The area under the curve & lines: \[y = x^2\] \[x = 2\] \[x = 3\]is
If \[f(x) = x^2 +2\] \[g(x) = 2x-3\] are real functions than, (fog)(x) is:
The maximum value of \[{tan}^{-1}\frac{1+x}{1-x}\]
if \[ \vec{a} = 3\vec{i}-2\vec{j} +\vec{k} \] & \[ \vec{b} = 4\vec{i} +3\vec{j}+λ\vec{k}\] are orthogonal vectors than λ is
\(\lim_{{x \to 0}} \frac{1 – \cos(mx)}{1 – \cos(nx)} \) : Solve for limit x tends to 0
What is the general solution of following equation:
Solve: \(\int_0^{\frac{\pi}{4}} \sin^3(\theta) \, d\theta\)
If A = \( \begin{bmatrix} 1 & 2 & 3 \\ 3 & 4 & 5 \\ 5 & 6 & 7\end{bmatrix} \) and B = \( \begin{bmatrix} 1 & 1 & 1 \\ 2 & 2 & 2 \\ 3 & 3 & 3\end{bmatrix} \) then det(A+B) is
The sum of distances from origin to (0,5,5) and (5,8,6) is:
The product of the cofactor’s of 3 and -2 in the matrix \( \begin{bmatrix} 1 & 0 & -2 \\ 3 & -1 & 2 \\ 4 & 5 & 6 \end{bmatrix} \)
If two unbiased six faced dice are thrown, the probability that the sum of the numbers on both the faces turned up, is a prime number greater than 5 is:
Solve the equation: \(\sqrt{2+\sqrt{2(1+\cos(4x))}}\)
y = \({u^2}+log u\) & u = \(\exp(x)\) , find \(\frac{dy}{dx}\)
If a, b, c, d are the position vectors of the points A, B, C, D, respectively, such that no three of them are collinear and a + c – b + d, then the quadrilateral ABCD is:
If * is binary operation defined as a*b -(ab/3), than identity element with respect to binary operation is
The solution of the system of equations: \[ \begin{align*} 3x + 2y – 6z &= 1 \\ 2x – 3y + 3z &= -1 \\ x – 4y + z &= -6 \end{align*} \] is
If A, B and C are angles of a triangle, then which of the following is correct?
Given that a = 3i-8j+k & b = 4i+3j-λk . If a+b = 7i-5j-3k , than value of λ is
The equation of the plane which contain the points (0,6,0) and (-2, -3,4) and which is parallel to the ray with direction ratios (2,3, -2) is:
If y = \({x^{\sec^2(x)} \cdot \frac{1}{\tan^2(x)}}\), than \(\frac{dy}{dx}\) =
Solve the equation \(\int \frac{\arctan(x)}{1+x^2} \, dx\)
The area of the triangle (in unit2) whose vertices are A(4, 8), B(-6, 2) and C(5, 4) is:
The function \(\frac{x}{1 + x^4}\) from Rto R is
If y= \({2^x} + xlog(x)\) , than \(\frac{dy}{dx}\) is
Solve \(\int \frac{2x+3}{x^3 + x^2 -2x} \, dx\)
The equation X = 0 represents:
In a certain college, 25% of boys and 10% of girls are studying Mathematics. The girls constitute 60% of the student body. The probability that mathematics being studied is:
If the direction ratios of two lines are (1, 2, 3) and (-2, 3, -4). Then the angle between the lines is:
Solve the equation: \(\sin^{-1}\left(\frac{4}{5}\right)\) – \(\sin^{-1}\left(\frac{5}{13}\right)\)
The value of \[\sin(10^\circ)-cos(10^\circ)\]
The area bound by the parabolas\[y=3x^2 \] and \[x^2 – y + 4 = 0\]
If A={1,2,3,4,5}, the the relation R = {(2,3),(3,4),(2,4)} on A is:
If \[ \sin^2(x) + b \cos^2(x) = c \], than \[ \tan^2(x)\]=?
