Dear Students/Parents We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center. We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching. Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears. We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth. Committed to excellence... With best wishes. S . Iqbal ( Motivator & Mentor)

1. Stable & Best Faculty
Best System
Proven Result
Ultimate Care
Near Jaipuriya Mall
Special Individual A en on :One on one classes or doubt classes apart from
the regular classes give individual a en on to each student. The doubt clearing
sessions which will give the student the right push to their goal.
Faculty :This is one of the most important considera ons while deciding about a
coaching centre. We believe good teachers have the ability to transform students
en rely from non‐thinkers to intense‐thinkers.It is your responsibility to find out
whether the Ins tute does have Strong Pool of Full me Faculty Members or not.
This is important in case a Faculty leaves the Ins tute midway so that Ins tute is
capable of filling that vacancy with a Faculty of same Calibre & Exper se, eventually
safeguarding your future.
Result :So many coaching ins tutes show their results but don’t tell about the
selec on ra o, how many students were enrolled for a course, like, say IIT‐JEE
or AIPMT, how many were successful, what percentage of students secured ranked.
Student Teacher Ra o : Number of students per class is also a factor, the less
number of students for class the more is the a en on by the teacher on the
students and also by the students towards teaching. So check out for number of
students the ins tute divides for a single class.
ADMISSION CUM SCHOLARSHIP TEST
2Oth March,3rd & 10th April 2016
For students moving in class 8th,9th, 10th,11th & 12th
Our results reflects our excellence and credibility. Apexian selected in68%
IIT‐Main 56% IIT‐Advancedand in . 100% students got more than 80% marks
in their Board Exam, Apex topper scored 96% marks in Board Exam.
APEX ,panel of teaching staff comprises of IITians, NITians, Doctors .
APEX follows a very Strong, Systema c & Objec ve Selec on Process. Apex
conduct demo classes and mock sessions for students to help in making
correct and wise decisions.
At APEX the Student‐Teacher Ra o is less than 25:1,even at the peak me.
This facilitates proper Student‐Faculty interac on. Our faculty is always
willing to clear doubts of Students even individually, if required.
Apex consider doubts as the stepping stones towards understanding. each
me a modules gets completed its is followed by a doubt class. A doubt class
on any topic can be demanded by the student, throughout the year round.
Tes ng & Feedback system The only parameter to judge one's posi on in the race
is by analyzing the performance in tests. If students are to benefit from feedback,it
must not only be mely and frequent, but also useful for improving performance by
addressing three areas: what students did well, what students need to improve on,
and how to make this improvement.
At Apex, aspirants are exposed through weekly test and all India test series.
The weekly tests ensure that aspirants keep their pace with content coverage
and keep iden fying their week areas. Regular tests are conducted and results
of tests are also sent to aspirants and parents through SMS.
Some questions to ask before choosing a coaching institute
Registration Open
MOCK TEST PAPER
MATHEMATICS
(class10th)
Boost your IIT-JEE / AIPMT Preparation

2. MATHS X TERM-II
MODEL TEST PAPER-2 (UNSOLVED)
[For Summative Assessment-2 (Term - II)]
[Based on the latest CBSE Sample Question Paper]
Time : 3 hours M.M. : 80
General Instructions : Same as in CBSE Sample Question Paper.
SECTION A
(Question numbers 1 to 10 carry 1 mark each. For each of the questions 1 to 10, four
alternative choices have been provided of which only one is correct. You have to select the
correct choice.)
1. If x = 2 is a root of the quadratic equation 3x2 – 2kx + 5 = 0, then k is equal to :
(a)
4
17
(b)
17
4
(c)
1
17
(d)
1
4
2. If the sum of n terms of an A.P. be 3n2 – n and its common difference is 6, then its
first term is :
(a) 2 (b) 3 (c) 1 (d) 4
3. PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter
of the circle such that ∠POR = 120°, ∠OPQ is :
(a) 50° (b) 40° (c) 30° (d) 25°
4. In the figure, ∆ABC is circumscribed touching the circle
at P, Q, R. If AP = 4 cm, BP = 6 cm, AC = 12 cm and
BC = x cm. Then, x = ?
(a) 10 cm (b) 6 cm
(c) 14 cm (d) 18 cm
5. The length of the tangent drawn from a point, whose distance from the centre of a
circle is 20 cm and radius of the circle is 16 cm, is :
(a) 12 cm (b) 13 cm (c) 17 cm (d) 25 cm
6. If four sides of a quadrilateral ABCD are tangential to a circle. Then :
(a) AC + AD = BC + DB (b) AC + AD = BD + CD
(c) AB + CD = AC + BC (d) AB + CD = BC + AD
7. A race track is in the form of a ring whose inner and outer circumferences are
437 m and 503 m respectively. The width of the track is :
(a) 10.5 m (b) 20.5 m (c) 21 m (d) 30 m
APEX INSTITUTE FOR IIT-JEE / MEDICAL / NTSE
Head office: 62 Nitikhand-III, Indirapuram; | Contact: 0120-4331180, 9990495952 |
Web: www.apexiit.co.in/

