C.	319
D.	None of these

If the zeros of the polynomial ^@ x^3 + 7 x^2 - 74 x - 168 ^@ are ^@(a - b), a, (a + b)^@, find ^@ a ^@ and ^@ b ^@.

A.	^@ a = \dfrac { 3 } { -7 } \space \text{and} \space b = \pm \sqrt{\dfrac { 271 } { 3 }} ^@
B.	^@ a = \dfrac { -7 } { 3 } \space \text{and} \space b = \pm \sqrt{\dfrac { 271 } { 3 }} ^@
C.	^@ a = \dfrac { -7 } { 3 } \space \text{and} \space b = \pm \sqrt{\dfrac { 271 } { 2 }} ^@
D.	^@ \text{ None of these } ^@

Kate went to a bank to withdraw ^@ $ 750^@. She asked the cashier to give ^@$ 50^@ and ^@$ 100^@ notes only. Kate got ^@10^@ notes in all. Find the number of ^@$ 50 ^@ and ^@$ 100^@ notes she received.

A.	^@6^@ and ^@8^@
B.	^@7^@ and ^@6^@
C.	^@5^@ and ^@5^@
D.	^@8^@ and ^@7^@

Find the roots of the quadratic equation ^@ y^2-3y + 1 = 0 ^@.

A.	^@ \dfrac{ -3 + \sqrt{ 5 } } { 2 } \text{ or } \dfrac{ -3 - \sqrt{ 5 } } { 2 } ^@
B.	^@ \dfrac{ 3 + \sqrt{ 5} } { 2 } \text{ or } \dfrac{ 3 - \sqrt{ 5} } { 2 } ^@
C.	^@ \dfrac{ -3 + \sqrt{ 6 } } { 2 } \text{ or } \dfrac{ -3 - \sqrt{ 6 } } { 2 } ^@
D.	^@ \dfrac{ 3 + \sqrt{ 6 } } { 2 } \text{ or } \dfrac{ 3 - \sqrt{ 6 } } { 2 } ^@

If the 10^th element of an arithmetic progression is -125 and the difference between the 41^st element and the 26^th element is -255, then what is the first element of the AP?

A.	45
B.	62
C.	11
D.	28

In the given figure, ^@ \Delta OQP \sim \Delta OAB^@,^@ \angle OPQ = 57^\circ ^@, and ^@ \angle BOQ = 114^\circ ^@. Find ^@ \angle OAB ^@.

A.	^@ 114^\circ ^@
B.	^@ 119^\circ ^@
C.	^@ 57^\circ ^@
D.	^@\text{None of these }^@

Find the values of ^@y^@ for which the distance between the points ^@A(6, 7)^@ and ^@B(39, y)^@ is 65 units.

A.	^@ -51 ^@ ^@ \text{ and } ^@ ^@ 61 ^@
B.	^@ 63 ^@ ^@ \text{ and } ^@ ^@ -49 ^@
C.	^@ -48 ^@ ^@ \text{ and } ^@ ^@ 64 ^@
D.	^@ -47 ^@ ^@ \text{ and } ^@ ^@ 65 ^@

If ^@ x = r{\space} sin{\space} \alpha {\space}cos{\space}\beta^@, ^@y = r{\space} sin {\space}\alpha{\space} sin{\space}\beta^@ and ^@z = r{\space} cos {\space}\alpha^@, then ^@{\space}x^2 + y^2 + z^2 ^@ is equal to:

A.	^@ r^2 ^@
B.	^@ r ^@
C.	^@ 0 ^@
D.	^@ \text{ None of these }^@

In the given figure, AB is the diameter of a circle with center ^@O^@ and ^@AT^@ is a tangent. If ^@\angle AOQ = 65^\circ ^@, find ^@\angle ATQ^@.

A.	^@ 57.5^\circ ^@
B.	^@ 32.5^\circ ^@
C.	^@ 52.5^\circ ^@
D.	^@ \text{ None of these } ^@

A.
B.
C.
D.

Find the area of the square that can be inscribed in a circle of radius ^@5 \space cm^@.

A.	^@ 50 \space cm^2 ^@
B.	^@ 10 \space cm^2 ^@
C.	^@ 70 \space cm^2 ^@
D.	^@ \text { None of these } ^@

A wooden pillar consists of a right circular cylinder and a cone as shown in the picture. The radius of the cone and the cylinder is 3 cm. The height of the cylinder and the cone is 18 cm and 9 cm respectively. If the density of wood is 2 grams per cm³, find the weight of the wooden pillar. (Assume π =  

22

7

 )

A.	1.188 kg
B.	3.564 kg
C.	2.376 kg
D.	1.782 kg

Find the mean of the following data.

^@ \text{ Marks obtained (in ) }^@	^@ \text{ Number of students }^@
^@ \text{ Less than } 3 ^@	^@ 39 ^@
^@ \text{ Less than } 6 ^@	^@ 61 ^@
^@ \text{ Less than } 9 ^@	^@ 76 ^@
^@ \text{ Less than } 12 ^@	^@ 106 ^@
^@ \text{ Less than } 15 ^@	^@ 132 ^@
^@ \text{ Less than } 18 ^@	^@ 144 ^@

A.	^@2.75^@
B.	^@ 1.75 ^@
C.	^@2.29^@
D.	^@-0.25^@

A box contains 5 green and 6 pink balls. Caitlin takes out a ball, puts it back, and then takes out another ball. What is the probability that both balls were green?

A.	5 121
B.	5 11
C.	25 66
D.	25 121

If ^@ a = 5 \sqrt7 ^@ and ^@ 3 a = \sqrt{ 7 x}, ^@ then find the value of ^@x.^@

A.	^@ 15 ^@
B.	^@ 225 ^@
C.	^@ 14 ^@
D.	^@ 9 ^@

Faces of a cube are marked with A,B,C,D,E and F. If three views of cube are as shown below, what will be there on the face opposite to face B?

A.	B
B.	A
C.	E
D.	F

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

A.	9
B.	4
C.	5
D.	3

Find the next term of given sequence.
24, 26, 29, 34, 41, 52, 65, ....

A.	85
B.	90
C.	75
D.	82

Which of the following choices would replace the blank below
FGHI:KLMN::KLMN:____

A.	PQRR
B.	PQRS
C.	QRST
D.	OPQR

Find the next term of given sequence ..
8, 16, 28, 44, 64, ....

A.	97
B.	95
C.	82
D.	88