MCQ Questions for Class 9 Science Chapter 1 Matter in our Surroundings with Answers

MCQ Questions for Class 9 Science Chapter 1 Matter in our Surroundings with Answers

MCQ Questions for Class 9 Science Chapter 1 Matter in our Surroundings with Answers

MCQs from Class 9 Science Chapter 1 – Matter in Our Surroundings are provided here to help students prepare for their upcoming Science exam.

MCQs from CBSE Class 9 Science Chapter 1: Matter in Our Surroundings

1. In which of the following conditions, the distance between the molecules of hydrogen gas would increase?
(i) Increasing pressure on hydrogen contained in a closed container
(ii) Some hydrogen gas leaking out of the container
(iii) Increasing the volume of the container of hydrogen gas
(iv) Adding more hydrogen gas to the container without increasing the volume of the container
(a) (i) and (iii)
(b) (i) and (iv)
(c) (ii) and (iii)
(d) (ii) and (iv)

Answer/ Explanation

(c) (ii) and (iii)


2. When a gas jar full of air is placed upside down on a gas jar full of bromine vapours, the red-brown vapours of bromine from the lower jar go upward into the jar containing air. In this experiment:

(a) Air is heavier than bromine
(b) Both air and bromine have the same density
(c) Bromine is heavier than air
(d) Bromine cannot be heavier than air because it is going upwards against gravity

Answer/ Explanation

(c) Bromine is heavier than air


3. A form of matter has no fixed shape but it has a fixed volume. An example of this form of matter is
(a) Krypton
(b) Kerosene
(c) Carbon steel
(d) Carbon dioxide

Answer/ Explanation

(b) Kerosene


4. Which one of the following statements is not true?
(a) The molecules in a solid vibrate about a fixed position
(b) The molecules in a liquid are arranged in a regular pattern
(c) The molecules in a gas exert negligibly small forces on each other, except during collisions
(d) The molecules of a gas occupy all the space available

Answer/ Explanation

(b) The molecules in a liquid are arranged in a regular pattern


5. The correct procedure of heating iron-sulphur mixture to prepare iron sulphide is: :
(a) Heat the powder mixture at the base of the test tube using a blue flame throughout.
(b) Heat the iron filings and sulphur mixture in the middle of the test tube using yellow flame throughout.
(c) Heat the powder mixture at the top of the test tube using an orange flame throughout.
(d) Heat the iron filings-sulphur mixture at 3/4 quarters of the test tube using a red flame throughout.

Answer/ Explanation

(a) Heat the powder mixture at the base of the test tube using a blue flame throughout.


6. When water at 0°C freezes to form ice at the same temperature of 0°C, then it:
(a) Absorbs some heat
(b) Releases some heat
(c) Neither absorbs nor releases heat
(d) Absorbs exactly 3.34 x 105J/kg of heat

Answer/ Explanation

(b) Releases some heat


7. When heat is constantly supplied by a burner to boiling water, then the temperature of water during vaporisation :
(a) Rises very slowly
(b) Rises rapidly until steam is produced
(c) First rises and then becomes constant
(d) Does not rise at all

Answer/ Explanation

(d) Does not rise at all


8. Which one of the following set of phenomena would increase on raising the temperature?
(a) Diffusion, evaporation, compression of gases
(b) Evaporation, compression of gases, solubility
(c) Evaporation, diffusion, expansion of gases
(d) Evaporation, solubility, diffusion, compression of gases

Answer/ Explanation

(c) Evaporation, diffusion, expansion of gases


9. On converting 308 K, 329 K and 391 K to Celsius scale, the correct sequence of temperatures will be:
(a) 33°C, 56°C and 118°C
(b) 35°C, 56°C and 119°C
(c) 35°C, 56°C and 118°C
(d) 56°, 119°C and 35° C

Answer/ Explanation

(c) 35°C, 56°C and 118°C


10. Four students took separately the mixture of sand, common salt and ammonium chloride in beakers, added water, stirred the mixture well and then filtered. They reported their observations as shown below

Student As residue In the filtrate
I
II
III
IV
Ammonium chloride
Common salt, Sand
Sand, Ammonium chloride
Sand
Sand, Common salt
Ammonium chloride
Common salt
Ammonium chloride, Common salt

Who reported the observations in the correct order of the components as residue and in the filtrate?
(a) I
(b) IV
(c) III
(d) II

Answer/ Explanation

(b) IV


11. Which of the following phenomena always results in the cooling effect?
(a) Condensation
(b) Evaporation
(c) Sublimation
(d) None of these