3. 2
8. The total surface area of a hemisphere of radius 7 cm is :
(a) 447 π cm2
(b) 239 π cm2
(c) 147 π cm2
(d) 174 π cm2
9. If the angle of elevation of a building from a distance of 100 m from its foot is 60°,
then the height of the building is :
(a) 100 3 m (b)
100
3
m (c) 50 3 m (d)
200
3
m
10. The probability of selecting an even prime number from 1 to 50 is :
(a)
1
50
(b)
2
25
(c)
1
25
(d) none of these
SECTION B
(Question numbers 11 to 18 carry 2 marks each)
11. Find the roots of the following equation :
1 1 11
; 4, 7
4 7 30
x
x x
− = ≠ −
+ −
12. Find a, b and c such that the following numbers are in A.P. a, 7, b, 23, c.
13. In two concentric circles, prove that a chord of larger circle which is tangent to
smaller circle is bisected at the point of contact.
14. An arc of a circle is of length 5π cm and the sector it bounds has an area of 20π cm2.
Find the radius of the circle.
15. Determine the ratio of the volume of a cube to that of a sphere which will exactly
fit inside the cube.
16. If the points A(4, 3) and B(x, 5) are on the circle with centre O(2, 3), find the
value of x.
17. Find the value of k, if the points (7, –2), (5, 1) and (3, k) are collinear.
18. Two dice are thrown together. Find the probability of getting a total less than 6.
OR
Two coins are tossed simultaneously. Find the probability of getting atleast one head.
SECTION C
(Question numbers 19 to 28 carry 3 marks each)
19. Solve for x :
4 3 2 1 1 3
10 3; – ,
2 1 4 3 2 4
x x
x x
x x
− +   
− = ≠ ≠      + −
OR
A passenger train takes 2 hours less for a journey of 300 km, if its speed is increased
by 5 km/hr from its usual speed. Find the usual speed of the train.
t
APEX INSTITUTE FOR IIT-JEE / MEDICAL / NTSE
Head office: 62 Nitikhand-III, Indirapuram; | Contact: 0120-4331180, 9990495952 |
Web: www.apexiit.co.in/

4. 3
20. Determine the A.P. whose 3rd term is 16 and 7th term exceeds the 5th term by 12.
21. In the figure, O is the centre of the circle, AB is a diameter and AD is a tangent. If
∠BOC = 120°, find ∠ADC.
OR
In ∆PQR, ∠Q = 90°, a circle with centre O and radius 2 cm has been inscribed in
the triangle. If QR = 6 cm, find the perimeter of ∆PQR.
22. Construct a ∆ABC in which BC = 6.5 cm, AB = 4.5 cm and ∠ABC = 60°. Construct
another triangle similar to ∆ABC such that each side of new triangle is
4
5
of the
corrresponding sides of ∆ABC.
23. Four equal circles, each of radius 5 cm, touch each other, as shown in the figure below.
Find the area included between them. (Take π = 3.14)
24. Find the number of metallic discs with 1.5 cm base diameter and of height 0.2 cm, to be
melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
OR
Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively, are melted to form a
single solid sphere. Find the radius of the resulting sphere.
APEX INSTITUTE FOR IIT-JEE / MEDICAL / NTSE
Head office: 62 Nitikhand-III, Indirapuram; | Contact: 0120-4331180, 9990495952 |
Web: www.apexiit.co.in/

