Navodaya Vidyalaya Class 11 Entrance Exam Mock Test

Navodaya Vidyalaya Class 11 Entrance Exam Mock Test

Navodaya Vidyalaya Class 11 Entrance Exam – Mock Test Paper

Time: 3 Hours | Total Marks: 100 | Questions: 60

🔹 SECTION A – MATHEMATICS (Q1–Q20)

Each question carries 4 marks.

Q1. Solve for xxx:

x2−6x+8=0x^2 – 6x + 8 = 0x2−6x+8=0

Q2. Find the roots of the quadratic equation 2x2+5x−3=02x^2 + 5x – 3 = 02×2+5x−3=0.

Q3. If f(x)=3x2−4x+1f(x) = 3x^2 – 4x + 1f(x)=3×2−4x+1, find f(2)f(2)f(2).

Q4. The sum of the roots of the quadratic equation 3x2+4x−5=03x^2 + 4x – 5 = 03×2+4x−5=0 is:

Q5. If tan⁡θ=2\tan \theta = 2tanθ=2, find sin⁡θ\sin \thetasinθ and cos⁡θ\cos \thetacosθ.

Q6. Find the value of log⁡232\log_{2} 32log2​32.

Q7. Solve the system of equations:

3x+2y=123x + 2y = 123x+2y=12
4x−3y=54x – 3y = 54x−3y=5

Q8. The roots of the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0 are given by:

Find the sum and product of the roots in terms of a,b,a, b,a,b, and ccc.

Q9. If the area of a circle is 154 cm², find its radius.

Q10. Solve:

log⁡10(x2)=4\log_{10} (x^2) = 4log10​(x2)=4

Q11. Prove that:

cos⁡2θ+sin⁡2θ=1\cos^2 \theta + \sin^2 \theta = 1cos2θ+sin2θ=1

Q12. Simplify the expression:

(x+2)(x−3)x2−x−6\frac{(x + 2)(x – 3)}{x^2 – x – 6}x2−x−6(x+2)(x−3)​

Q13. Find the value of cos⁡(45∘)+sin⁡(45∘)\cos(45^\circ) + \sin(45^\circ)cos(45∘)+sin(45∘).

Q14. The length of a diagonal of a square is 10210 \sqrt{2}102​. Find the area of the square.

Q15. Find the value of xxx if log⁡2(x+3)=4\log_{2} (x + 3) = 4log2​(x+3)=4.

Q16. In a triangle, the lengths of two sides are 7 cm and 9 cm. If the included angle is 60°, find the area of the triangle.

Q17. If θ=30∘\theta = 30^\circθ=30∘, find the value of tan⁡2θ\tan 2\thetatan2θ.

Q18. Solve for xxx:

x+3x−1=5\frac{x + 3}{x – 1} = 5x−1x+3​=5

Q19. The sum of the first 50 natural numbers is:

Q20. Find the equation of the line passing through the points (1,2)(1, 2)(1,2) and (3,6)(3, 6)(3,6).

🔹 SECTION B – MENTAL ABILITY / REASONING (Q21–Q40)

Each question carries 2 marks.

Q21. Find the next number in the series:

2, 6, 12, 20, 30, ___

Q22. If the word “COMPUTER” is coded as “DPNVSFST,” what is the code for “MATH”?

Q23. Find the odd one out:

36, 49, 64, 81, 100

Q24. A man walks 10 km towards the North, then turns right and walks 5 km. In which direction is he from his starting point?

Q25. If x=3x = 3x=3 and y=4y = 4y=4, find the value of 2x+3y−52x + 3y – 52x+3y−5.

Q26. Complete the analogy:

Hand : Finger :: Foot : ___

Q27. If 7x – 2 = 5x + 10, find the value of xxx.

Q28. Find the missing number:

8, 12, 16, ___, 24

Q29. What comes next in the series:

5, 10, 20, 40, ___

Q30. In a group of 120 students, 60 are boys. What percentage of the students are boys?

Q31. If the perimeter of a rectangle is 40 cm and its length is 12 cm, find its width.

Q32. What is the least common multiple (LCM) of 15, 20, and 25?

Q33. If x+5=12x + 5 = 12x+5=12, what is the value of xxx?

Q34. Find the next number in the series:

1, 3, 9, 27, ___

Q35. In a right-angled triangle, one of the angles is 45°. What is the other angle?

Q36. A family has 4 children. The probability of selecting a boy is:

Q37. If 2x+4=122x + 4 = 122x+4=12, find xxx.

Q38. Find the next term in the series:

1, 4, 9, 16, ___

Q39. If x2+2x−8=0x^2 + 2x – 8 = 0x2+2x−8=0, find xxx.

Q40. If a person travels 8 km East, then 6 km South, how far is he from his starting point?

🔹 SECTION C – ENGLISH GRAMMAR & VOCABULARY (Q41–Q60)

Each question carries 1 mark.