Answer/ Explanation

(b) Evaporation


12. Which of the following cannot be considered a form of matter?
(a) Atom
(b) Water
(c) Humidity
(d) Electron

Answer/ Explanation

(c) Humidity


13. Which of the following causes the temperature of a substance to remain constant while it is undergoing a change in its state?
(a) Latent heat
(b) Lattice energy
(c) Loss of heat
(d) None of these

Answer/ Explanation

(a) Latent heat


14. Which of the following statement is correct?
(a) Materials existing as liquids at room temperature have their melting and boiling points lower than that of room temperature.
(b) The phenomenon involving the transition of a substance from solid to liquid state is called sublimation.
(c) To convert a temperature on the Celsius scale to Kelvin scale, subtract 273 from the given temperature
(d) The density of ice is less than that of water.

Answer/ Explanation

(d) The density of ice is less than that of water.


15. Which of the following statement is not true regarding the characteristic of matter?
(a) Particles of a matter are randomly moving in all directions.
(b) Kinetic energy of the particles increases with a rise in temperature
(c) Kinetic energy of the particles of all maters remains the same at a particular temperature.
(d) Particles of matter diffuse into each other on their own.

Answer/ Explanation

(c) Kinetic energy of the particles of all maters remains the same at a particular temperature.


Maths MCQs for Class 12 Chapter Wise with Answers

Maths Multiple Choice Questions With Answers For Class 12 Pdf Free Download is very important for students who want to score good marks in their CBSE board examination. Students who can Practice CBSE Maths MCQs For Class 12 With Answers Pdf to improve your score in Board Exams.

Maths MCQ Questions for Class 12 with Answers Pdf Download

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We hope the given MCQ Questions For Class 12 Maths With Answers will help you. If you have any query regarding CBSE Class 12 Maths Multiple Choice Questions with Answers, drop a comment below and we will get back to you at the earliest.

Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability

Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 5 Continuity and Differentiability. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Continuity and Differentiability MCQs Pdf with Answers to know their preparation level.

Continuity and Differentiability Class 12 Maths MCQs Pdf

1. Given functions f(x) = \(\frac{x^{2}-4}{x-2}\) and g(x) = x + 2, x <= R. Then which of the following is correct?
(a) f is continuous at x = 2,
g is continuous at x = 2
(b) f is continuous at x = 2,
g is not continuous at x = 2
(c) f is not continuous at x = 2,
g is continuous at x = 2
(d) f is not continuous at x = 2,
g is not continuous at x = 2

Answer/Explanation

Answer: c
Explaination: (c), as f(2) is not defined so / is not continuous at x = 2 ‘g’ is a polynomial function, so continuous at x = 2.


2.
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 2

Answer/Explanation

Answer: d
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 18


3.
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 3
for x = 2, then value of k for which f is continuous is
(a) -2
(b) -1
(c) 0
(d) 1

Answer/Explanation

Answer: d
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 19


4. A function /is said to be continuous for x ∈ R, if
(a) it is continuous at x = 0
(b) differentiable at x = 0
(c) continuous at two points
(d) differentiable for x ∈ R

Answer/Explanation

Answer: d
Explaination: (d), as differentiable functions is continuous also.


5. Afunction
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 4
is continuous at x = 0 for
(a) k = 1
(b) k = 2
(c) k = \(\frac{1}{2}\)
(d) k = \(\frac{3}{2}\)

Answer/Explanation

Answer: a
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 21


6. Write the number of points where f(x) = |x + 2| + |x – 3| is not differentiable.
(a) 2
(b) 3
(c) 0
(d) 1

Answer/Explanation

Answer: a
Explaination: (a), as f(x) = |x – a| is continuous at x = a but not differentiable thereat.


7. Derivative of cot x° with respect to x is
(a) cosec x°
(b) cosec x° cot x°
(c) -1° cosec2 x°
(d) -1° cosec x° cot x°

Answer/Explanation

Answer: c
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 30


8.
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 13
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 14

Answer/Explanation

Answer: a
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 31


9. If f(x) = \(\log _{x^{2}}(\log x)\), then f(e) is
(a) 0
(b) 1
(c) \(\frac{1}{e}\)
(d) \(\frac{1}{2e}\)

Answer/Explanation

Answer: d
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 40


10. If f(x) = ex and g(x) = loge x, then (gof)’ (x) is
(a) 0
(b) 1
(c) e
(d) 1 + e

Answer/Explanation

Answer: b
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 41


11.
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 15
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 16

