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What is the range of $f\left(x\right)=\frac{1}{x^2+6x+6}$

What is the minimum value of p and q in the equation $x^3-p{x}^2+qx-8=0$ where p and q are positive real numbers and roots of the equation are real?

A takes 3 hours more than B in walking 30 km. If A starts jogging at a speed of twice his walking speed, he takes 2 hrs less than B. Find the speed of A.

A number is added to $2\frac{1}{2}$ and the sum is multiplied by $4\frac{1}{2}$. Then 3 is added to the product and the sum is divided by $1\frac{1}{5}$ which gives the quotient as 25. What is the number?

If a is an integer lying in $(-5,30]$, then probability that the graph of $y=x^2+2(a+4)x-5a+64$ is strictly above the x-axis is

The total number of students who visited Jodhpur is approximately what percent of the number of girls who visited Delhi?

$\text{If}x=\frac{1}{3}\text{is a solution of the equation}a{x}^2+(a-1)x+4=a,\text{find the value of a}$

A dishonest trader using a faulty balance makes a profit of 5% while buying as well as while selling his goods. His actual gain percent in the whole process amounts to,

If A (1, 2) and B (5, 6) are the coordinates of an equilateral triangle. Then what can we say about the abscissa of the third vertex?

Suppose there are $6$ pairs of different colored balls and $4$ balls are selected. If same colored ball is different and

$A$ denote the number of ways when no pair of same colored ball is selected,

$B$ denote the number of ways exactly one pair of same colored ball is selected,

$C$ denote the number of ways at least one pair of same colored ball is selected,

then

The number of common roots of the equations

$x^2$ – 7x + 10 = 0 and $x^2$ – 10x + 16 = 0 is

1. 240

If $x=\sqrt{2}-1(x-\frac{1}{x}{)}^3$ = ______

a, b, c, d and e are integers such that $1\le a<b<c<d<e$. If a, b, c, d and e are geometric progression and lcm (m, n) is the least common multiple of m and n, then maximum value of
$\frac{1}{lcm(a,b)}+\frac{1}{lcm(b,c)}+\frac{1}{lcm(c,d)}+\frac{1}{lcm(d,e)}$ is

A right triangle ABC circumscribes a circle of radius r. If AB and BC are of length 8 cm and 6 cm respectively, find the value of r?

What is the maximum value of the function f(x) = min (7 - 9x, 3x + 4) for 0 < x < 9?

The value of the assets distributed among Neeta, Seeta and Geeta was in the ratio of 1:2:3, while the gold coins were distributed among them in the ratio of 2:3:4. One child got all three flats and she did not get the house. One child, other than Geeta, got Rs. 30 lakh in bank deposits.
How many gold coins did the old woman have?

If the Organizers want to ensure that all participants travelling from S to T take the same time (travelling time and task time combined) regardless of the route they choose and the street from B to C is under repairs (and hence unusable), then a feasible set of task time (in hours) at junctions A, B, C, and D respectively to achieve this goal is:

A die is thrown twice and the sum of the numbers appearing is observed to be 9 What is the conditional probability that the number 4 has appeared atleast once ?

Anil has bought a new game, which is in the form of 6 concentric circles.The 6th circle has a radius of 6 and it has 6 openings. A ball is positioned on the circumference of the innermost circle and it finally exits from the circumference of the outermost circle. Thus, the ball starts travelling from the smallest circle 1 and leaves it at the point of opening on the normal to reach the next circle 2, then it moves in a similar manner to 3 and so on.The total number of different paths in which the ball can take to come out of the 6th circle is?

What are the last two digits of ${3844}^{47}$?

If the underlying principle is to be satisfied in such a way that the journey between any two cities can be performed using only direct (not-stop) flights, then the minimum number of direct flights to be scheduled is:

If three numbers in the ratio 3 : 2: 5 be such that the sum of their squares is 1862, the middle number will be

In the figure given below ABCD is a square and ΔPDC is isosceles with PD = PC. If the area of $\Delta$PDC is twice the area of the square, then find the ratio of the area of $\Delta$PDC that lies outside the square to the area of the square.

A, B and C are the sides of a right triangle where C is the hypotenuse. A circle of radius r touches the sides of the triangle prove that r is equal to $\frac{a+b-c}{2}$.

1. 525

In the oral healthcare market, Bolgate and Lipsudent are the market leaders. In the month of March, Bolgate and Lipsudent sold products worth Rs. x and Rs. 1.5x respectively. This value increased by 250% and 100% respectively for the month of April. Among the options given below, which graph depicts this data accurately?

Show that one and only one out of $n,n+1,n+2$ is divisible by $3$, where $n$ is any positive integer

What is the ratio of the average production of Company X in the period 1998 – 2000 to the average production of company Y in the same period?

Additional Information :

1. The minimum marks scored by the student in any subject is 40 % of the maximum marks of that subject.

2. The marks in no two subjects in a particular test or 2 tests in a particular subject is the same.