Algebra PYQ — Page 39

The probability that the study time of students is exactly 2 hours

If $f:\mathbb{R} \to [-5, \infty)$ is defined as $f(x) = x^2 - 5$, then the function f is A. one-one B. many-one C. onto D. into Which of the above statements are true? Choose the correct answer from the options given below:

A die is tossed four times. The probability of getting an odd number at least once, is

The minimum cost of the mixture is-

The area of rectangular field is:

If the points $(2, -3)$, $(\lambda, -1)$ and $(0, 4)$ are collinear, then the value of $\lambda$ is :

In Binomial distribution with parameters $n = 12$ and $p = \frac{1}{3}$, value of $E(X^2) + E(X)$ is :

A letter is expected to come either from city 'SURAT' or from city 'RAMPUR' through post office. If on the way, envelope containing the letter is damaged and only two consecutive alphabets RA are visible on it, then the probability that letter comes from the city 'SURAT' is :

The 10th term of AP: 3, 7, 11, 15, ... is

Match List I with List II: Given that A and B are invertible matrices of size $3 \times 3$ | List I | List II | |---|---| | A. $\lvert AB \rvert$ | I. $\frac{1}{\lvert A \rvert}$ | | B. $\lvert \operatorname{Adj} A \rvert$ | II. $\lvert A \rvert \lvert B \rvert$ | | C. $\lvert A^{-1} \rvert$ | III. $B^{-1} \cdot A^{-1}$ | | D. $(AB)^{-1}$ | IV. $\lvert A \rvert^2$ | Choose the correct answer from the options given below:

The value of the expression $\frac{x^2 + y^2}{x - y}$ is:

Which of the following figures shows a bijective function from set $X_1$ to set $X_2$ :  Choose the correct answer from the options given below :

If $\theta$ is the acute angle between two unit vectors $\vec{a}$ and $\vec{b}$, then $\cos\frac{\theta}{2} =$

When the doctor arrives late, what is the probability that he comes by other means of transport?

Which of the following statements are true? (A) $f:\mathbb{R} \to \mathbb{R}$ given by $f(x) = 3x$ is one-one onto. (B) $f:\mathbb{R} \to \mathbb{R}$ given by $f(x) = x^4$ is one-one and onto. (C) $f:\mathbb{Z} \to \mathbb{Z}$ given by $f(x) = x^2$ is neither one-one nor onto. (D) $f:\mathbb{R} \to \mathbb{R}$ given by $f(x) = |x|$ is neither one-one nor onto. (Where $\mathbb{R}$ is the set of all real numbers and $\mathbb{Z}$ is the set of all integers) Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 1 & -1 & 1 \\ 1 & -2 & -2 \\ 2 & 1 & 3 \end{bmatrix}$ and square matrix $B$ satisfy $AB = 8I$, then the value of $|B|$ is:

Let L be the set of all lines in a plane and R be the relation in L defined as $R = \{(l_1, l_2) : l_1 \text{ is perpendicular to } l_2, \text{ where } l_1, l_2 \in L\}$. Choose the correct answer :

If $\begin{bmatrix} 2x-1 & -3 & 6 \\ 3 & 3y-2 & 4 \\ -6 & -4 & 4z-3 \end{bmatrix}$ is skew symmetric matrix, then $xyz$ is equal to

The set of all values of $\alpha$ for which the system of linear equations $x + y + z = 1$ $x + 2y + 4z = \alpha$ $x + 4y + 10z = \alpha^2$ is consistent, is

Bag I contains 3 red and 4 black balls while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. The probability that it was drawn from Bag II is :

The value $x$ is:

Let the matrix $A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}$ and $AB = \begin{bmatrix} 5 & 6 & 7 \\ 8 & 9 & 10 \end{bmatrix}$ then order of B is :

Area of the rectangular plot is:

If $A = \begin{bmatrix} 6 & -8 \\ -2 & 5 \end{bmatrix}$ and $A^2 - 10A = C$ then C is equal to