Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev

DC Pandey Solutions for JEE Physics

NEET : Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev

The document Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev is a part of the NEET Course DC Pandey Solutions for JEE Physics.
All you need of NEET at this link: NEET

Section-II: Subjective Questions
Trigonometry

Q1. Find the value of
(a) cos 120° 
(b) sin 240°
(c) tan (-60°) 
(d) cot 300° 
(e) tan 330° 
(f) cos (-60°) 
(g) sin (-150°) 
(h) cos (-120°) 
(e) tan 330° 
(f) cos (-60°)
(g) sin (-150°) 
(h) cos (-120°)

Ans.Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev


Q2. Find the value of 
(a) sec2θ - tan2θ 
(b) cosec2θ - cot2θ - 1 
(c) 2 sin 45°cos 45°
(d) 2sin 15°cos 45°

Ans.Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev


Calculus

Q3. Differentiate the following functions with respect to x 
(a) x4 + 3x2 - 2x 
(b) x2 cos x 
(c) (6x + 7 )4
(d) exx5

(e) (1 + x) / ex

Ans.

(a) 4x3 + 6x - 2
(b) 2x cosx - x2 sinx
(c) 24(6x + 7)3 
(d) 5exx4 + exx5 
(e) -xe-x



Q4. Integrate the following functions with respect to t
(a) ∫(3t2 - 2t)dt    
(b) ∫(4 cos t + t2) dt
(c) ∫(2t - 4)-4 dt

(d) ∫ dt / (6t - 1)

Ans.

(a) t3 - t2 + C
Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev
Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev
Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev


Q5. Integrate the following functions
Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev
Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev
Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev
Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev
Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev

Ans.

(a) 4

(b) (√3 - 1) / 2
(c) In (5/2)
(d) Zero
(e) - 1


Q6. Find maximum/minimum value of y in the functions given below
(a) y = 5 - (x - 1)2
(b) y = 4x2 - 4x + 7 
(c) y = x3 - 3x
(d) y = x3 - 6x2 + 9x+ 15
(e) v = (sin 2x - x),Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev

Ans.

(a) ymax = 5 at x = 1
(b) ymin = 6 at x = 1/2
(c) ymin = - 2 at x = 1 and ymax = 2 at x = - 1
(d) ymin = 15 at x = 3 and ymax = 19 at x = 1
Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRevBasic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev


Graphs

Q7. Draw the graphs corresponding to the equations 
(a) y = 4x 
(b) y = - 6x 
(c) y = x + 4 
(d) y = -2x + 4 
(e) y = 2x - 4 
(f) y = -4x - 6

Ans.

Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRevBasic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRevBasic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRevBasic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev


Q8. For the graphs given below, write down their x-y equations
Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev

Ans.

(a) y = x
Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev
Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev
(d) y = - x + 2


Q9. For the equations given below, tell the nature of graphs.
(a) y = 2x2
(b) y = -4x2 +6
(c) y = 6e -4x
(d) y = 4 (1 - e -2x)
(e) y = 4/x
Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev

Ans.

(a) parabola passing through origin
(b) parabola not passing through origin
(c) exponentially decreasing graph
(d) exponentially increasing graph
(e) Rectangular hyperbola in first and third quadrant
(f) Rectangular hyperbola in second and fourth quadrant


Q10. Value of y decreases exponentially from y = 10 to y = 6 Plot an x-y graph. 

Ans.

Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev


Q11. Value of y increases exponentially from y = -4 to y = +4. Plot an x- y graph.

Ans.

Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev


Q12. The graph shown in the figure is exponential. Write down the equation corresponding to the graph.

Ans.
Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev

y = 4 + 8e -Kx Here, K is a positive constant


Q13. The graph shown in the figure is exponential. Write down the equation corresponding to the graph.

Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev

Ans.

y = - 4 + 10(1 - e-Kx)Here, K is positive constant


Significant Figures

Q14. Write down the number of significant figures in the following. 
(a) 6428 
(b) 62.00 m 
(c) 0.0628 cm 
(d) 1200 N

Ans.

(a) Four
(b) Four
(c) Three
(d) Four


Q15. Round off to four significant figures. 
(a) 45.689 
(b) 2.0082

Ans.

(a) 45.69
(b) 2.008


Q16. Add 6.75 x 103 cm and 4.52x 102 cm with due regards to significant figures.