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 43


12. If y = xx-∞, , then x(l -y log x)\(\frac{d y}{d x}\) is equal to
(a) x²
(b) y²
(c) xy²
(d) x²y

Answer/Explanation

Answer: b
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 50


13. The derivative of sin x with respect to log x is
(a) cos x
(b) x cos x
(c) \(\frac{\cos x}{\log x}\)
(d) \(\frac{1}{x}\) cos x

Answer/Explanation

Answer: b
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 51


14. Ify = Ae5x,+ Be-5x x then \(\frac{d^{2} y}{d x^{2}}\) is equal to
(a) 25y
(b) 5y
(c) -25y
(d) 10y

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 54


15. Given the functionMaths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 1
the function is continuous at x = 0, state true or false.

Answer/Explanation

Answer:
Explaination: False, as ‘f’ is not defined at x = 0. i.e.f (0) does not exist.


46. The function f(x) = \(\frac{x+1}{1+\sqrt{1+x}}\) continuous at x = 0 if/(0) is _________ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 20


17. A function f(x) = \(\frac{x}{x-5}\) x ∈ R, is a continuous function. State true or false.

Answer/Explanation

Answer:
Explaination: False, as for x = 5, f(5) is not defined.


18. A function f(x) = sin x + cos x is continuous function. State true or false.

Answer/Explanation

Answer:
Explaination: True, as sum of two continuous functions is a continuous function.


19. Discuss the continuity of the function fix)= \(\frac{1}{x-5}\) for x ∈ R.

Answer/Explanation

Answer:
Explaination: f(x) = \(\frac{1}{x-5}\), as f(5) is not defined, therefore function is not continuous at x = 5.


20. Discuss the continuity of the function
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 5

Answer/Explanation

Answer:
Explaination:
f(x)= \(\frac{x^{2}-25}{x-5}\), x ≠ 5. As x ≠ 5, therefore, value of function exists for all x(≠5) ∈ R.
Also \(\lim _{x \rightarrow a}\) f(x) = f(a) = a + 5, (a ≠ 5). Hence, continuous.


21. Check whether the function f(x) = 2x² + 1 is continuous at x = 0.

Answer/Explanation

Answer:
Explaination: f(x) = 2x² + 1, as \(\frac{x^{2}-25}{x-5}\) f(x) = f(0) = 1. Hence, continuous


22. Give an example of a function which is continuous but not differentiable at exactly two points.

Answer/Explanation

Answer:
Explaination:
We know function f(x)=|x – a| is continuous at x = a but not differentiable at x = a.
∴ functions |x| and |x – 1| are continuous but not differentiable at x = 0 and 1.
∴ function is h(x) = |x| + |x – 1|.


23. Determine the value of the constant ‘k’
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 6

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 22


24. Determine the value of ‘k’ for which the following function is continuous at x = 3:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 7

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 23


25. For what value of ‘k’ is the function
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 8
continuous at x = 0?

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 24
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 25


26. Find the value of k, so that the function
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 9
is continuous at x = 1

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 26


27. Determine the value of the constant ‘k’ so that the function
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 10
is continuous at x = 0. [Delhi]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 27


28. For what value of ‘k’ is the function
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 11
continuous at x = 0? [Foreign]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 28


29. The derivative of
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 12
State true or false.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 29


30. Find \(\frac{d y}{d x}\), if x² + y² = 5

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 32


31. Differentiate sin-1x², with resepct to x.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 33


32. Find \(\frac{d y}{d x}\), if sin y + x = log x

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 34


33. Find \(\frac{d y}{d x}\) at x = 1, y = \(\frac{\pi}{4}\) if sin²y + cos xy = K. [Delhi 2017]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 35
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 36


34. Differentiate tan-1 \(\left(\frac{1+\cos x}{\sin x}\right)\) with respect to x. [CBSE 2018]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 37


35. If y = 2√x, then \(\frac{d y}{d x}\) is _______ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 38


36. If y = log (tan x) + log (cot x), then \(\frac{d y}{d x}\) is _______ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 42


37. If \(f(x)=9^{x^{2}+2 x}\), then f(-1) is _______ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 44


38. Differentiate e-2x with respect to x.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 45


39. Differentiate 5sin x, with respect to x.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 46


40. Differentiate loge(sin x) with respect to x.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 47


41. Differentiate log x² w.r.t x.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 48


42. If y = e-3 log x then find \(\frac{d y}{d x}\).

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 49


43.
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 17

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 52


44. Find \(\frac{d y}{d x}\) at t = \(\frac{2 \pi}{3}\) when x = 10(t – sin t) and y = 12(1 – cos t). [Foreign 2017]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 53


45. Find \(\frac{d^{2} y}{d x^{2}}\), if y = log x

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 55


46. If y = sin 3x, find y2

Answer/Explanation

Answer:
Explaination:
y = sin 3x
y1 = 3 cos 3x
y2 = -9 sin 3x.


