Major Competitive Exams

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Q. For the reaction: A(g) + B(g) ⇌ C(g) + D(g), if the volume of the container is decreased, what will be the effect on the equilibrium? (2023)
  • A. Shift to the left
  • B. Shift to the right
  • C. No effect
  • D. Increase the concentration of A
Q. For the reaction: A(g) ⇌ B(g) + C(g), if the concentration of A is increased, what will happen to the equilibrium position?
  • A. Shift to the left
  • B. Shift to the right
  • C. No change
  • D. Depends on temperature
Q. For the set E = {1, 2, 3, 4}, how many subsets contain the element 1?
  • A. 4
  • B. 8
  • C. 12
  • D. 16
Q. For the set E = {1, 2, 3, 4}, how many subsets have exactly 2 elements?
  • A. 4
  • B. 6
  • C. 8
  • D. 10
Q. For the set F = {a, b, c}, how many subsets have exactly 2 elements?
  • A. 1
  • B. 2
  • C. 3
  • D. 4
Q. For the vectors A = (1, 0, 0) and B = (0, 1, 0), what is the scalar product A · B?
  • A. 0
  • B. 1
  • C. 2
  • D. 3
Q. For vectors A = (2, 3) and B = (4, 5), find the scalar product A · B.
  • A. 23
  • B. 22
  • C. 21
  • D. 20
Q. For vectors A = (3, -2, 1) and B = (1, 4, -2), find A · B.
  • A. -1
  • B. 0
  • C. 1
  • D. 2
Q. For vectors A = 2i + 3j and B = 5i + 6j, what is A · B?
  • A. 28
  • B. 30
  • C. 32
  • D. 26
Q. For vectors A = 2i + j and B = 3i + 4j, what is the scalar product A · B?
  • A. 14
  • B. 10
  • C. 12
  • D. 8
Q. For vectors A = 4i + 3j and B = 3i - 4j, find A · B.
  • A. -6
  • B. 0
  • C. 6
  • D. 12
Q. For vectors A = 6i + 8j and B = 2i + 3j, find A · B.
  • A. 42
  • B. 48
  • C. 36
  • D. 30
Q. For what value of b is the function f(x) = { x^3 - 3x + b, x < 1; 2x + 1, x >= 1 continuous at x = 1?
  • A. 0
  • B. 1
  • C. 2
  • D. 3
Q. For which of the following diatomic molecules is the bond order equal to 2?
  • A. C2
  • B. N2
  • C. O2
  • D. F2
Q. For which of the following molecules is the bond order equal to 0?
  • A. He2
  • B. H2
  • C. Li2
  • D. Be2
Q. For which of the following molecules is the molecular orbital diagram similar to that of O2?
  • A. N2
  • B. F2
  • C. C2
  • D. Ne2
Q. For which of the following pairs of molecules is the bond order the same?
  • A. N2 and C2
  • B. O2 and F2
  • C. B2 and C2
  • D. N2 and O2
Q. For which value of a is the function f(x) = x^2 + ax + 1 differentiable at x = -1?
  • A. -1
  • B. 0
  • C. 1
  • D. 2
Q. For which value of a is the function f(x) = x^2 + ax + 1 differentiable everywhere?
  • A. -1
  • B. 0
  • C. 1
  • D. 2
Q. For which value of a is the function f(x) = x^2 - ax + 2 differentiable at x = 1?
  • A. 0
  • B. 1
  • C. 2
  • D. 3
Q. For which value of a is the function f(x) = x^2 - ax + 4 differentiable at x = 2?
  • A. 0
  • B. 2
  • C. 4
  • D. 6
Q. For which value of a is the function f(x) = x^3 - 3ax + 2 differentiable at x = 1?
  • A. 0
  • B. 1
  • C. 2
  • D. 3
Q. For which value of a is the function f(x) = x^3 - 3ax^2 + 3a^2x + 1 differentiable at x = 1?
  • A. 0
  • B. 1
  • C. 2
  • D. 3
Q. For which value of a is the function f(x) = { 2x + a, x < 0; x^2 + 1, x >= 0 continuous at x = 0?
  • A. -1
  • B. 0
  • C. 1
  • D. 2
Q. For which value of a is the function f(x) = { 3x + a, x < 2; 4x - 1, x >= 2 continuous at x = 2?
  • A. -1
  • B. 0
  • C. 1
  • D. 2
Q. For which value of a is the function f(x) = { ax + 1, x < 0; 2, x = 0; 3x - 1, x > 0 } continuous at x = 0?
  • A. -1
  • B. 0
  • C. 1
  • D. 2
Q. For which value of a is the function f(x) = { ax + 1, x < 0; 2x + a, x >= 0 } continuous at x = 0?
  • A. -1
  • B. 0
  • C. 1
  • D. 2
Q. For which value of a is the function f(x) = { ax + 2, x < 1; 3, x >= 1 } continuous at x = 1?
  • A. 1
  • B. 2
  • C. 3
  • D. 4
Q. For which value of a is the function f(x) = { x^2 + a, x < 1; 3, x >= 1 } continuous at x = 1?
  • A. 1
  • B. 2
  • C. 3
  • D. 0
Q. For which value of a is the function f(x) = { x^2 - a, x < 0; 2x + 1, x >= 0 } continuous at x = 0?
  • A. -1
  • B. 0
  • C. 1
  • D. 2
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