The value of K for which straight line x=y=3z=o=2x=y-z-3 is parallel to the plane 3x=2y=kx-4=0 is:
A coin is tossed in times. If the probability of getting at least two heads is greater than that of getting at least three tails by 21/128 , the is :
If A and B are mutually exclusive events with P(A)=2/2 P(B), then P(A)=?
If 3sin x+3sin 4x=sin y and 3cos x+3 cos 4x=cos y, then cos 3x=?
If f(x)=6-5x,f : \(\mathbb{R} \rightarrow \mathbb{R}\) , where R is a set of all the real numberas, then f is:
If P(2,34),Q(5,8,7) and R(-1,-2,1) ate collinear, then R divides PQ in the ratio:
5 apples and 6 oranges are kept in a box. If fruits are chosen at random, then the probability that 2 apples and one orange are picked is :
The angle between the lines 3x=3y=-2z and 2x=-y=-3z is
The point (a,b,0) lie on:
The coordinates of a point dividing the line segment joining (3,4,5) and (1,3,6) externally in the ratio 3:1 are:
Let the matrix A order (pxq) and matrix Q order (rxs) . The product AB exists when:
Given that P is a square matrix of order 3 and |P|=-4. Then |adj P| is equal to:
The local minimum value of the function \(f(x)=x^3\)-\(6x^2+9x+15\) is:
The number of commutative binary operation on the set A={1,2} is ________.
Set P has 4 elements and set Q has 5 elements. How many numbers of injections are defined from P to Q?
Find the angle between the planes x+y+z=1 and x-2y+3z=1.
Let a binary operation ‘*’ be defined on a set P. The operation will be commutative if________.
A teacher has 6 red balls, 7 blue balls, 8 purple balls and 4 black balls in a basket. A student reaches into the basket and randomly selects a ball. What is the probability that the ball will be either blue or black?
If two dice are thrown simultaneously, then what are total number of possible outcomes?
Find \(\frac{dy}{dx}\) given following implicit equation:
Find the area under the curve y=\(\3x^2\)-2x from x=2 to x=4.
The value of cos(\(45^0\)+\(\theta\)) -sin(\(45^0\)+\(\theta\)) is:
Simplyfy \(\frac{\cos(x)}{1-\sin(x)}\) using Trignometric identifies:
What is the condition for two vectors to be Collinear?
If g(x)=\(\int^x_o\)\(\sqrt{1-t^2}\) dt, then the domain of g'(x) is :
Let the sets A and B have 3 and 4 elements, respectively. The total number of possible relations from A to B is ____.
The value of \(tan315^0\) is the same as the value of :
A rectangular area of sides 4.0 cm and 5.0 cm is placed in an electric field
In a traingle ABC, secA(sinB cosC + cosB sinC) equals:
If a line makes an angle of \(60^\circ\), \(135^\circ\), \(120^\circ\) with the positive x,y,z-axis, respectively, then find the direction cosiness.
Find the area of the region bounded above by y=\(e^x\), bounded below by y=x, and boiunded on the sides by x=0_0 and x=1.
Find the maximum value of f(x)=\(x^3\) – \(6x^2\) + 9x + 15.
Differentiate.
Find.
Let A be {l,m,n} . Let the relations R be {}. Which of the following about R is true?
Two charges, A (48 pC) and B (36 pC), are located at (3 cm, 0 cm) and (0 cm. 4 cm), respectively. The magnitude of electric field at point (3 cm. 4 cm) due to these two charges is:
Find parametric equations of the line that passes through the points A(2,4,-3) and B(3,-1,1)..
The equation of the plane that passes through (1,-1,2) and has direction ratios (1,2,3) is:
The set of all possible outcomes is known
The probability of three persons A. B and C becoming clerks of a certain administrative office are 3 : 2 : 4. The probabilities that incentive will be introduced if they become clerks are 0.4, 0.5 and 0.3, respectively.
Find the value of \(\frac{dy}{dx}\) if x=cos t, y = sin t.