47. Find \(\frac{d^{2} y}{d x^{2}}\) if y = e-3x

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 56
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 57


48. Verify the Rolle’s Theorem for the function f(x) = x² in the inverval [-1, 1].

Answer/Explanation

Answer:
Explaination:
Function f(x) = x² is continuous in [-1,1 ], differentiable in ( -1, 1) and f(-1) = f(1). Hence, Rolle’s Theorem verified.
⇒ f'(c) = 0
⇒ 2c = 0
⇒ c = 0 for c ∈ (-1, 1)


49. Verify the Rolle’s Theorem for die functiony(x) = |x| in the inverval [-1, 1]. [HOTS]

Answer/Explanation

Answer:
Explaination: Not verified, as /(x) =|x| is not derivable at x = 0.


50. Verify the Rolle’s Theorem for the function f(x) = sin 2x in [0, π].

Answer/Explanation

Answer:
Explaination:
Function f(x) = sin 2x is continuous in [0, π], differentiable in (0, π) and (0)= f(π)
Hence, Rolle’s theorem verified.
⇒ f'(c) = 2 cos 2c
⇒ 2cos 2c = 0
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 58


We hope the given Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability will help you. If you have any query regarding CBSE Class 12 Maths Continuity and Differentiability MCQs Pdf, drop a comment below and we will get back to you at the earliest.

Maths MCQs for Class 12 with Answers Chapter 4 Determinants

Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 4 Determinants. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Determinants MCQs Pdf with Answers to know their preparation level.

Determinants Class 12 Maths MCQs Pdf

1.
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 1

Answer/Explanation

Answer: d
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 24


2.
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 2

Answer/Explanation

Answer: a
Explaination: (a), Δ = 6(-1)- 1(1) = -7.


3.
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 9

Answer/Explanation

Answer: d
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 27


4. Let A be a square matrix of order 2 × 2, then |KA| is equal to
(a) K|A|
(b) K²|A|
(c) K3|A|
(d) 2K|A|

Answer/Explanation

Answer: b
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 28


5.
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 10

Answer/Explanation

Answer: a
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 31


6. Let x, yeR, then the determinant
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 11

Answer/Explanation

Answer: a
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 32


7.
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 16

Answer/Explanation

Answer: d
Explaination: (d), as value of determinant is sum of the product of elements of any row and column and then- respective cofactor.


8. A and B are invertible matrices of the same order such that |(AB)-1| = 8, If |A| = 2, then |B| is
(a) 16
(b) 4
(c) 6
(d) \(\frac{1}{16}\)

Answer/Explanation

Answer: d
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 48


9. Determinant is a number associated to a matrix, state true or false.

Answer/Explanation

Answer:
Explaination: False, as determinant is a number associated to a square matrix.


10.
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 3

Answer/Explanation

Answer:
Explaination: (a + ib) (a – ib) – (c + id) (c – id) = a² + b² – c² – d².


11.
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 4

Answer/Explanation

Answer:
Explaination:
sin 30° cos 60° + cos 30° sin 60°
= sin(30° + 60°) = sin 90° = 1.


12.
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 5

Answer/Explanation

Answer:
Explaination:
18x + 45 – 15x -6 = 0
⇒ 3x = -39
⇒ x = -13.


13. Evaluate the determinant
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 6

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 25


14.
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 7

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 26


15. Value of determinant
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 8
is 0, state true or false.

Answer/Explanation

Answer:
Explaination: True, as on performing C3 → C3 + C2 we notice elements of C1 and C3 are proportional.


