Aspire Faculty ID #3634 · Topic: NIMCET 2012 · Just now
NIMCET 2012

A determinant is chosen at random from the set of all determinants of matrices of order 2 with elements 0 and 1 only. The probability that the determinant chosen is non-zero is:

Solution

Total $2\times2$ matrices with entries $0$ or $1$: $2^4 = 16$ 
Determinant: $ad - bc$ 
Non-zero determinant occurs in two cases. 

Case 1: $ad = 1$ and $bc = 0$ 
$a = 1, d = 1$ $(b,c)$ can be $(0,0), (0,1), (1,0)$ 
→ 3 matrices 

Case 2: $bc = 1$ and $ad = 0$ 
$b = 1,c = 1$ $(a,d)$ can be $(0,0), (0,1), (1,0)$ 
→ 3 matrices 
Total non-zero determinants = $3 + 3 = 6$
$P(\text{non-zero determinants})=\dfrac{6}{16}=\dfrac{3}{8}$
← Previous Next →

Previous 10 Questions — NIMCET 2012

Nearest first
1
The value of integral $\displaystyle \int_{0}^{\pi/2} \log \tan x dx$ is
Topic: NIMCET 2012
 2
If $ I_1 = \displaystyle \int_{0}^{1} 2^{x^2},dx,\quad I_2 = \displaystyle \int_{0}^{1} 2^{x^3},dx,\quad I_3 = \display…
Topic: NIMCET 2012
 3
The point on the curve $y = 6x - x^2$ where the tangent is parallel to the x-axis is:
Topic: NIMCET 2012
 4
The value of $\displaystyle \lim_{n\to\infty} \frac{\pi}{n}\left[\sin\frac{\pi}{n}+\sin\frac{2\pi}{n}+\cdots+\sin\frac{…
Topic: NIMCET 2012
 5
Normal to the curve $y = x^3 - 3x + 2$ at the point $(2,4)$ is:
Topic: NIMCET 2012
 6
The value of $\cot^{-1}(21) + \cot^{-1}(13) + \cot^{-1}(-8)$ is:
Topic: NIMCET 2012
 7
The sum $^{20}C_8 + ^{20}C_9 + ^{21}C_{10} + ^{22}C_{11} - ^{23}C_{11}$
Topic: NIMCET 2012
 8
The number of values of $k$ for which the system of equations $(k+1)x + 8y = 4k$ and $kx + (k+3)y = 3k-1$ has infinit…
Topic: NIMCET 2012
 9
If $H$ is the harmonic mean between $P$ and $Q$, then $\dfrac{H}{P} + \dfrac{H}{Q}$ is
Topic: NIMCET 2012

Next 10 Questions — NIMCET 2012

Ascending by ID
1
If $\sin^2 x = 1 - \sin x$, then $\cos^4 x + \cos^2 x$ is equal to:
Topic: NIMCET 2012
 2
The equation of the plane passing through the point $(1,2,3)$ and having the normal vector $N = 3\mathbf{i} - \mathbf{j…
Topic: NIMCET 2012
 3
The value of $\displaystyle \int_{0}^{\sin^2 x} \sin^{-1}\sqrt{t} dt + \int_{0}^{\cos^2 x} \cos^{-1}\sqrt{t} dt$ is:
Topic: NIMCET 2012
 4
Coefficients a, b, c of $ax^2 + bx + c = 0$ are chosen by tossing 3 fair coins. Head means 1, Tail means 2. Find the pr…
Topic: NIMCET 2012
 5
In a class of 100 students, 55 passed in Mathematics and 67 passed in Physics.The number of students who passed in Phys…
Topic: NIMCET 2012
 6
If $(4,-3)$ and $(-9,7)$ are two vertices of a triangle and $(1,4)$ is its centroid, find the area of the triangle.
Topic: NIMCET 2012
 7
The equation of ellipse with major axis along the x–axis and passes through the point $(4,3)$ and $(-1,4)$.
Topic: NIMCET 2012
 8
If the circles $ x^2 + y^2 + 2x + 2ky + 6 = 0$ and $x^2 + y^2 + 2ky + k = 0$ intersect orthogonally, then $k$ is:
Topic: NIMCET 2012
 9
Focus of the parabola $x^2 + y^2 - 2xy - 4(x + y - 1) = 0$ is:
Topic: NIMCET 2012
 10
If $\mathbf{a},\; \mathbf{b},\; \mathbf{c}$ are unit vectors such that $\mathbf{a} + \mathbf{b} + \mathbf{c} = 0$, …
Topic: NIMCET 2012
Ask Your Question or Put Your Review.

loading...