5. 4
APEX INSTITUTE FOR IIT-JEE / MEDICAL / NTSE
Head office: 62 Nitikhand-III, Indirapuram; | Contact: 0120-4331180, 9990495952 |
Web: www.apexiit.co.in/
25. The shadow of a tower standing on ground level is found to be 45 m longer when
sun’s altitude is 30°, then when it was 60°. Find the height of the tower.
26. Prove that the points (0, 0), (5, 5) and (–5, 5) are the vertices of a right
isosceles triangle.
27. If the coordinates of the mid-points of the sides of a triangle are (1, 1), (2, –3) and
(3, 4). Find its centroid.
28. What is the probability that a number selected at random from the numbers
1, 2, 2, 3, 3, 3, 4, 4, 4, 4, will be their average?
SECTION D
(Question numbers 29 to 34 carry 4 marks each)
29. Show that the equation 2(a2 + b2) x2 + 2(a + b) x + 1 = 0 has no real roots, when
a ≠ b.
OR
By increasing the list price of a book by Rs 10 a person can buy 10 books less for
Rs 1200. Find the original list price of the book.
30. Find the sum of all natural numbers between 250 and 1000 exactly divisible by 3.
31. Prove that opposite sides of a quadrilateral circumscribing a circle subtend
supplementary angles at the centre of the circle.
32. A drain cover is made from a square metal plate of side 40
cm having 441 holes of diameter 1 cm each drilled in it. Find
the area of the remaining square plate.
OR
Find the area of the shaded region in the given figure, if
PQ = 24 cm, PR = 7 cm and O is the centre of the circle.
33. An oil funnel of tin sheet consists of a cylindrical portion 10 cm long attached to a
frustum of a cone. If the total height of the funnel be 22 cm, diameter of the
cylindrical portion be 8 cm and the diameter of the top of the funnel be 18 cm, find
the area of the tin required to make the funnel.
34. As observed from the top of a lighthouse, 100 m above sea level, the angle of
depression of a ship, sailing directly towards it, changes 30º to 45°. Determine the
distance travelled by the ship during the period of observation.

6. Prakhar Goel
Student of APEX
One year classroom Program.
He is studying MBBS in Maulana
Azad Medical college Delhi.
Siddhant Rathore
CBSE : 91.6%
Student of APEX
ree year classroom Program.
He is studying Mechanical
Engineering in BITS Goa.
Dhwani Jain
Student of APEX
ree year classroom Program.
She is studying Chemical
Engineering in NUS Singapore.
Selected in NUS
National University of Singapore: 1st Rank in Asia
AIPMT AIR 427(GE)
Prerna Kashyap
CBSE : 96%
Student of APEX
Two year classroom Program.
She is studying in NIT Kurukshetra.
IIT-Main AIR 521(GE)
Apeksha Garg
CBSE : 96%
Student of APEX
One year classroom Program.
Vibhav Singh
CBSE : 96%
Student of APEX
One year classroom Program.
M-95, C-98, P-95 B-98, C-97, P-95
School : Cambridge Indirapuram
School : Amity Noida
Student of APEX
Four year classroom Program.
She is studying in Delhi Technical
Univercity(DTU) .
IIT-Main Score: 186
School : DPS Noida
School : Ryan Noida
STAR PERFORMERS OF THE YEAR
Arindham Roy
CBSE : 95%
Student of APEX
Two year classroom Program.
He is studying in NIT Patna.
IIT-Main Score : 158
School : Cambridge Indirapuram
BITS SCORE: 329
Sharvi Tomar
CBSE : 95.4%
Shubham Mukharjee
Student of APEX
One year classroom Program.
He is studying in IIT Guahati.
IIT(Adv.)AIR 1823(GE)
Shaurya Tomar
CBSE : 93.2%
Student of APEX
Four year classroom Program.
He is studying in Thapar
Institute Patiyala.
IIT-Main Score : 149
School : DPS Noida
Rishab Gupta
CBSE : 92.8%
Student of APEX
Four year classroom Program.
He is studying in Government
Engineering College Bilaspur.
IIT-Main Score :158
School : KV Noida
CBSE TOPPERS
68% Selections in IIT-Main
Selections in IIT-Advanced56%
60%Selections in AIPMT
Shreya
CBSE : 94%
Student of APEX
Twor year classroom Program.
Sharvi Tomar
CBSE : 95.4%
Student of APEX
Four year classroom Program.
M-95, C-96, P-95 M-95, C-95, P-91
School : DPS Noida School : Modern school Noida
Shaurya Tomar
CBSE : 93.2%
Student of APEX
Four year classroom Program.
M-95, C-97, P-92
School : DPS Noida
Pranjal Singh
CBSE : 90.4%
Student of APEX
Two year classroom Program.
Areesha
CBSE : 91%
School : Genesis global school
Deepti
CBSE : 88%
Aarushi
CBSE : 88%
School : St. Teresa Indirapuram School : Ralli Int. schoolSchool : St. Francis Indirapuram
Student of APEX
One year classroom Program.
Student of APEX
Four year classroom Program.
Student of APEX
Two year classroom Program.
Apex topper scored
96%
marks in Board Exam.
100%
students got more
than 85% marks in
Board Exam.
.......and many more
Unmatched results in IITJEE & Medical consistently
Near Jaipuriya Mall
Call for Free Demo classes @ 9990495952
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YASH SHARMA
SCHOOL: DPS Indirapuram