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A bag contains 5 red, 6 white and 7 black balls. Two balls are drawn at random.
What is the probability that both balls are red or both are black?

Let $A$ be a vector parallel to line of intersection of planes $P_1:x=0$ and $P_2:x-y-z=0$ through origin. The acute angle between $A$ and $2\hat{i}+\hat{j}-2\hat{k}$ is

Integrate the following functions.
$\int e^{(2x+3)}dx$

The probability that a bulb produced by a factory will fuse after 150 days of used is 0.05. Find the probability that out of 5 such bulbs
(i) none

(ii) not more than one

(iii) more than one

(iv) atleast one will fuse after 150 days of use

If $f:Q\to Q$ is defined as $f\left(x\right)=x^2$, then $f^{-1}\left(9\right)$ is equal to

If $a_1$,$a_2$, $a_3$($a_1>0)$ are three successive terms of a G.P. with common ratio r, the value of r for which $a_3>4a_2-3a_1$ holds is given by

In a single throw of three dice, find the probability of sett ing a total of 17 or 18.

Choose the correct answer.

$\text{The value of}{\int }_0^{1}ta{n}^{-1}\left(\frac{2x-1}{1+x-x^2}\right)dxis\left(a\right)1\left(b\right)zero\left(c\right)-1\left(d\right)\frac{\pi }{4}$

If x satisfies $\left(x-1\right|+\left(x-2\right|+\left(x-3\right|\ge 6$, then

Five cards are drawn successively with replacement from well- shuffled deck of 52 cards. What is the probability that

(ii) only 3 cards are spades?

Hi Sir/Mam

If x + y = 4

Find the value of x^{​​​​​​3} - 64 + y^{​​​​​​3}

Pls help me solve this question

Thnx

The equation of the image of the circle $x^2+y^2-6x-4y=0$ in the bisector of $2^{\text{nd}}$ and $4^{\text{th}}$ quadrant is

$(13\times 9)-17=$

The total number of ways of selecting two number from the set $\{1,2,3,4,....,3n\}$, so that their sum is divisible by $3$, is equal to

$\underset{x\to 0}{lim}\frac{1-cosx}{x^2}is-------------$

A hyperbola is given as $x^2.se{c}^2\alpha -y^2.cose{c}^2\alpha =1$

What's the eccentricty of the hyperbola?

Prove that tan1 is greater than tan–¹π/4

Let $|a|=3$ and $|b|=4.$ The value of $\mu$ for which the vectors $a+\mu b$ and $a-\mu b$ will be perpendicular is

Solve : 31x + 23y = 39 And 23x + 31y = 15

If roots of the equation $a{x}^3+b{x}^2+cx+d=0$ remain unchanged by increasing each coefficient by one unit, then

Which of the following statement(s) is/are correct?

A and B take 30 days to finish a work, B and C take 24 days to finish that particular work, C and A take 20 days to finish the same work. All of them can finish the work in 10 days and If B and C leave the job, then how many days does A take to finish the same work?

The value of $\sqrt{2}\int \frac{\sin xdx}{\sin (x-\frac{\pi }{4})}$ is

A committee of 5 is to be formed from a group of 10 people consisting of 4 single men, 4 single women and a married couple. The committee is to consist of a chairman, who must be a single man , two other men, and two women.
(i) Find total number of committees formed.
(ii) How many of these would include the married couple ?

Column – 1 : represent different words
Column – 2 : represent number ways of selecting five letters from the word in column – 1
Column – 3 : represent total number of possible words with or without meaning, using all the alphabets of word in such that all the vowels are together.
$\begin{array}{ccc}Column1& Column2& Column3\\ \left(I\right)INDEPENDENT& \left(i\right)41& \left(p\right){24.}^8{C}_6{.}^6{C}_3{.}^3{C}_2{.}^3{C}_2\\ \left(II\right)INSTITUTE& \left(ii\right)60& \left(Q\right){24.}^8{C}_5{.}^5{C}_3\\ \left(III\right)CURRICULUM& \left(iii\right)72& \left(R\right){12.}^7{C}_3{.}^4{C}_3{.}^3{C}_2\\ \left(IV\right)MATHEMATICS& \left(iv\right)179& \left(S\right){24.}^6{C}_3{.}^3{C}_2\end{array}$
Which of the following options is the only CORRECT combination?

If two sets $A$ and $B$ are such that $n\left(A\right)=20$, $n(A\cap B)=4$, and $n(A\cup B)=42$, then

If $2$ and $3$ are the lengths of the segments of any focal chord of a parabola $y^2=4ax$ made by the axis of the parabola, then the length of the latus rectum is

Find the value of x if ${|x+1|}^2$ - 5| $|x+1|$ + 6 = 0

The value of $i^{57}+\frac{1}{i^{125}}$ is :

Let I (n)=2cos n x, $nϵN$, then I(1)I(n+1)-I(n)=___

If f(x) = x + tan x and f is inverse of g, then g’(x) is equal to

If $A=\{\alpha ,\beta ,\gamma \},B=\{1,2,3,4\}$, then the number of elements in set $A\times B\times B$ is

If $a{x}^3+b{y}^3+c{x}^{2}y+dx{y}^2=0$ represents three distinct straight lines such that each line bisects the angle between the other two, then which of the following is (are) CORRECT?

The general solution of $\frac{dy}{dx}=\frac{1-3y-3x}{1+x+y}$ is
(where ${}^{\prime }{c}^{\prime }$ is constant of integration)

While doing an experiment in chemistry lab, Komal found that a substance loses its moisture at a rate proportional to the moisture content. If the same substance loses half of its moisture during the first hour, when will it lose 99% ?

Sin5x-Sinx expressed as a product is

If U = {1, 2, 3, .. ,15}, A = {2, 4}, B = {3, 4, 6, 10, 12, 15}, then (A U C)^c is:

The probability that a person is not a swimmer is 0.3 the probability that out of 5 persons 4 are swimmers is