Find the distance between two points (2,6,5) and(2,3,9).
Find the value of integral \(\int1n\) (x) dx.
The S.I. unit for torque experienced by an electric dipole in a uniform electric field is given by :
Consider a pair of coils arranged coaxially parallel to each other, in a vertical plane. When the current in one coil increase from 0 to 10 A in 0.5 s, the emf induced in the other coil is 20 V.
Which of the following relations is symmetric but neither reflexive nor transitive for a set A = {a, b, c}?
The derivation of the function \(\int\)(x)=\(-3x^2+6x-4\) is given by:
A tank is filled with a liquid to a depth of 80 cm. A point source of lights is placed at the bottom.
Find the general solution of equation \(tan x=\frac{1}{\sqrt3}\)
A relation R is said to be an equivalence relation if :
Find the value of
The domain of \(sin^{-1}(\frac{x+1}{3})\) is:
What is wrong with the following calculation?
The area enclosed by the curves y=x-1 and \(y^2=2x+6\)
Evaluate
Which of the following represents direction cosines of the line?
A cricket club has 1.5 members, of whom only 5 can bolt what is the probality that in a team of 11 members at least three bowless are selected ?
A set of linear equations is represented by the matrix equation Ax – b. The necessary condition for the existence of a solution for this system is:
Find the magnitude of the shortest distance between the lines \(\frac{x-0}{2}\)=\(\frac{y-0}{-3}\)=\(\frac{z-0}{1}\) and \(\frac{x-2}{3}\)=\(\frac{y-1}{-5}\)=\(\frac{z+2}{2}\)
The probability of drawing any one spade card is:
Let \(\theta\) and \(\emptyset\) be an acute angle such that \(sin \theta=\frac{1}{\sqrt{2}}\) and \(cos \emptyset\frac{1}{3}\) , the value of \(\theta\) + \(\emptyset\) is:
Consider the set G = {a + b \(\sqrt{2}\) : a, b \(\epsilon\) Q} the set of all rational numbers} with respect to binary operation usual addition. Which condition fails for G?
Which of the following is the correct value of \(tan 10^\circ tan 20^\circ tan 60^\circ tan 70^\circ tan 80^\circ\)?
Find mid point of (4,3,6) and (6,5,12).
Find a vector perpendicular to the plane that passes through the points P (1,4,6) Q (-2, 5, -1) and R (1,-1,1).
Find
If \(x^4+y^4=16\) then find the second derivate
Find the area bounded by the curve y=\(x^2 + x + 4\), the x – axis and the ordinates x = 1 and x =3.
Let A be the set {1, 2, 3, 4}. Which ordered pairs are in the relation R = {(a, b): a divides b}?
If (x)=\(\frac{1-x}{2+x}\), then find f'(x).
What is the area of the triangle with vertices (3,-2) (4,0), (0,-4)?
Let R be the set of all real numbers and a function f-R-R be defined by f(x) = ax + b, where a, b are constants and a +0. Is f invertible? If it is so, find the inverse of f.
Find the angle between the lines \(\frac{x-3}{1}=\frac{y-2}{1}=\frac{z+1}{2}\) and \(\frac{x-0}{1}=\frac{y-5}{2}=\frac{z-2}{6}\)
The angle between the lines \(\frac{x-4}{2}=\frac{y}{1}=\frac{z+1}{-2}=\frac{x-1}{4}=\frac{y+1}{-4}=\frac{z-2}{2}\)
Find all values of x in the interval [0, 2} such that sinx = sin2 x?
The value of 7 \(\pi/6\) into degrees should be:
\(\int dx/x=log[(x)]\) is not possible when:
\(\frac{d}{dx}\int^x_2\) Int dt = ?
Consider the following relations on the set {1, 2, 3, 4]:
Find the first derivative of \(e^{x In a}+e^{a In x}+e^{a In a}.
Find the angle between the pair of lines
Find the probability of occurrence of at least one of A and B, If A and B are two independent events?
Find degree measure of 6 radians?
