MCQOPTIONS
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MCQOPTIONS
This section includes 462 Mcqs, each offering curated multiple-choice questions to sharpen your SRMJEEE knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If f(x) = x and g (x) = |x| then f o g (- 3.5) ? |
| A. | 3.5 |
| B. | - 3.5 |
| C. | f o g does not exists |
| D. | None of these |
| Answer» B. - 3.5 | |
| 2. |
If the number 235 in decimal system is converted into binary system, then what is the resulting number? |
| A. | (11110011)2 |
| B. | (11101011)2 |
| C. | (11110101)2 |
| D. | (11011011)2 |
| Answer» C. (11110101)2 | |
| 3. |
For x > 1, if (2x)2y = 4e(2x-2y), then \({\left( {1 + lo{g_e}2x} \right)^2}\frac{{dy}}{{dx}}\) is equal to |
| A. | \(\frac{{(xlo{g_e}{\rm{\;}}2x + lo{g_e}{\rm{\;}}2}}{x}\) |
| B. | \(\frac{{(xlo{g_e}{\rm{}}2x - lo{g_e}{\rm{\;}}2}}{x}\) |
| C. | x loge 2x |
| D. | loge 2x |
| Answer» C. x loge 2x | |
| 4. |
If x is any real number, then \(\frac{{{{\rm{x}}^2}}}{{1 + {{\rm{x}}^4}}}\) belongs to which one of the following intervals? |
| A. | (0, 1) |
| B. | \(\left( {0,\frac{1}{2}} \right]\) |
| C. | \(\left( {0,\frac{1}{2}} \right)\) |
| D. | [0, 1] |
| Answer» C. \(\left( {0,\frac{1}{2}} \right)\) | |
| 5. |
If \({\rm{f}}\left( {{{\rm{x}}_1}} \right) - {\rm{f}}\left( {{{\rm{x}}_2}} \right) = {\rm{f}}\left( {\frac{{{{\rm{x}}_1} - {{\rm{x}}_2}}}{{1 - {{\rm{x}}_1}{{\rm{x}}_2}}}} \right)\) for x1, x2 ∈ (-1, 1), then what is f(x) equal to? |
| A. | \({\rm{In\;}}\left( {\frac{{1 - {\rm{x}}}}{{1 + {\rm{x}}}}} \right)\) |
| B. | \({\rm{In\;}}\left( {\frac{{2 + {\rm{x}}}}{{1 - {\rm{x}}}}} \right)\) |
| C. | \({\tan ^{ - 1}}\left( {\frac{{1 - {\rm{x}}}}{{1 + {\rm{x}}}}} \right)\) |
| D. | \({\tan ^{ - 1}}\left( {\frac{{1 + {\rm{x}}}}{{1 - {\rm{x}}}}} \right)\) |
| Answer» B. \({\rm{In\;}}\left( {\frac{{2 + {\rm{x}}}}{{1 - {\rm{x}}}}} \right)\) | |
| 6. |
Let A = {x ∈ R : x is not a positive integer}. Define a function \(f:A \to R{\rm{\;as\;}}f\left( x \right) = \frac{{2x}}{{x - 1}}\) then f is: |
| A. | not injective |
| B. | neither injective nor surjective |
| C. | surjective but not injective |
| D. | injective but not surjective |
| Answer» E. | |
| 7. |
If \(f\left( x \right) = \frac{{x - 2}}{{x + 2}},\;x \ne - 2\), then what is f-1(x) equal to? |
| A. | \(\frac{{4\left( {x + 2} \right)}}{{x - 2}}\) |
| B. | \(\frac{{x + 2}}{{4\left( {x - 2} \right)}}\) |
| C. | \(\frac{{x + 2}}{{x - 2}}\) |
| D. | \(\frac{{2\left( {1 + x} \right)}}{{1 - x}}\) |
| Answer» E. | |
| 8. |
If log102 = 0.3010 and log103 = 0.4771, then the value of log100 (0.72) is equal to |
| A. | 0.9286 |
| B. | \(\bar 1.9286\) |
| C. | 1.8572 |
| D. | \(\bar 1.8572\) |
| Answer» C. 1.8572 | |
| 9. |
If E is the universal set and A = B ∪ C, then the set E - (E - (E - (E - (E - A)))) is same as the set |