16. If A is a matrix of order 3 × 3, then |KA| = _______ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 29
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 30


17. The determinant
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 12

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 33


18. Evaluate the determinant
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 13

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 34


19. What is the value of the following determinant?
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 14

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 35


20. If for any 2 × 2 square matrix A, A(adj A)
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 15

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 36


21. If area of a triangle with vertices (3, 2), (-1,4) and (6, k) is 7 sq units, then possible values of k are ______ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 37


22. The points (a + 5, a – 4), (a – 2, a + 3) and (a, a) are non-collinear for any value of a. State true or false.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 38


23. Find the area of the triangle with vertices (-1, 2), (4, 0) and (3, 9).

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 39


24. Find the value of x, such that the points (0, 2), (1, x) and (3, 1) are collinear.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 40


25. Show that points A(a, b + c), B(b, c + a) and C(c, a + b) are collinear. [NCERT]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 41
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 42


26. Find the cofactor of a12 of the determinant
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 17

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 43


27.
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 18
cofactor of the element a21 [Foreign 2015]

Answer/Explanation

Answer:
Explaination: Cofactor of a2l = (-1)3 (18 – 21) = 3


28. In the determinant
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 19 find
(i) minor of element 3
(ii) cofactor of element 5.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 44


29. If A and B are invertible matrices of the same order (AB)-1 is _____ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 45


30.
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 20

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 46


31. A is invertible matrix of order 3 × 3 and |A| = 9, then value of |A-1|is

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 47


32. If the value of a third order determinant is 7, then the value of a determinant formed by replacing each element by its cofactor will be 49. State true or false.

Answer/Explanation

Answer:
Explaination: True, as |adj.A| = |A|<sup>n-1</sup>, A is matrix of order 3 × n


33. Inverse of matrix
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 21
exists, state true or false.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 49


34. For what value of k, the matrix \(\left[\begin{array}{ll}{k} & {2} \\ {3} & {4}\end{array}\right]\) has no inverse?

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 50


35. Write A-1 for A = \(\left[\begin{array}{ll}{2} & {5} \\ {1} & {3}\end{array}\right]\) [Delhi 2011]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 51


36. Given a square matrix A of order 3 × 3, such that |A| = 12, find the value of |A. adj A|. [HOTS]

Answer/Explanation

Answer:
Explaination:
|A adj A| = |A|3 as matrix A is of order 3 × 3.
∴ |A adj A| = |A|3 = (12)3 = 1728


37. If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A-1) = (det A)k

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 52


38.
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 22

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 53
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 54


39. If for any 2 × 2 square matrix A, A(adj A) = \(\left[\begin{array}{ll}{8} & {0} \\ {0} & {8}\end{array}\right]\), then write the value of |A|. [Delhi 2017]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 55


40.
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 23

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 56
Maths MCQs for Class 12 with Answers Chapter 4 Determinants 57


We hope the given Maths MCQs for Class 12 with Answers Chapter 4 Determinants will help you. If you have any query regarding CBSE Class 12 Maths Determinants MCQs Pdf, drop a comment below and we will get back to you at the earliest.

Maths MCQs for Class 12 with Answers Chapter 3 Matrices

Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 3 Matrices. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Matrices MCQs Pdf with Answers to know their preparation level.

Matrices Class 12 Maths MCQs Pdf

1. If a matrix has 6 elements, then number of possible orders of the matrix can be
(a) 2
(b) 4
(c) 3
(d) 6

Answer/Explanation

Answer: b
Explaination: (b), as 6 → 1 × 6, 2 × 3, 3 × 2, 6 × 1.


2. If A = [aij] is a 2 × 3 matrix, such that aij = \(\frac{(-i+2 j)^{2}}{5}\).then a23 is
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 1

Answer/Explanation

Answer: d
Explaination: (d), as a23 = \(\frac{(-2+6)^{2}}{5}=\frac{16}{5}\)


3. If A = diag(3, -1), then matrix A is
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 2

Answer/Explanation

Answer: c
Explaination: (c), as diag (3, -1) is a diagonal matrix. Its order is 2 × 2 with diagonal elements 3 and (-1).


4. Total number of possible matrices of order 2 × 3 with each entry 1 or 0 is
(a) 6
(b) 36
(c) 32
(d) 64

Answer/Explanation

Answer: d
Explaination: (d), as total elements are 6 and each entry can be done in 2 ways. Hence, total possibilities = 26 = 64.


5. If A is a square matrix such that A²=A, then (I + A)² – 3A is
(a) I
(b) 2A
(c) 3I
(d) A

Answer/Explanation

Answer: a
Explaination: (a), as (I + A)² -3A = I² + IA + AI + A² – 3A = I + A + A + A – 3A=I


6. If matrices A and B are inverse of each other then
(a) AB = BA
(b) AB = BA = I
(c) AB = BA = 0
(d) AB = 0, BA = I

Answer/Explanation

Answer: b
Explaination: (b), by definition.


