All questions
- The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is The correct answer is option C) 77 solution:: there can be two cases numbers can be case 1 :: 1, 1, 1, 1, 2, 2, 2 possible 7 digits number b... 1
- If a, b, c are odd positive integers, then number of integral solutions of a + b + c = 13, is The correct answer is option b) 21 explaination :: Let a = 2k + 1, b = 2l + 1, c = 2m + 1 where k, l, m are whole number a + b + c = 13 2k +... 1
- The total number of positive integral solution for x, y, z such that xyz = 24, is The correct answer is option a)30 solution::: xyz = 24 xyz = 2³ × 3¹ The number of ways of distributing 'n' identical balls into 'r' differe... 1
- Two numbers are chosen from 1, 3, 5, 7,… 147, 149 and 151 and multiplied together in all possible ways. The correct answer is d) 1020 In the given numbers 1, 3,5,7,…, 147, 148, 151the numbers which are multiple of 5 are 5, 15, 25, 35,…, 145 whi... 1
- Ammonolysis of alkyl halide to prepare primary, secondary and tertiary amines followed by NaOH is The correct answer is option 1 to remove acidic impurities 2
- A planet is revolving around sun in elliptical orbit. Maximum & minimum distance of planet from sun are respectively 1.6 × 1012 m and 6 × 1010 m. Answer: (2) 3 × 10³ m/s Gravity on the planet acts along the line to the Sun, so the planet's angular momentum about the Sun is conserved. A... 1
- A particle of mass m1 = m moving with velocity 10root3 m/s ˆ i collides with a particle of mass m2 = 2m at rest. Correct answer is 30 vec p_f=vec p_i M × 10 hat j + m vec v = m × 10 sqrt 3hat i vec v=10sqrt3 hat i+10hat j 2
- A particle of mass rotates in a circle which has a vertical boundary of radius 0.2 meter, rotating in horizontal plane. The correct option is option 1) 9.8 × 10^(–4) N N=mω²R =(0.2)[ 4π²over T²](R) =0.24(9.8)over 1600(0.2) =9.8×10⁻⁴ N 1
- A bar magnet of length 14 cm is placed along N-S direction with north of magnetic along north direction. If horizontal component The correct option is 1) 2.88 Am^(2 ) 1
- An antenna of length 25 m is mounted on top of a building of height 75 m. The correct option is 1)100 m Length of antenna ≥ λover 4 λ ≤ 4×25 λ ≤100m 1
- Three gases O2, N2 and Co2 having masses 16g, 28g and 44g respectively are filled in a container of volume V The correct option is 4) 5over 2 RTover V PV=(16over32+ 28over28+ 44over44)RT p=5over 2 RTover V 1
- Four small balls are placed at the corner of a square of length l. Evaluate MOI of system about a line passing through A and parallel to BD. The correct option is 2) 3 ml² I=2m(loversqrt2)² +m(sqrt2l)² =2ml²over 2+2ml²=3ml² 1
- In photoelectric effect stopping potential for electromagnetic radiations depends on Correct option is 4)frequency In photoelectric effect stopping potential for electromagnetic radiations depends on frequency 1
- A simple pendulum attached to ceiling of lift has time period T when lift is at rest. The correct option is 1) √(2over 3)T T=2π lover g T'=2π lover g+gover2 therefore T'over T= sqrt gover 3g over2 T'=Tsqrt 2over3 1
- Relation between voltage, current and resistance is given by R=V/I Measured value of voltage (50 ±2) volt, measured value of current is (20 ±2)A. Answer: 14% For R = V/I , the maximum relative error is the sum of the relative errors: Δ R/R = Δ V/V + Δ I/I Here V = 50 V, Δ V = 2 V, I =... 1
- Relation between energy density of electric field (UE) and magnetic field (UB) will be: correct answer is 3) U_E=U_(B ) Average energy density of electric field and magnetic field are same. 1
- A body crosses the topmost point of a vertical circle with critical speed. What will be its centripetal acceleration when the string is horizontal: The correct answer is c) 3g V=√(3gr) a=v²over r Then , a=3grover r= 3g 1
- A bucket tied at the end of a 1.6 m long string is whirled in a vertical circle with constant speed. What should be the minimum speed The correct answer is option A) 4m/s Explaination :: V=√(gr) V=√(10×1.6)=√(16) V=4 m/s 1
- An electromagnetic wave of frequency 5 GHz, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are 2. The correct answer is 15 n=√(μ_r ε_r)=2 v=cover n = 3×10⁸over 2 =15×10^(7 )m/s Hence X=15 the answer 1
- A common transistor radio set requires 12V (D.C.) for its operation. The D.C. source is constructed by using a transformer The correct answer is 440 N_pover N_s=V_pover V_s N_pover24=220over12 N_p=200×24over12 N_p=440 1
- An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging The correct answer is 75 I₀cos²30°=100×(sqrt3over2)² =100×3over4 =75 1
- The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. the correct answer is 25 N Given:: μ_s = 0.2 Solution:: m=0.5 kg g=10 m/s² We know that f_s= μ N To keep the block adhere to the wall here N... 1
- An audio signal υm = 20sin2π(1500t) amplitude modulates a carrier υc =80 sin 2π (100,000t). The value of percent modulation is ________. Correct answer is 25 v_m = 20 sin [100π t+πover4] :v_c = 80 sin [10⁴π t+πover6] we know that, modulation index = A_mover A_c from given equa... 1
- A resonance circuit having inductance and resistance 2 × 10–4 H and 6.28 Ω respectively oscillates at 10 MHz frequency. correct answer is 2000 R = 6.28 Ω f = 10 MHz L = 2 × 10⁻⁴ Henry We know that quality factor Q is given by ⇒ Q = X_L / R = ωL / R also, ω = 2... 1