List of practice Questions

If x = -9 is a root of A = $\begin{vmatrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \\ \end{vmatrix}$ = 0, then other two root are

The values of $\alpha$ for which the system of equation x + y + z = 1, x + 2y + 4z = $\alpha$, x + 4y + 10z = $\alpha^2$ is consistent are given by

Let A=$\begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 &t \\ 4&7-t&-6 \\ \end{bmatrix}$, then the values of t for which inverse of A does not exist

If $\alpha \, and \, \beta$ are the roots of the equation ax+bx+c=0, then the value of $\alpha^{3} \, + \, \beta^{3}$ is

An equation of the plane passing through the line of intersection of the planes x + y + z = 6 and 2x + 3y + 4z + 5 = 0 and passing through (1, 1, 1) is

The length of the shortest distance between the lines $\vec{r}=3\hat{i}+5\hat{j}+7\hat{k}+\lambda(\hat{i}-2\hat{j}+\hat{k})$ and $\vec{r} = -\hat{i}-\hat{j}-\hat{k}+\mu (7\hat{i}-6\hat{j}+\hat{k})$ is

The particular integral of $\frac{d^2y}{dx^2}+2y=x^2$is

The value of the integral $\int\limits_{0}^{\frac{\pi}{2}} log \left(tan\,x\right)dx=$

How many asymmetric carbon atoms are present in : (i) $1,2$-dimethylcyclohexane, (ii) $3$-methylcyclopentene and (iii) $3$-methylcyclohexene ?

When glucose reacts with bromine water the main product is :

The probability of finding the electron in the orbital is :

In the reaction $CH_3CN + 2H \xrightarrow [SnCl_2] {HCl}X \xrightarrow {\text{boiling} \, H_2 O} Y, $ The term $Y$ is :

\(SO_2\) does not acts as :

The distance between the pair of parallel lines $ x^2 + 2xy + y^2 - 8ax - 8ay - 9a^2 = 0$ is :

Which of the following is called Berthelot�s salt ?

The molar volume of $CO_2$ is maximum at:

The crystal field splitting energy for octahedral $(\Delta_0)$ and tetrahedral $(\Delta_{t})$ complexes is related to :

An application was received by inward clerk in the afternoon of a week day. Next day, he forwarded it to the table of the senior clerk, who was on leave that day. The senior clerk put up the application to the desk officer next day in the evening. The desk officer studied the application and disposed off the matter on the same day, ie Friday. The application was received by the inward clerk on

In a queue of children, Kashish is fifth from the left and Mona is sixth from the right. When they interchange their places among themselves, Kashish becomes thirteenth from the left. Then, what will be Mona's position from the right?

If the numbers from 1 to 45 which are exactly divisible by 3 are arranged in ascending order, minimum number being on the top, then which number would come at the ninth place from the top?

Which letter should be the ninth letter to the left of the ninth letter from the right, if the first half of the alphabets of English are reversed?

In a family, a couple has a son and a daughter.The age of the father is three times that of hisdaughter and the age of the son is half of his mother.The wife is 9 years younger to her husbandand the brother is seven years older to his sister. What is the age of the mother?

A number of friends decided to go on a picnic and planned to spend Rs 96 on eatables. Four of them did not turn up. As a consequence, each of the remaining ones had to contribute Rs 4 extra. The number of those who attended the picnic was

Out of a total of 120 musicians in a club, \(5\%\) can play all the three instruments ––– guitar, violin and flute. It so happens that the number of musicians who can play any two and only two of the above instruments is 30. The number of musicians who can play the guitar alone is 40. What is the total number of those who can play violin alone or flute alone?