| A. | B’ ∪ C’ |
| B. | B ∪ C |
| C. | B’ ∩ C’ |
| D. | B ∩ C |
| Answer» D. B ∩ C | |
| 10. |
Let f be a differentiable function such that f(1) = 2 and f(x) = f(x) for all x ∈ R If h(x) = f(f(x)), then h' (1) is equal to |
| A. | 400 |
| B. | 4e |
| C. | 2e |
| D. | 200 |
| Answer» C. 2e | |
| 11. |
Let f : R → R and g : R → R be continuous function. Then the value of the integral \(\int_{ - \pi /2}^{\pi /2} {\left[ {f(x) + f( - x)} \right]} \left[ {g(x) - g( - x)} \right]dx\) is: |
| A. | π |
| B. | 1 |
| C. | -1 |
| D. | 0 |
| Answer» E. | |
| 12. |
Convert 109 from decimal number system to binary number system. |
| A. | 1101111 |
| B. | 1111101 |
| C. | 1101101 |
| D. | 1110111 |
| Answer» D. 1110111 | |
| 13. |
If log10(x2 - 6x + 45) = 2, then the value of x are: |
| A. | 6, 9 |
| B. | 9, -5 |
| C. | 10, 5 |
| D. | 11, -5 |
| Answer» E. | |
| 14. |
If the function of \(f(x)=\dfrac{x}{x-1}\) express f(3x) in terms of f(x) |
| A. | \(\dfrac{3f(x)}{2f(x)+1}\) |
| B. | \(\dfrac{3f(x)}{3f(x)-1}\) |
| C. | \(3f(x) - 1\) |
| D. | \(\dfrac{3f(x)}{3f(x)-3}\) |
| Answer» B. \(\dfrac{3f(x)}{3f(x)-1}\) | |
| 15. |
Let f : [-1, 3] → R be defined as\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}{\left| x \right| + \left[ x \right],}&{ - 1 \le x < 1}\\{x + \left| x \right|,}&{1 \le x < 2}\\{x + \left[ x \right],}&{2 \le x \le 3}\end{array}} \right.\) where [t] denotes the greatest integer less than or equal to it. Then, f is discontinuous at: |
| A. | only one point |
| B. | only two points |
| C. | only three points |
| D. | four or more points |
| Answer» D. four or more points | |
| 16. |
Let \({\rm{f}}\left( {\rm{x}} \right):\left\{ {\begin{array}{*{20}{c}} {{\rm{x}},{\rm{\;\;\;x\;\;is\;rational}}}\\ {0,{\rm{\;\;\;x\;is\;irrational}}} \end{array}} \right.\) and \({\rm{g}}\left( {\rm{x}} \right):{\rm{\;}}\left\{ {\begin{array}{*{20}{c}} {0,{\rm{\;\;\;x\;is\;rational}}}\\ {{\rm{x}},{\rm{\;\;\;x\;is\;irrational}}} \end{array}} \right.\)If f : R → R and g : R → R, then (f – g) is |
| A. | one-one and into |
| B. | neither one-one nor onto |
| C. | many-one and onto |
| D. | one-one and onto |
| Answer» B. neither one-one nor onto | |
| 17. |
If n = 100!, then what is the value of the following?\(\rm \dfrac{1}{log_2n}+\dfrac{1}{log_3n}+\dfrac{1}{log_4n}+{.....}+\dfrac{1}{log_{100}n}\) |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» C. 2 | |
| 18. |
IF x + log15 (1 + 3x) = x log15 5 + log15 12, where x is an integer, then what is x equal to? |
| A. | -3 |
| B. | 2 |
| C. | 1 |
| D. | 3 |
| Answer» D. 3 | |
| 19. |
If x = logc (ab), y = loga (bc), z = logb (ca), then which of the following is correct? |
| A. | xyz = 1 |
| B. | x + y + z = 1 |
| C. | (1 + x)-1 + (1 + y)-1 + (1 + z)-1 = 1 |
| D. | (1 + x)-2 + (1 + y)-2 + (1 + z)-2 = 1 |
