Mathematics - Class 12 Mock Test 3

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Question 1 of 10

1. Find the minor of the element 2 in the determinant Δ=\(\begin{vmatrix}1&9\\2&3\end{vmatrix}\)?

Question 1 of 10

Question 2 of 10

2. Which of the following conditions holds true for a system of equations to be consistent?

It should have exactly one solution

It should have exactly two solutions

It should have one or more solutions

It should have no solutions

Question 2 of 10

Question 3 of 10

3. What is value of \(\frac{dy}{dx}\) if x-y = 1?

-1

Question 3 of 10

Question 4 of 10

4. Find the derivative of f(x) = sin(x²).

-2xcos(x²)

-2xsin(x²)

-sin(x²)

2xcos(x²)

Question 4 of 10

Question 5 of 10

5. If f(x) = \(\begin{vmatrix}1 & a & bc \\1 & b & ca \\1 & c & ab \end {vmatrix}\) = \(\begin{vmatrix}1 & a & a^2 \\1 & b & b^2 \\1 & c & c^2 \end {vmatrix}\) then which one among the following is correct?

(a – b)(b – c)(c – a)

a, c, b are in G.P

b, c, a are in G.P

a, b, c are in G.P

Question 5 of 10

Question 6 of 10

6. Differentiate 3e^3x³ w.r.t x.

27x^-2 e^3x³

27x² e^3x³

-27x^-2 e^3x³

-27x² e^3x³

Question 6 of 10

Question 7 of 10

7. What is the area of the triangle whose vertices are (0,1), (0,2), (1,5)?

2 sq.units

\(\frac{1}{2}\) sq.units

\(\frac{1}{3}\) sq.units

1 sq.unit

Question 7 of 10

Question 8 of 10

8. Find the value of k if the area is \(\frac{7}{2}\) sq. units and the vertices are (1,2), (3,5), (k,0).

-\(\frac{8}{5}\)

-\(\frac{7}{3}\)

-\(\frac{8}{3}\)

\(\frac{8}{3}\)

Question 8 of 10

Question 9 of 10

9. Find the value of k for which (1,2), (3,0), (2,k) are collinear.

-1

Question 9 of 10

Question 10 of 10

10. Which of the following is the formula for calculating the inverse of the matrix?

\(\frac{1}{|A|}\) adj A

\(\frac{1}{|2A|}\) adj A

\(\frac{2}{|A|}\) adj A

\(\frac{-1}{|A|}\) adj A

Question 10 of 10