If $N$ is the sum of the first $13986$ prime numbers, then $N$ is always divisible by

A.	$8$
B.	$4$
C.	$6$
D.	None of these

If α and β are the zeros of quadratic polynomial x² + 3px - 2q, find the value of α² + β².

A.	18p2 + 4q
B.	9p2 + 8q
C.	9p2 + 2q
D.	9p2 + 4q

Graph of a homogeneous system of equations is

A.	always intersecting
B.	parallel
C.	always coincident
D.	intersecting or coincident

Find the values of $k$ for which $45 x^2 + k x + 8$ $= 0$ has real roots.

A.	$k \geq \sqrt{ 1440 }$
B.	$k \geq \dfrac { 529 } { 8 }$
C.	$k \leq 180$
D.	None of these

The sum of the first three terms of an AP in decreasing order is -3, and their product is 35. What is the value of the 15^th term?

A.	-61
B.	-79
C.	-97
D.	-91

The areas of two similar triangles are $121\space cm^2$ and $4\space cm^2$ respectively. If the altitude of the bigger triangle is $8.8 \space cm$, find the corresponding altitude of the smaller triangle.

A.	$2.6 \space cm$
B.	$3.6 \space cm$
C.	$0.6 \space cm$
D.	$1.6 \space cm$

If the points $(a, 0),(0, b)$ and $(1, 1)$ are collinear then which of the following is true?

A.	$\dfrac{1}{a} + \dfrac{1}{b} = 1$
B.	$\dfrac{1}{a} - \dfrac{1}{b} = 2$
C.	$\dfrac{1}{a} - \dfrac{1}{b} = 1$
D.	$\dfrac{1}{a} + \dfrac{1}{b} = 2$

If $sin \theta = \dfrac { 12 } { 20 }$. Find the value of $\sqrt { 2 + \dfrac { 5 sec^2 \theta - cos^2 \theta } { 7 cos^2 \theta + sec^2 \theta } }$.

A.	$\sqrt { \dfrac { 7713 } { 2429 } }$
B.	$\sqrt { \dfrac { 7703 } { 2417 } }$
C.	$\sqrt { \dfrac { 7718 } { 2422 } }$
D.	None of these

A circle is inscribed in a $\triangle ABC$, touching $BC, CA,$ and $AB$ at points $P, Q,$ and $R$ respectively. If $AB = 11 \space cm, AQ = 8 \space cm$ and $CQ = 6 \space cm$ then find the length of $BC$.

A.	$9 \space cm$
B.	$11 \space cm$
C.	$3 \space cm$
D.	$\text{ None of these }$

A.
B.
C.
D.

Find the area of the major sector of a circle with radius $10 \space cm$ when the angle subtended by the minor arc is $90^\circ$.(Use $\pi = 3.14$)

A.	$270 \space cm^2$
B.	$75 \space cm^2$
C.	$235.5 \space cm^2$
D.	$\text { None of these }$

Selena filled a glass with milk. The lower base radius and the upper base radius of the glass is $5 \space cm$ and $7 \space cm$ respectively. The height of the glass is $16 \space cm$. At first, the glass is filled full with milk and the milk is poured into another container which is cylindrical in shape with the diameter and the height as $26 \space cm$ and $20 \space cm$ respectively. Again the glass is filled one-fourth with milk and then this milk is poured into the same cylindrical container. How much more milk is to be put into the cylindrical container so as to fill the container up to the brim? (Where $\pi = 3.14$)

A.	$8433.99 \space cm^3$
B.	$8331.49 \space cm^3$
C.	$8421.49 \space cm^3$
D.	$8393.99 \space cm^3$

A survey regarding the age of people was conducted and the data was recorded in the table given below.

$\begin{align} \text { Age (in years) } \end{align}$ $2 - 11$ $12 - 21$ $22 - 31$ $32 - 41$ $42 - 51$ $52 - 61$ $\begin{align} \text { Number of people } \end{align}$ $10$ $8$ $5$ $14$ $17$ $15$

Which of the following option is correct.

A.	$\text { mode } > \text { mean }$
B.	$\text { mode } = \text { mean }$
C.	$\text { mode } < \text { mean }$
D.	$\text{None of these}$

One card is drawn at random from a well-shuffled deck of 52 playing cards. Find the probability that the card drawn is either a red card or a jack.

A.	$\dfrac { 3 } { 13 }$
B.	$\dfrac { 5 } { 13 }$
C.	$\dfrac { 7 } { 13 }$
D.	$\dfrac { 6 } { 13 }$

$sin (A + B) = \dfrac{ 1 } { \sqrt{ 2 } }$ and $cos (A - B) = \dfrac{ \sqrt{3} }{ 2 }$

If $0^\circ < (A+B) \le 90^\circ$ and $A > B,$ find value of $A.$

A.	$37.5^\circ$
B.	$35^\circ$
C.	$40^\circ$
D.	$42.5^\circ$

Faces of a cube are marked with 1,2,3,4,5 and 6. If two views of a cube are as shown below, what will be there on the top when 6 is at the bottom?

A.	3
B.	1
C.	2
D.	Cannot be determined

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

A.	4
B.	5
C.	8
D.	1

Find the next term of given sequence.
12, 27, 63, 153, 387, ....

A.	1010
B.	1017
C.	1020
D.	1260

Which of the following choices would replace the blank below?
EGIK:____::HJLN:LNPR

A.	KMOQ
B.	IKMO
C.	MOQS
D.	LNPQ

Find the next term of given sequence ..
9, 17, 29, 45, 65, ....

A.	89
B.	99
C.	96
D.	82