| Answer» D. (1 + x)-2 + (1 + y)-2 + (1 + z)-2 = 1 | |
| 20. |
If ϕ is the Euler’s Totient function, then ϕ(92) is: |
| A. | 44 |
| B. | 46 |
| C. | 48 |
| D. | 42 |
| Answer» B. 46 | |
| 21. |
Let A, B, and C be sets such that ϕ ≠ A ∩ B ⊆ C. Then which of the following statements is not true? |
| A. | B ∩ C ≠ ϕ |
| B. | If (A – B) ⊆ C, then A ⊆ C |
| C. | (C ∪ A) ∩ (C ∪ B) = C |
| D. | If (A – C) ⊆ B, then A ⊆ B |
| Answer» E. | |
| 22. |
Consider the following statements:Statement 1: The function f : R → R such that f(x) = x3 for all x ∈ R is one-oneStatement 2: f(a) = f(b) ⇒ a = b for all a, b ∈ R if the function f is one-one.Which one of the following is correct in respect of the above statements? |
| A. | Both the statements are true and Statement 2 is the correct explanation of Statement 1. |
| B. | Both the statements are true and Statement 2 is not the correct explanation of Statement 1. |
| C. | Statement 1 is true but Statement 2 is false. |
| D. | Statement 1 is false but Statement 2 is true |
| Answer» B. Both the statements are true and Statement 2 is not the correct explanation of Statement 1. | |
| 23. |
If f(x) = log10 (1 + x), then what is 4f(4) + 5f(1) – log10 2 equal to? |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 4 |
| Answer» E. | |
| 24. |
If f : R → S defined by f(x) = 4 sin x – 3 cos x + 1 is onto, then what is S equal to? |
| A. | [-5, 5] |
| B. | (-5, 5) |
| C. | (-4 , 6) |
| D. | [-4, 6] |
| Answer» E. | |
| 25. |
f(xy) = f(x) + f(y) is true for all |
| A. | Polynomial function f |
| B. | Trigonometric function f |
| C. | Exponential function f |
| D. | Logarithmic function f |
| Answer» E. | |
| 26. |
Number of onto (surjective) functions from A to B if n(A) = 6 and n(B) = 3, is |
| A. | 26 - 2 |
| B. | 36 - 3 |
| C. | 340 |
| D. | 540 |
| Answer» E. | |
| 27. |
If (0.2)x = 2 and log10 2 = 0.3010, the what is the value of x to the nearest tenth? |
| A. | - 10.0 |
| B. | - 0.5 |
| C. | - 0.4 |
| D. | - 0.2 |
| Answer» D. - 0.2 | |
| 28. |
If (x0, y0) is the solution of the equations (2x)ln 2 = (3y)ln 3 and 3ln x = 2ln y, then x0 is: |
| A. | \(\frac{1}{6}\) |
| B. | \(\frac{1}{3}\) |
| C. | \(\frac{1}{2}\) |
| D. | 6 |
| Answer» D. 6 | |
| 29. |
For 3 sets A, B, C if A ⊂ B, B ⊂ C then |
| A. | A ⋃ B ⊂ C |
| B. | C ⊂ A ⋃ B |
| C. | A - B = C |
| D. | None of these |
| Answer» B. C ⊂ A ⋃ B | |
| 30. |
If log102 = 0.3010, the value of log5 1024 is - |
| A. | 4.306 |
| B. | 3.01 |
| C. | 6.931 |
| D. | 1.386 |
| Answer» B. 3.01 | |
| 31. |
If f: R → R, g: R → R be two functions given by f(x) = 2x – 3 and g(x) = x3 + 5, then (fog)-1(x) is equal to |
| A. | \({\left( {\frac{{{\rm{x}} + 7}}{2}} \right)^{\frac{1}{3}}}\) |
| B. | \({\left( {\frac{{{\rm{x}} - 7}}{2}} \right)^{\frac{1}{3}}}\) |
| C. | \({\left( {{\rm{x}} - \frac{7}{2}} \right)^{\frac{1}{3}}}\) |