Q41. Choose the correct form:

She ____ going to the market.
a) is
b) are
c) am
d) be

Q42. Fill in the blank:

I _____ a book right now.
a) read
b) reads
c) is reading
d) am reading

Q43. Choose the antonym of “Happy”:

a) Sad
b) Joyful
c) Content
d) Excited

Q44. Complete the sentence:

She _______ her homework before dinner.
a) has finished
b) finishes
c) finishing
d) finish

Q45. Find the synonym of “Brave”:

a) Coward
b) Bold
c) Shy
d) Weak

Q46. The word “childish” is derived from which word?

a) Child
b) Children
c) Childlike
d) Childishness

Q47. Fill in the blank:

He was _______ tired to continue working.
a) too
b) so
c) very
d) enough

Q48. Choose the correct sentence:

a) He don’t like apples.
b) He doesn’t like apples.
c) He not like apples.
d) He isn’t like apples.

Q49. What is the opposite of “Expensive”?

a) Cheap
b) Rich
c) Expensive
d) Costly

Q50. Choose the correct form of the verb:

I _____ there tomorrow.
a) will be
b) am being
c) am
d) will

Q51. Complete the sentence:

By the time we arrived, they _____ already left.
a) have
b) had
c) has
d) having

Q52. What is the plural of “Crisis”?

a) Crisises
b) Crises
c) Crissis
d) Crisii

Q53. Choose the correct preposition:

She is fond ___ music.
a) on
b) of
c) at
d) in

Q54. Choose the correct word:

The book ___ in the bag.
a) is
b) are
c) has
d) were

Q55. What is the synonym of “Difficult”?

a) Hard
b) Easy
c) Simple
d) Clear

Q56. Identify the correct sentence:

a) He can speaks five languages.
b) He speaks five languages.
c) He speak five languages.
d) He is speak five languages.

Q57. Choose the correct conjunction:

I like to swim, ___ I don’t like to run.
a) but
b) and
c) or
d) so

Q58. Which of the following words is a verb?

a) Happy
b) Sing
c) Bright
d) Slow

Q59. Fill in the blank:

She _______ to the shop every day.
a) goes
b) going
c) went
d) will go

Q60. Find the antonym of “Polite”:

a) Rude
b) Gentle
c) Kind
d) Nice

Disclaimer:
This mock test paper is created for educational and practice purposes only. It is not an official Navodaya Vidyalaya or Sainik School question paper, but is based on the pattern and difficulty of previous year questions (PYQs).

SECTION A – MATHEMATICS (Q1–Q20)

Q.NoAnswer
Q1( x = 4, 2 )
Q2( x = \frac{-5 + \sqrt{49}}{4}, \frac{-5 – \sqrt{49}}{4} )
Q3( f(2) = 3(2)^2 – 4(2) + 1 = 3(4) – 8 + 1 = 12 – 8 + 1 = 5 )
Q4Sum = ( -\frac{4}{3} )
Q5( \sin \theta = \frac{2}{\sqrt{5}}, \cos \theta = \frac{1}{\sqrt{5}} )
Q65
Q7( x = 3, y = 2 )
Q8Sum = ( -\frac{b}{a}, \text{Product} = \frac{c}{a} )
Q9Radius = 7 cm
Q10( x = 100 )
Q11Proved by Pythagoras identity
Q12( \frac{x+2}{x-2} )
Q13( \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2} = \sqrt{2} )
Q14Area = 100 cm²
Q15( x = 13 )
Q16Area = ( \frac{1}{2} \times 7 \times 9 \times \sin(60^\circ) = 22.91 ) cm²
Q17( \tan 60^\circ = \sqrt{3} )
Q18( x = 8 )
Q191275
Q20( y = 2x + 4 ), Line equation is ( y = 2x + 4 )

SECTION B – MENTAL ABILITY / REASONING (Q21–Q40)

Q.NoAnswer
Q2142
Q22MATM
Q2340
Q24South-East
Q2517
Q26Toe
Q27( x = 6 )
Q2820
Q2980
Q3050%
Q318 cm
Q32300
Q337
Q3481
Q3545°
Q36( \frac{1}{2} )
Q37( x = 4 )
Q3825
Q39( x = 2, -4 )
Q4010 km

SECTION C – ENGLISH GRAMMAR & VOCABULARY (Q41–Q60)

Q.NoAnswer
Q41a) is
Q42d) am reading
Q43a) Sad
Q44a) has finished
Q45b) Bold
Q46a) Child
Q47a) too
Q48b) He doesn’t like apples.
Q49a) Cheap
Q50d) will
Q51b) had
Q52b) Crises
Q53b) of
Q54a) is
Q55a) Hard
Q56b) He speaks five languages.
Q57a) but
Q58b) Sing
Q59a) goes
Q60a) Rude