Free JEE Main Maths, Physics & Chemistry practice set

Q1. The sum of the roots of x² − 5x + 6 = 0 is:

(a)−5(b)5(c)6(d)−6

Q2. d/dx (eˣ sin x) equals:

(a)eˣ cos x(b)eˣ (sin x − cos x)(c)eˣ (sin x + cos x)(d)−eˣ sin x

Q3. ∫₀¹ 2x dx equals:

(a)0(b)1/2(c)1(d)2

Q4. In how many distinct ways can the letters of the word LEVEL be arranged?

(a)30(b)60(c)120(d)20

Q5. A projectile is launched at 20 m/s at 45° to the horizontal (g = 10 m/s²). Its horizontal range is:

(a)20 m(b)40 m(c)40√2 m(d)80 m

Q6. Resistors of 4 Ω and 12 Ω are connected in parallel. The equivalent resistance is:

(a)16 Ω(b)8 Ω(c)3 Ω(d)1/3 Ω

Q7. The hybridisation of each carbon atom in ethyne (C₂H₂) is:

(a)sp(b)sp²(c)sp³(d)sp³d

Q8. The equation of the line through (1, 2) with slope 3 is:

(a)y = 3x + 2(b)y = 3x − 1(c)y = 3x + 1(d)y = x + 1

Q9. A first-order reaction has k = 0.0693 s⁻¹. Its half-life is:

(a)1 s(b)6.93 s(c)10 s(d)100 s

Q10. A wire is stretched to double its length, keeping its volume constant. Its resistance becomes:

(a)R/2(b)2R(c)4R(d)R