| D. | \({\left( {{\rm{x}} + \frac{7}{2}} \right)^{\frac{1}{3}}}\) |
| Answer» C. \({\left( {{\rm{x}} - \frac{7}{2}} \right)^{\frac{1}{3}}}\) | |
| 32. |
It is given that log10 2 = 0.301 and log10 3 = 0.477. How many digits are there in (108)10? |
| A. | 19 |
| B. | 20 |
| C. | 21 |
| D. | 22 |
| Answer» D. 22 | |
| 33. |
If loga(ab) = x, then what is logb(ab) |
| A. | \(\frac{1}{x}\) |
| B. | \(\frac{x}{{x + 1}}\) |
| C. | \(\frac{x}{{1 - x}}\) |
| D. | \(\frac{x}{{x - 1}}\) |
| Answer» E. | |
| 34. |
A function f from the set of natural numbers to integers is defined by:\(f\left( n \right)=\left\{ \begin{matrix} \frac{n-1}{2}~when~n~is~odd \\ -\frac{n}{2}when~n~is~even \\ \end{matrix} \right.\)then function is: |
| A. | one - one but not onto |
| B. | onto but not one - one |
| C. | one - one and onto both |
| D. | neither one - one nor onto |
| Answer» D. neither one - one nor onto | |
| 35. |
If \(f(x) = {\sin ^{ - 1}}\left[ {\frac{{\sqrt 3 }}{2}x - \frac{1}{2}\sqrt {1 - {x^2}} } \right]\), \(x \in \left[ { - \frac{1}{2},1} \right]\), then f(x) will be |
| A. | \({\sin ^{ - 1}}\left( {x - \frac{\pi }{2}} \right)\) |
| B. | \({\sin ^{ - 1}}\left( {x - \frac{\pi }{3}} \right)\) |
| C. | \({\sin ^{ - 1}}x ~-\frac{\pi}{6}\) |
| D. | \({\sin ^{ - 1}}\left( {x - \frac{\pi }{4}} \right)\) |
| Answer» D. \({\sin ^{ - 1}}\left( {x - \frac{\pi }{4}} \right)\) | |
| 36. |
Let XYZ be an equilateral triangle in which XY = 7 cm. If A denotes the area of the triangle, then what is the value of log10A4? (Given that log101050 = 3.0212 and log1035 = 1.5441) |
| A. | 5.307 |
| B. | 5.37 |
| C. | 5.5635 |
| D. | 5.6535 |
| Answer» B. 5.37 | |
| 37. |
Let A∪B = {x|(x - a)(x - b) > 0, where a < b}. What are A and B equal to? |
| A. | A = {x|x > a} and B = {x|x > b} |
| B. | A = {x|x < a} and B = {x|x > b} |
| C. | A = {x|x < a} and B = {x|x < b} |
| D. | A = {x|x > a} and B = {x|x < b} |
| Answer» C. A = {x|x < a} and B = {x|x < b} | |
| 38. |
If the function f given byf(x) = x3 – 3(a – 2) x2 + 3ax + 7 for some a ∈ R is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation, \(\frac{{{\rm{f}}\left( {\rm{x}} \right) - 14}}{{{{({\rm{x}} - 1)}^2}}} = 0\left( {{\rm{x}} \ne 1} \right)\)is |
| A. | -7 |
| B. | 6 |
| C. | 7 |
| D. | 5 |
| Answer» D. 5 | |
| 39. |
Let X be a non-empty set and let A, B, C be subsets of X, consider the following statements:1) A ⊂ C ⇒ (A ∩ B) ⊂ (C ∩ B), (A ∪ B) ⊂ (C ∪ B)2) (A ∩ B) ⊂ (C ∪ B) for all sets B ⇒ A ⊂ C3) (A ∪ B) ⊂ (C ∪ B) for all sets B ⇒ A ⊂ CWhich of the above statements is/are correct? |
| A. | 1 and 2 only |
| B. | 2 and 3 only |
| C. | 1 and 3 only |
| D. | 1, 2 and 3 |
| Answer» D. 1, 2 and 3 | |
| 40. |
If 0 < a < 1, the value of log10 a is negative. This is justified by |
| A. | Negative power of 10 is less than 1 |