Determine the value of \(sin\frac{21\pi}{2}\) and \(cos -1740^\circ\)?
If the arcs of the same lengths in two circles subtend angles 70° and 120° at the centre, determine the ratio of their radii?
Urn A consists 3 blue and 4 green balls while another urn B consists 5 blue and 6 green balls.
Which of the following measures as vector quantity?
Which of the following is the direction cosines of z, y and x-axis?
A die is thrown 3 times. Events A and B stated below: 4 on the 3rd throw 6 on the 1st and 5 on the 2nd throw
If an event E has only one sample point of a sample space, it is called a ______.
60 is the total number of words with or without definition which can be made using all letters of the word AGAIN.
Determine the probability that an aspirant selected randomly is graduate given that the selected aspirant is a female?
Determine the direction cosines of the line passing through the two points (-2, 3, -4) and (1, 2, 3)?
A line is uniquely determined if ______.
What will be the number of permutations of n objects taken all at a time where P1object are of first kind P2 object are of second kind… Pk object are ok Kth kind and rest if any are all different?
Determine the quantity of different signals that can be created by organizing at least 2 flags in sequence (one below the other) on a vertical staff,
An international team has two boxers picked for an international sport event.
Figure-out the number of ways can 5 women and 3 men be seated in a row so that two men are together?
A batch comprises of 4 red and 7 green uniform boys. Figure out the number of methods can a squad of 5 unit be picked
If \(cos x = \frac{5}{13}x\), lies in the third quadrant, the value of other five trigonometric functions?
Find the vector and Cartesian equations of the plane which passes through the point (5, 2, -4) and perpendicular to the line with direction ratios 2, 3, -1?
Light with an energy flux of \(18 W/cm^2\) falls on a non-reflecting surface at normal incidence. If the surface has an area of \(20 cm^2\)
A galvanometer coil has resistance 20 Ω and the metre shows full scale deflection for a current of 2 mA. How will you convert the metre into an ammeter of range 0 to 6 A?
At what depth from surface of water, the pressure will be equal to three time the atmosphere pressure? Given atmospheric pressure = \(10 N/cm^2\) and g = \(9.8 ^2\)
An object of mass 5 kg is sliding with a constant velocity of 12 m/s on a frictionless horizontal table
A body cools from 70°C to 40°C in 5 minute. Calculate the time it takes to cool from 50°C to 20°C, the temperature of the surroundings is 10°C. The following
Which of the following is true, if none of the angles x, y and (\(x \pm y\)) is a multiple of TT?
Determine the value of \(tan\frac{\pi}{8}\)?
What is the principal solutions of the equation \(tanx=-\frac{1}{\sqrt{3}}\)?
Find the probability that they speak the same fact if A speaks truth in 60% cases and B speaks truth in 75% cases?
A man is known to speak truth 2 out of 3 times. He throws a die and reports that it is a six. Find the the probability that it is actually a six?
Which of the following is INCORRECT if E and F are independent?
Evaluate the value of x if \(\frac{1}{8!}+{1}{9!}=\frac{x}{10!}\)?
If\(C_9=^nC_8\), find \(^nC_{17}\)?
If \(P(A)=\frac{4}{9}\),\(P(B)=\frac{2}{9}\) and \(P(A \cup B)=\frac{5}{9}\),
Determine the area of the triangle with vertices X(1,1,2), Y(2,3,5) and Z(1,5,5)?
Ten coins numbered 1 to 10 are kept in a packet, merged rigorously and then one coin is taken out randomly.
Evaluate r, if 5 \(^4P_r=6\) \(^5P_{t-1}\)
Determine the value of \(tan\frac{13\pi}{12}\) and the sin \(15^\circ\)?
The probability of a bowler in ten pin bowling hitting a target is \(\frac{3}{4}\). .
Given that \(^nP_4/^{n-1}P_4\)=5/3, n>4. Determine the value of n?
In a dog race there are 5 dogs named as A, B, C, D, and E. Find the probability that A, B and C are first 3 to finish (in any order)?
