The $L.C.M.$ and $H.C.F.$ of marks scored by Ikhlaas and Spectra in a math test are $3510$ and $20$ respectively. If Spectra's score is $135,$ what is Ikhlaas's score?

A.	$530$
B.	$519$
C.	$517$
D.	$520$

If two zeros of polynomial $x^3 + bx^2 + cx + d$ are $4 + \sqrt{ 3 }$ and $4 - \sqrt{ 3 }$, find its third zero.

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

In a two digit number,its unit's digit is 4 more than ten's digit. If sum of this number and the number obtained by reversing the order of its digits is 132, find the number.

A.	37
B.	48
C.	84
D.	59

The sum of a number and its reciprocal is $\dfrac { 13 } { 6 }$. Find the number.

A.	$\dfrac{1} { 3 }$ or $3$
B.	$\dfrac {1}{ 4 }$ or $4$
C.	$\dfrac { 2 } { 3 }$ or $\dfrac { 3 } { 2 }$
D.	$\dfrac { 2 } { 4 }$ or $\dfrac { 4 } { 2 }$

Find the middle term of the sequence formed by all three-digit numbers which leave a remainder $1$ when divided by $2$.

A.	$549 \text { and } 551$
B.	$551 \text { and } 555$
C.	$545 \text { and } 553$
D.	$\text{ None of these}$

In an equilateral $\triangle ABC$, if $AD$ is altitude, then $AD^2$ is equal to

A.	$CA^2$
B.	$4BD^2$
C.	$3CD^2$
D.	$3CA^2$

Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are $A(12,-2)$, $B(8,6)$, and $C(16,10)$.

A.	$10 { \space } \text{ sq. unit }$
B.	$15{ \space } \text{ sq. unit }$
C.	$20{ \space } \text{ sq. unit }$
D.	$\text{ None of these }$

 

sin235° + sin255°

cos235° + cos255°

  + sin²55° + sin 35° cos 55° = ?

A.	1
B.	0
C.	3
D.	2

In the given figure, a circle is inscribed in a $\triangle PQR.$ $PQ = 9 \space cm, QR = 7 \space cm,$ and $PR = 11 \space cm.$ What is the length of $QM$ ?

A.	$6.5 \space cm$
B.	$2.5 \space cm$
C.	$8.5 \space cm$
D.	$4.5 \space cm$

A.
B.
C.
D.

An umbrella has $6$ ribs which are equally spaced as given in the figure. Assuming the umbrella to be a flat circle of radius $29 \space cm$, find the area between two consecutive ribs of the umbrella.$\bigg[ \pi = \dfrac { 22 } { 7 } \bigg]$

A.	$440.52 \space cm^2$
B.	$690.52 \space cm^2$
C.	$540.52 \space cm^2$
D.	$\text { None of these }$

Gemma and his wife are busy in making jaggery out of sugarcane juice. They have processed the sugarcane juice to make the molasses which are poured into the moulds of the shape shown in the figure. It will be cooled to solidify in this shape to be sent to the market. Each mould is in the shape of a frustum of a cone having the radii of its two circular faces as $21 \space cm$ and $33 \space cm$ and the height of the mould is $18 \space cm$. If each $cm^3$ of molasses weighs about $2 \space gm$, find the weight of molasses that can be poured into each mould. (Take $\pi = \dfrac { 22 } { 7 }$)

A.	$838.4 \space kg$
B.	$83.84 \space kg$
C.	$848.4 \space kg$
D.	$\text { None of these }$

Data regarding the salary of employees of company $X$ is given below.

$\begin{align} \text { Salary (in thousands) } \end{align}$	$40 - 42$	$42 - 44$	$44 - 46$	$46 - 48$	$48 - 50$
$\begin{align} \text { Number of employees } \end{align}$	$17$	$15$	$11$	$10$	$20$

Find the mean salary of the employees using the assumed mean method.

A.	$41.03 \space thousands$
B.	$45.29 \space thousands$
C.	$47.03 \space thousands$
D.	$45.03 \space thousands$

A die is thrown $200$ times and the outcomes are noted as given below.

$Outcome$	$1$	$2$	$3$	$4$	$5$	$6$
$Frequency$	$30$	$40$	$20$	$50$	$10$	$50$

From the above table find the probability of getting $3$?

A.	$0.2$
B.	$0.25$
C.	$1$
D.	$0.1$

Two tangents $PA$ and $PB$ are drawn to a circle with center $O$ from an external point $P$, then $\angle APB$ is equal to:

A.	$\angle PAB$
B.	$2 \angle OAB$
C.	$3 \angle OAB$
D.	$\angle OAB$

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 1 ?

A.	6
B.	5
C.	2
D.	Cannot be determined

Which of following shows relation between Pigeon, Bird and Parrot.

A.
B.
C.
D.

Find the next term of given sequence ..
$7, 23, 71, 215, 647, 1943, ....$

A.	5827
B.	5833
C.	5831
D.	5836

Which of the following is the next term in the series:
Y, V, U, R, Q, N, M, ___

A.	L
B.	I
C.	J
D.	H

Which of the following is the next term in the series:
E, H, F, I, G, J, H, ___

A.	K
B.	W
C.	C
D.	X