7.
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 11

Answer/Explanation

Answer: d
Explaination:
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 26


8. The diagonal elements of a skew symmetric matrix are
(a) all zeroes
(b) are all equal to some scalar k(≠ 0)
(c) can be any number
(d) none of these

Answer/Explanation

Answer: a
Explaination:
(a), as in skew symmetric matrix, aij = -aji
⇒ aii = – aii
⇒ 2aii = 0
⇒ aii = 0, i.e. diagonal elements are zeroes.


9. If A = \(\left[\begin{array}{ll}{5} & {x} \\ {y} & {0}\end{array}\right]\) and A = A’ then
(a) x = 0, y = 5
(b) x = y
(c) x + y = 5
(d) x – y = 5

Answer/Explanation

Answer: b
Explaination:
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 38


10. If a matrix A is both symmetric and skew symmetric then matrix A is
(a) a scalar matrix
(b) a diagonal matrix
(c) a zero matrix of order n × n
(d) a rectangular matrix.

Answer/Explanation

Answer: c
Explaination: (c), as it satisfies aij = aji, = -aji and aii = 0


11.
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 3

Answer/Explanation

Answer:
Explaination: False, as their orders are different.


12. If a matrix has 5 elements, write all possible orders it can have. [AI2011]

Answer/Explanation

Answer:
Explaination: Possible orders are 1 × 5, 5 × 1.


13. If A is a 3 × 3 matrix, whose elements are given by aiij = \(\frac{1}{3}\)|-3i + j|, then write the value a23. [Foreign 2013]

Answer/Explanation

Answer:
Explaination: Given aij = \(\frac{1}{3}\)|-3i + j|
∴ a23 = \(\frac{1}{3}\)|-6 + 3| = 1.


14.
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 4

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 24


15.
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 5

Answer/Explanation

Answer:
Explaination: x + y + z = 9, x + z = 5, y + z = 1, on solving we get
x = 2, y = 4, z = 3


16.
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 6

Answer/Explanation

Answer:
Explaination:
cos α = 1, sin α = 0
⇒ α = 0°


17.
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 7

Answer/Explanation

Answer:
Explaination: 3a22 – 4a33 = 3 × 5 – 4 × 4 = -1


18.
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 8

Answer/Explanation

Answer:
Explaination: These matrices are not equal as their orders are not same.


19.
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 9

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 25


20. If matrix X is such that
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 10
then order of matrix X is ______ .

Answer/Explanation

Answer:
Explaination: 2 × 2, as (2 × 2) × (2 × 3) = 2 × 3


21. If A and B are matrices of order 3 × m and 3 × n respectively such that m = n, then order of 2A + 7B is _____ .

Answer/Explanation

Answer:
Explaination: 3 × m or 3 × n, as order of sum of two matrices is same as order of given matrices.


22. Matrix multiplication is commutative, state true or false.

Answer/Explanation

Answer:
Explaination: False, as AB ≠ BA in general.


23. The negative of matrix is obtained by multiplying the matrix by _____ .

Answer/Explanation

Answer:
Explaination: -1, as (-1)A = -A.


24.
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 12

Answer/Explanation

Answer:
Explaination: a22 + b21 = 4 – 3 = 1


25.
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 13
then write the value of k.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 27


26.
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 14

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 28


27. Find x and y, if
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 15

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 29


28.
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 16
find the value of x [Delhi 2012]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 30


29.
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 17

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 31


30. Find a matrix X such that 2A + B + X =
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 18

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 32
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 33


31. If A is a square matrix such that A² = A, then write the value of (I + A)² – 3A. [Foreign 2012]

Answer/Explanation

Answer:
Explaination: (I + A)² – 3A = I² + IA+ AI + A² -3A = I + A+ A+ A – 3A = I


32.
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 19

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 34


33. If matrix A = \(\left[\begin{array}{cc}{a} & {b} \\ {c} & {-a}\end{array}\right]\) is the square root of the 2 × 2 identity matrix, then find the relation a between a, b and c.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 35


34.
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 20

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 36
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 37


35. If A and B are symmetric matrices, then AB -BA is a _______ matrix.

Answer/Explanation

Answer:
Explaination:
skew symmetric, as (AB – BA)’
= (AB)’ – (BA)’
= B’A’ – A’B’ = BA- AB = -(AB – BA) (∵ A’ =A,B’ = B)


36. If A is a skew symmetric matrix then A² is a ______ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 39


37. If A and B are two matrices such that their multiplication is defined, then (AB)’ = _____ .

Answer/Explanation

Answer:
Explaination: B’A’, as result


38. If matrix A = [1 2 3] then find AA’, where A’ is the transpose of matrix A.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 40


39.
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 21

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 41


40. For what value of x, is the matrix
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 22
a skew symmetric matrix ? [AI 2013]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 42


41. If A and B are symmetric matrices, show that AB is symmetric, if AB = BA.

Answer/Explanation

Answer:
Explaination: Given, A’ = A, B’ = B and if AB is symmetric, then
(AB)’ =AB … (i)
Also, (AB)’ = B’A’ = BA … (ii)
From (i) and (ii), we get AB = BA.


