CBSE Class 12 Mathematics Matrices and Determinants MCQs Set 02

Question: Area of the triangle whose vertices are (a, b + c), (b, c + a) and (c, a + b), is
(a) 2 sq units
(b) 3 sq units
(c) 0 sq unit
(d) None of these
Answer: c

Question: Given : 2x – y – 4z = 2, x – 2y – z = – 4, x + y + λz = 4, then the value of λ such that the given system of equation has NO solution, is
(a) 3
(b) 1
(c) 0
(d) – 3
Answer: d

Question: In how many ways, the determinant of order 3 can be expanded?
(a) 5
(b) 4
(c) 3
(d) 6
Answer: d

Question: If the area of a triangle ABC, with vertices A(1, 3), B(0, 0) and C(k, 0) is 3 sq. units, then the value of k is
(a) 2
(b) 3
(c) 4
(d) 5
Answer: a

Question: The system of linear equations : x + y + z = 0, 2x + y – z = 0, 3x + 2y = 0 has :
(a) no solution
(b) a unique solution
(c) an infinitely many solution
(d) None of these
Answer: c

ASSERTION – REASON TYPE QUESTIONS

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Question: Assertion: The points A (a, b + c), B (b, c + a) and C (c, a + b) are collinear.
Reason: Area of a triangle with three collinear points is zero.
Answer: a

Question: Let A be a 2 × 2 matrix
Assertion: adj (adj A) = A
Reason: |adj A |= |A|
Answer: b

Question: Assertion: The value of determinant of a matrix and the value of determinant of its transpose are equal.
Reason: The value of determinant remains unchanged if its rows and columns are interchanged.
Answer: a
 

Case Based Questions

A company produces three products every day. Their production on certain day is 45 tons. It is found that the production of third product exceeds the production of first product by 8 tons while the total production of first and third product is twice the production of second product.

Using the concepts of matrices and determinants, answer the following questions:

Question: If x, y and z respectively denotes the quantity (in tons) of first, second and third product produced, then which of the following is true?
(a) x + y + z = 45
(b) x + 8 = z
(c) x – 2y + z = 0
(d) All of these
Answer: d

Question: Which of the following is not true?
(a) |A| = |A′|
(b) (A′)^–1 = (A^–1)′
(c) A is skew-symmetric matrix of order 3 then |A| = 0
(d) |AB| = |A| + |B|
Answer: d

Question: x : y : z is equal to
(a) 12 : 13 : 20
(b) 11 : 15 : 19
(a) 15 : 19 : 11
(b) 13 : 12 : 20
Answer: b

Question: Which of the following is not true in the given determinant of A, where A = [a_q]_3×3?
(a) Order of minor is less than order of the determinant A.
(b) Minor of an element can never be equal to cofactor of the same element.
(c) Value of a determinant is obtained by multiplying elements of a row of column by corresponding cofactors.
(d) Order of minors and cofactors of same elements of A is same.
Answer: b

Each triangular face of the Pyramid of Peace in Kazakhstan is made up of 25 smaller equilateral triangles as shown in the figure.
Using the above information and concept of determinants, answer the following questions

Question: If the vertices of one of the smaller equilateral triangle are (0, 0), (3, √3) and (3,− √3), then the area of such triangle is
(a) √3 sq. units
(b) 2√3sq. units
(c) 3√3 sq. units
(d) none of these
Answer: c

Question: If (2, 4) and (2, 6) are two vertices of a smaller equilateral triangle, then the third vertex will lie on the line represented by
(a) x + y = 5
(b) x = 1 + √3
(c) x = 2 ± 3 √3
(d) 2x + y = 3
Answer: c

Question: The area of a face of the Pyramid is
(a) 25 √3 sq. units
(b) 50 √3 sq. units
(c) 75 √3 sq. units
(d) 35 √3 sq. units
Answer: c

Question: Let A(a, 0), B(0, b) and C(1, 1) be three points. If 1/a + 1/b, then the three points are
(a) vertices of an equilateral triangle
(b) vertices of a right angled triangle
(c) collinear
(d) vertices of an isosceles triangle
Answer: c

Question: The length of a altitude of a smaller equilateral triangle is
(a) 2 units
(b) 3 units
(c) √3 units
(d) 4 units
Answer: b
 

The upward speed v(t) of a rocket at time t is approximated by v(t) = at² + bt + c, 0 ≤ t ≤ 100, where a, b and c are constants. It has been found that the speed at times t = 3, t = 6 and t = 9 seconds are respectively 64, 133 and 208 miles per second.

Question: The value of a + c is
(a) 1
(b) 20
(c) 4/3
(d) none of these
Answer: c

Question: The value of b + c is
(a) 20
(b) 21
(c) 3/4
(d) 4/3
Answer: b

Question: The time at which the speed of rocket is 784 miles/sec. is
(a) 20 seconds
(b) 30 seconds
(c) 25 seconds
(d) 27 seconds
Answer: d

Question: The speed at time t = 15 seconds is
(a) 346 miles/sec.
(b) 356 miles/sec
(c) 366 miles/sec
(d) 376 miles/sec
Answer: d