IISER IAT Question Bank

1620 IAT-pattern MCQs across Physics, Chemistry, Mathematics and Biology. Search by keyword or filter by subject, chapter, topic and year, then reveal the answer and explanation.

1620 questions found. Year tags appear only on verified past-paper questions; untagged questions are Prepkunj practice questions on the IAT pattern, not official IAT papers.

MathematicsVectors and Three Dimensional GeometryDot ProductPracticeeasy
If a · b = 0 and neither vector is zero, then a and b are:
- A. Parallel
- B. Perpendicular
- C. Equal
- D. Collinear
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MathematicsVectors and Three Dimensional GeometryMagnitudePracticeeasy
The magnitude of î + 2ĵ + 2k̂ is:
- A. 3
- B. 5
- C. √5
- D. 9
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MathematicsVectors and Three Dimensional GeometryCross ProductPracticeeasy
a × a equals:
- A. |a|²
- B. 0 (zero vector)
- C. 2a
- D. 1
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MathematicsVectors and Three Dimensional GeometryDirection CosinesPracticeeasy
Direction cosines satisfy:
- A. l + m + n = 1
- B. l² + m² + n² = 1
- C. lmn = 1
- D. l² + m² + n² = 0
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MathematicsVectors and Three Dimensional GeometryTriple ProductPracticeeasy
The scalar triple product [a b c] equals zero when the vectors are:
- A. Perpendicular
- B. Coplanar
- C. Unit vectors
- D. Equal in magnitude
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MathematicsVectors and Three Dimensional GeometryCross ProductPracticeeasy
The area of a parallelogram with adjacent sides a and b is:
- A. a · b
- B. |a × b|
- C. ½|a × b|
- D. |a||b|
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MathematicsVectors and Three Dimensional GeometryLinesPracticeeasy
The vector equation of a line through a with direction b is:
- A. r = a + λb
- B. r · b = a
- C. r × a = b
- D. r = λ(a + b)
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MathematicsVectors and Three Dimensional GeometryPlanesPracticeeasy
The normal vector to the plane 2x − y + 3z = 5 is:
- A. (2, −1, 3)
- B. (5, 0, 0)
- C. (1, 1, 1)
- D. (−2, 1, 3)
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MathematicsVectors and Three Dimensional GeometryDot ProductPracticeeasy
î · ĵ equals:
- A. 1
- B. 0
- C. k̂
- D. −1
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MathematicsVectors and Three Dimensional GeometryCross ProductPracticeeasy
î × ĵ equals:
- A. k̂
- B. −k̂
- C. 0
- D. 1
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MathematicsVectors and Three Dimensional GeometryDot ProductPracticemoderate
The angle between a = î + ĵ and b = ĵ + k̂ is:
- A. 30°
- B. 45°
- C. 60°
- D. 90°
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MathematicsVectors and Three Dimensional GeometryProjectionPracticemoderate
The projection of a = 2î + 3ĵ + 2k̂ on b = î + 2ĵ + k̂ is:
- A. 10/√6
- B. 5/√6
- C. 10/6
- D. √6
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MathematicsVectors and Three Dimensional GeometryCross ProductPracticemoderate
The area of the triangle with vertices A(1,1,1), B(1,2,3), C(2,3,1) is:
- A. ½√21
- B. √21
- C. ½√14
- D. √14
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MathematicsVectors and Three Dimensional GeometryTriple ProductPracticemoderate
The volume of the parallelepiped with edges î, ĵ + k̂ and î + ĵ + k̂ is:
- A. 0
- B. 1
- C. 2
- D. 3
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MathematicsVectors and Three Dimensional GeometryPlanesPracticemoderate
The distance of the point (1, 2, 3) from the plane x + y + z = 3 is:
- A. √3
- B. 3/√3
- C. 1/√3
- D. 3
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MathematicsVectors and Three Dimensional GeometryLinesPracticemoderate
Lines r = î + λ(2î + ĵ) and r = 2ĵ + μ(4î + 2ĵ) are:
- A. Intersecting
- B. Parallel
- C. Perpendicular
- D. Skew and perpendicular
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MathematicsVectors and Three Dimensional GeometryLagrange IdentityPracticemoderate
If |a| = 3, |b| = 4 and |a × b| = 6, then a · b equals:
- A. ±6√3
- B. ±12
- C. ±6
- D. 0
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MathematicsVectors and Three Dimensional GeometryPlanesPracticemoderate
The angle between the planes 2x − y + z = 4 and x + y + 2z = 3 is:
- A. 30°
- B. 45°
- C. 60°
- D. 90°
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MathematicsVectors and Three Dimensional GeometryVector Triple ProductPracticemoderate
a × (b × c) equals:
- A. (a·b)c − (a·c)b
- B. (a·c)b − (a·b)c
- C. (a×b)·c
- D. (b·c)a
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MathematicsVectors and Three Dimensional GeometrySection FormulaPracticemoderate
The point dividing the join of a and b in the ratio 2:1 internally is:
- A. (2b + a)/3
- B. (2a + b)/3
- C. (b − a)/3
- D. (a + b)/2
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MathematicsVectors and Three Dimensional GeometrySkew LinesPracticeexam
The shortest distance between the lines r = î + λ(2î − ĵ + k̂) and r = 2î + ĵ + μ(3î − 5ĵ + 2k̂) is:
- A. 10/√59
- B. 1/√59
- C. 10/59
- D. √59
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MathematicsVectors and Three Dimensional GeometryDot ProductPracticeexam
If a, b, c are unit vectors with a + b + c = 0, then a·b + b·c + c·a is:
- A. 0
- B. −3/2
- C. 3/2
- D. −1
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MathematicsVectors and Three Dimensional GeometryDirection CosinesPracticeexam
A line makes equal angles with all three coordinate axes. Each direction cosine is:
- A. 1/3
- B. ±1/√3
- C. 1/√2
- D. ±1
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MathematicsVectors and Three Dimensional GeometryPlanesPracticeexam
The plane through (1,0,0), (0,1,0) and (0,0,1) is:
- A. x + y + z = 1
- B. x + y + z = 0
- C. x − y + z = 1
- D. xyz = 1
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MathematicsVectors and Three Dimensional GeometryLine and PlanePracticeexam
The line r = a + λb lies in the plane r · n = q if:
- A. b · n = 0 only
- B. a · n = q only
- C. b · n = 0 and a · n = q
- D. b × n = 0
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