42.
Maths MCQs for Class 12 with Answers Chapter 3 Matrices 23
skew symmetric, find the values of ‘a’ and ‘b’ [CBSE 2018]

Answer/Explanation

Answer:
Explaination: For skew symmetric matrix, aij = – aji
⇒ a = – 2, b = 3.


43. Show that all the elements on the main diagonal of a skew symmetric matrix are zero. [Delhi 2017]

Answer/Explanation

Answer:
Explaination: A square matrix A = [aij is skew symmetric if
aij = –ji, ∀ i,j
Let i=j
⇒ aii = – aii
⇒ 2aii = 0
=> aii = 0
Hence, all the diagonal elements of a skew symmetric matrix are always zero.


44. If A and B are symmetric matrices, show that AB + BA is symmetric and AB – BA is skew symmetric. [Dehradun 2019]

Answer/Explanation

Answer:
Explaination: A’ =A,B’= B;
Consider (AB + BA)’ = (AB)’ + (BA)’
= B’A’ + A’B’
= BA+AB
= AB +BA.
Hence, symmetric.
Consider (AB – BA)’ = (AB)’ – (BA)’
= B’ A’- A’ B’
= BA – AB
= -(AB-BA)
Hence, skew symmetric.


45. Show that the matrix B’AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.

Answer/Explanation

Answer:
Explaination: Let A is symmetric then A’ = A …(i)
Now (B’AB)’ = B’A'(B’)’ = B’A’B = B’AB [using (i)]
Hence, symmetric.
Similarly, let A be skew symmetric then A’= -A
(B’AB)’ = B’A'(B’)’ = B’A’B
= B'(-A)B = -B’AB.
Hence, B’AB is skew symmetric.


We hope the given Maths MCQs for Class 12 with Answers Chapter 3 Matrices will help you. If you have any query regarding CBSE Class 12 Maths Matrices MCQs Pdf, drop a comment below and we will get back to you at the earliest.

Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions

Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Inverse Trigonometric Functions MCQs Pdf with Answers to know their preparation level.

Inverse Trigonometric Functions Class 12 Maths MCQs Pdf

1. Principal value of sin-1 \(\frac{1}{2}\) is
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 1

Answer/Explanation

Answer: d
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 11


2. sin-1{sin (\(\frac{2 \pi}{3}\))} = \(\frac{2 \pi}{3}\), state true or false.

Answer/Explanation

Answer:
Explaination: False, as –\(\frac{\pi}{2}\) ≤ sin<sup>-1</sup> x ≤ \(\frac{\pi}{2}\).


3. tan-1{sin (-\(\frac{\pi}{2}\))} is equal to
(a) -1
(b) 1
(c) \(\frac{\pi}{2}\)
(d) –\(\frac{\pi}{4}\)

Answer/Explanation

Answer: d
Explaination:
(d), as sin (-\(\frac{\pi}{2}\))= -1, and tan<sup>-1</sup>(-1) = – \(\frac{\pi}{4}\).


4. sec{tan-1 (-\(\frac{y}{3}\))} is equal to
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 2

Answer/Explanation

Answer: b
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 12


5. Principal branch of tan-1 x is ______ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 13


6. Principal value of the expression cos-1[cos(-680°)] is
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 3

Answer/Explanation

Answer: a
Explaination:
(a), as cos(-680°) = cos 680°
= cos(720° – 40°) = cos 40°
∴ cos<sup>-1</sup>[cos(-680°)J = cos<sup>-1</sup> (cos 40°)
= 40° = \(\frac{2 \pi}{9}\).


7. If tan-1x = sin-1(\(\frac{1}{\sqrt{2}}\)),then x is ______ .

Answer/Explanation

Answer:
Explaination: 1, as tan<sup>-1</sup> x = \(\frac{\pi}{4}\).


8. cos-1 \(\left(\cos \frac{7 \pi}{6}\right)=\frac{7 \pi}{6}\), state true or false.

