Top 20 Maths questions for NDA

NDA Maths – Practice Questions

Q1. Consider the question and two statements:

Question: Is $3x+2y$ positive?

• Statement I: x3=−29.8x^3 = -29.8x3=−29.8

• Statement II: $y=3x$

Which is correct?
a) Statement I alone is sufficient
b) Statement II alone is sufficient
c) Both I and II together are sufficient
d) Both I and II are not sufficient

Q2. Consider the question and two statements:

Question: Does the equation ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0 have real roots of opposite sign?

• Statement I: Discriminant $D>0$

• Statement II: $c/a<0$

Which is correct?
a) Statement I alone is sufficient
b) Statement II alone is sufficient
c) Both I and II together are sufficient
d) Both I and II are not sufficient

Q3. Consider the question and two statements:

Question: Is a2+b2+c2−ab−bc−caa^2 + b^2 + c^2 – ab – bc – caa2+b2+c2−ab−bc−ca (where $a,b,c$ are distinct real numbers) always positive?

• Statement I: $a>b>c$

• Statement II: $a+b+c=0$

Which is correct?
a) Statement I alone is required
b) Statement II alone is required
c) Both I and II are required
d) Neither I nor II is required

Q4. Consider the question and two statements:

Question: Is $y$ always greater than x2+yx2+y2\dfrac{x^2 + y}{x^2 + y^2}x2+y2x2+y​, given $x+y>0$?

• Statement I: $x>y$

• Statement II: x2+y2>2xyx^2 + y^2 > 2xyx2+y2>2xy

Which is correct?
a) Statement I alone is required
b) Statement II alone is required
c) Both I and II are required
d) Neither I nor II is required

Q5. Sudhir purchased a chair with three consecutive discounts of 20%, 12.5%, and 5%.

What is the actual deduction?

a) 25.35%
b) 30.33%
c) 31.35%
d) 33.50%

Q6. To maintain 8 cows for 60 days, a milkman spends ₹6,400.

To maintain 5 cows for $n$ days, he spends ₹4,800. Find $n$.

a) 68 days
b) 70 days
c) 72 days
d) 74 days

Q7. A student has to secure 40% to pass.

He scores 45 marks and fails by 5 marks. What are the maximum marks?

a) 120
b) 125
c) 130
d) 135

Q8. Five years ago, Ram was three times Shyam’s age.

Four years later, Ram will be twice Shyam’s age. Find Ram’s present age.

a) 28 years
b) 30 years
c) 32 years
d) 34 years

Q9. A boy goes to school at 12 km/h and returns at 8 km/h.

Total journey takes 50 minutes. What is the distance?

a) 2 km
b) 4 km
c) 6 km
d) 8 km

Q10. There are 350 boys in first three standards.

Ratio (1st:2nd) = 2:3, Ratio (2nd:3rd) = 4:5.
Find total boys in 1st and 3rd standards.

a) 210
b) 220
c) 230
d) 240

Q11. There are 8 lines in a plane, no two parallel.

Max intersection points = ?

a) 28
b) 26
c) 24
d) 22

Q12. An arc of a circle subtends angle $\pi$ at centre.

Arc length = 22 cm. Radius = ?

a) 9 cm
b) 7 cm
c) 5 cm
d) 3 cm

Q13. Rhombus diagonals = 20 cm, 48 cm.

Find side length.

a) 26 cm
b) 29 cm
c) 36 cm
d) 39 cm

Q14. A hollow cube is formed by 6 squares.

A cello tape (4 cm × 0.5 cm) is used on each edge.
Total tape area used = ?

a) 12 sq. cm
b) 20 sq. cm
c) 24 sq. cm
d) 36 sq. cm

Q15. Sets are defined:

• $A=\{x:x\text{ is a multiple of 7}\}$

• $B=\{x:x\text{ is a multiple of 5}\}$

• $C=\{x:x\text{ is a multiple of 35}\}$

Which is a null set?

a) (A – B) ∪ C
b) (A – B) – C
c) (A ∩ B) ∩ C
d) (A ∩ B) – C

Q16. For equations:

$Kx+3y+1=0$
$2x+y+3=0$

They intersect if:

a) K = 6
b) K ≠ 6
c) K = 0
d) K ≠ 0

Q17. How many prime numbers are less than 100?

a) 20
b) 25
c) 30
d) 35

Q18. If equations have a common root:

x2−px+q=0x^2 – px + q = 0x2−px+q=0
x2+qx−p=0x^2 + qx – p = 0x2+qx−p=0

Which condition holds?

a) p – q = 0
b) p + q – 2 = 0
c) p + q – 1 = 0
d) p – q – 1 = 0

Q19. 710−5107^{10} – 5^{10}710−510 is divisible by:

a) 5
b) 7
c) 9
d) 11

Q20. Which of the points P(5, –1), Q(3, –2), R(1, 1) lie in solution of:

• $x+y\le 4$

• $x–y\ge 2$

a) P and Q
b) Q and R
c) P and R
d) P, Q and R