| B. | Negative power of 10 is between 0 and 1 |
| C. | Negative power of 10 is positive |
| D. | Negative power of 10 is negative |
| Answer» C. Negative power of 10 is positive | |
| 41. |
A function f: A → R is defined by the equation f(x) = x2 – 4x + 5 where A = (1, 4). What is the range of the function? |
| A. | (2, 5) |
| B. | (1, 5) |
| C. | [1, 5) |
| D. | [1, 5] |
| Answer» D. [1, 5] | |
| 42. |
If \({\rm{f}}\left( {\rm{x}} \right) = {\log _{\rm{e}}}\left( {\frac{{1 + {\rm{x}}}}{{1 - {\rm{x}}}}} \right),{\rm{\;g}}\left( {\rm{x}} \right) = \frac{{3{\rm{x}} + {{\rm{x}}^3}}}{{1 + 3{{\rm{x}}^2}}}\) and g ∘ f(t) = g (f (t)), then what is g ∘ \({\rm{f}}\left( {\frac{{{\rm{e}} - 1}}{{{\rm{e}} + 1}}} \right)\) equal to? |
| A. | 2 |
| B. | 1 |
| C. | 0 |
| D. | 1/2 |
| Answer» C. 0 | |
| 43. |
If \({\rm{f}}\left( {\rm{x}} \right) = \left\{ {\begin{array}{*{20}{c}}{\frac{{{\rm{sin}}\left( {{\rm{p}} + 1} \right){\rm{x}} + {\rm{sinx}}}}{{\rm{x}}},}&{{\rm{x}} < 0}\\{q,}&{x = 0}\\{\frac{{\sqrt {{\rm{x}} + {{\rm{x}}^2}} - \sqrt {\rm{x}} }}{{{{\rm{x}}^{3/2}}}},}&{x > 0}\end{array}} \right.\)is continuous at x = 0, then the ordered pair (p, q) is equal to: |
| A. | \(\left( { - \frac{3}{2}, - \frac{1}{2}} \right)\) |
| B. | \(\left( { - \frac{1}{2},\frac{3}{2}} \right)\) |
| C. | \(\left( { - \frac{3}{2},\frac{1}{2}} \right)\) |
| D. | \(\left( {\frac{5}{2},\frac{1}{2}} \right)\) |
| Answer» D. \(\left( {\frac{5}{2},\frac{1}{2}} \right)\) | |
| 44. |
If A, B and C are subsets of a given set, then which one of the following relations is not correct? |
| A. | A∪ (A∩B) = A∪B |
| B. | A∩ (A∪B) = A |
| C. | (A∩B) ∪C = (A∪C) ∩ (B∪C) |
| D. | (A∪B) ∩C = (A∩C) ∪ (B∩C) |
| Answer» B. A∩ (A∪B) = A | |
| 45. |
Find the value of the log345 – log310 + log32 |
| A. | 1 |
| B. | 0 |
| C. | 3 |
| D. | 2 |
| Answer» E. | |
| 46. |
How many digits are there in (54)10? (Given that log102 = 0.301 and log103 = 0.477) |
| A. | 16 |
| B. | 18 |
| C. | 19 |
| D. | 27 |
| Answer» C. 19 | |
| 47. |
Consider the following statements for the two non-empty sets A and B:1) (A ∩ B) ∪ (A ∩ B̅) ∪ (A̅ ∩ B) = A ∪ B2) (A ∪ (A̅ ∩ B̅)) = A ∪ BWhich of the above statements is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» B. 2 only | |
| 48. |
A function f defined by f(x) = In \(\left( {\sqrt {{x^2} + 1} - x} \right)\) is |
| A. | an even function |
| B. | an odd function |
| C. | Both even and odd function |
| D. | Neither even nor odd function |
| Answer» C. Both even and odd function | |
| 49. |
If f(x) = 2x - x2, then what is the value of f(x + 2) + f(x - 2) when x = 0? |
| A. | -8 |
| B. | -4 |
| C. | 8 |
| D. | 4 |
| Answer» B. -4 | |
| 50. |
Let S = {2, 4, 6, 8, ______ 20}.What is the maximum number of subsets does S have? |
| A. | 10 |
| B. | 20 |
| C. | 512 |
| D. | 1024 |
| Answer» E. | |