Answer/Explanation

Answer:
Explaination: False, as \(\frac{7 \pi}{6}\) ∉ [0, π].


9. Find the value of tan-1 √3 – cot-1(-√3). [CBSE 2018]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 14


10. Find the principal value of cos-1 \(\frac{1}{2}\).

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 15


11. Find the principal value of
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 4

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 16


12. What is the domain of the function sin-1 x?

Answer/Explanation

Answer:
Explaination: -1 ≤ x ≤ 1 or [-1, 1]


13. Find the value of sin\(\left[\frac{\pi}{3}-\sin ^{-1}\left(-\frac{1}{2}\right)\right]\). [NCERT; Delhi 2011]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 17
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 18


14. Find the principal value of tan-1√3 sec-1(-2). [NCERT; AI 2012]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 19
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 20


15. If sin-1 x = \(\frac{\pi}{10}\), for some x ∈ R, then the value of cos-1 is ______ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 21


16. If tan-1 x -cot-1 = \(\frac{\pi}{6}\), then x is ______ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 22


17. The domain of the function^ = sin’ -‘(V) is
(a) [0, 1]
(b) (0, 1)
(c) [-1, 1]
(d) Φ

Answer/Explanation

Answer: c
Explaination:
(c), as -1 ≤ -x² < 1
⇒ 1 ≥ x² ≥ -1
⇒ 0 ≤ x² ≤ 1
⇒ |x| ≤ 1
⇒ -1 ≤ x ≤ 1.


18. If sec-1 x + sec-1 y = \(\frac{\pi}{2}\) the value of cosec-1x + cosec-1y is
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 5

Answer/Explanation

Answer: b
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 23


19. The value of tan²(sec-12) + cot2(cosec-13) is
(a) 5
(b) 11
(c) 13
(d) 15

Answer/Explanation

Answer: b
Explaination:
(b), as tan²(sec<sup>-1</sup>2) + cot²cosec<sup>-1</sup>3)
= sec²(sec<sup>-1</sup>2) – 1 + cosec²(cos 3) – 1
= (2)² – 1 +(3)² – 1
= 4 – 1 +9 – 1 = 11.


20. cot(\(\frac{\pi}{4}\) – 2 cot-13) = 7, state true or false.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 24


21. If 3 sin-1x + cos-1x = π, then x is equal to
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 6

Answer/Explanation

Answer: b
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 25


22.
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 7

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 26


23. If cos(tan-1x + cot-1√3) = 0, then value of x is _____ .

Answer/Explanation

Answer:
Explaination: √3, as tan-1x + cot-1 √3 = \(\frac{\pi}{2}\)
⇒ x = √3


24. If sin-1x + sin-1y + sin-1z = then the value of x + y² + z3 is
(a) 1
(b) 3
(c) 2
(d) 5

Answer/Explanation

Answer: b
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 27


25. The domain of y = cos-1(x² – 4) is
(a) [3, 5]
(b) [0, π]
(c) [-√5 ,-√3] ∩ [-√5,√3]
(d) [-√5 ,-√3] ∪ [√3, √5]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 28


26. Show that sin-1(2x\(\sqrt{1-x^{2}}\)) = 2 sin-1 – \(\frac{1}{\sqrt{2}}\) ≤ x ≤ \(\frac{1}{\sqrt{2}}\)

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 29


27. Find the value of sec(tan-1 –\(\frac{1}{2}\)).

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 30


28. If sin(sin-1\(\frac{1}{5}\) + cos-1x) = 1 then find the value of x. [NCERT; HOTS; Delhi 2014]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 31


29. Find the value of
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 8 [NCERT; Delhi 2013 (C), 2011]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 32


30.
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 9

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 33
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 34


31. Prove that 3 sin-1 x = sin-1(3x – 4x3),
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 39

Answer/Explanation

Answer:
Explaination:
Let x = sin θ
=> θ = sin-1x
RHS = sin-1(3x – 4x3)
= sin--1 [3 sin θ – 4 sin3 θ]
= sin-1 [sin 3θ] = 3θ = 3 sin-1x = LHS


32. Prove that sin-1x = tan-1\(\left(\frac{x}{\sqrt{1-x^{2}}}\right)\)

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 35


33.
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 10

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 36


34. If sin-1x + sin-1y = \(\frac{2 \pi}{3}\), then find the value of cos-1x + cos-1y.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 37


35. Find the value oftan(2 tan-1 \(\frac{1}{5}\)). [Delhi 2013]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions 38


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