Ans. 7.20 x 10cm


Q17. A thin wire has length of 21.7 cm and radius 0.46 mm. Calculate the volume of the wire to correct significant figures.

Ans. 0.14 cm3


Q18. A cube has a side of length of 2.342 m. Find volume and surface area in correct significant figures.

Ans. Area= 5.485 m2, volume= 12.85 m3


Q19. Find density when a mass of 9.23 kg occupies a volume of 1.1m3. Take care of significant figures.

Ans. Density = 8.4 kg/m3


Q20. Length, breadth and thickness of a rectangular slab are 4.234 m, 1.005 m and 2.01 cm respectively. Find surface area and volume to correct significant figures.

Ans. Area= 4.255 m2, volume = 8.55 m3


Q21. Solve with due regards to significant figures
(4.0 x 10-4 -2.5 x 10-6)

Ans. 4.0 x 10-4


Error Analysis

Q22. The refractive index (n) of glass is found to have the values 1.49, 1.50, 1.52,1.54 and 1.48. Calculate 
(a) the mean value of refractive index 
(b) absolute error is each measurement 
(c) fractional error and 
(d) percentage error

Ans.

(a) 1.51
(b) + 0.02,+ 0.01,- 0.01,- 0.03,+ 0.03
(c) ± 0.0132
(d) ± 1.32%


Q23. The radius of a sphere is measured to be (2.1 + 0.5)cm. Calculate its surface area with error limits.

Ans.

(55.4±26.4) cm2


Q24. Calculate focal length of a spherical mirror from the following observations. Object distance u = (50.1 + 0.5) cm and image distance v = (20.1 ± 0.2) cm.

Ans. (14.3 ± 0.4) cm


Q25. Find the percentage error in specific resistance given by Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRevwhere r is the radius having value (0.2+ 0.02)cm, R is the resistance of (60 ± 2) ohm and l is the length of (150 ± 0.1)cm.

Ans. 3.4%


Q26. A physical quantity ρ is related to four variables α, β, γ and η as 
Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev
The percentage errors of measurements in α, β, γ and η are 1%, 3%, 4% and 2% respectively. Find the percentage error in ρ.

Ans. 3%


Q27. The period of oscillation of a simple pendulum is Basic Mathematics and Measurement(Part- 2) - Physics, Solution by DC Pandey NEET Notes | EduRev Length L is about 10 cm and is known to 1 mm accuracy. The period of oscillation is about 0.5 s. The time of 100 oscillations is measured with a wristwatch of 1 s time period. What is accuracy in the determination of g?

Ans. 5%


Vernier Callipers and Screw Gauge

Q28. 19 divisions on the main scale of a vernier callipers coincide with 20 divisions on the vernier scale. If each division on the main scale is of 1 cm, determine the least count of instrument.

Ans. 0.05 cm


Q29. The pitch of a screw gauge is 1 mm and there are 100 divisions on the circular scale. While measuring the diameter of a wire, the linear scale reads 1 mm and 47th division on the circular scale coincides with the reference line. The length of the wire is 5.6 cm. Find the curved surface area (in cm2) of the wire inappropriate number of significant figures.

Ans. 2.6 cm2


Q30. The edge of a cube is measured using vernier callipers. [9 divisions of the main scale are equal to 10 divisions of vernier scale and 1 main scale division is 1 mm]. The main scale division reading is 10 and 1 division of the vernier scale was found to be coinciding with the main scale. The mass of the cube is 2.736 g. Calculate the density in g/cm3 upto correct significant figures.

Ans. 2.66 g/cm3

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Related Searches

MCQs

,

shortcuts and tricks

,

past year papers

,

Exam

,

pdf

,

Basic Mathematics and Measurement(Part- 2) - Physics

,

study material

,

practice quizzes

,

Summary

,

Extra Questions

,

ppt

,

Basic Mathematics and Measurement(Part- 2) - Physics

,

video lectures

,

Solution by DC Pandey NEET Notes | EduRev

,

mock tests for examination

,

Previous Year Questions with Solutions

,

Basic Mathematics and Measurement(Part- 2) - Physics

,

Solution by DC Pandey NEET Notes | EduRev

,

Sample Paper

,

Important questions

,

Solution by DC Pandey NEET Notes | EduRev

,

Objective type Questions

,

Viva Questions

,

Free

,

Semester Notes

;