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If f(x) is integrable over [1, 2], then ∫21 f(x) dx is equal to

Let p≡ "You apply for a driving licence.", q≡ "You should have a ration card." and r≡ "You should have a passport." What can be concluded from "To apply for a driving licence, you should have a ration card or a passport"

Let the mean and variance of four numbers 3,7,x and y(x&gt;y) be 5 and 10 respectively. Then the mean of four numbers 3+2x,7+2y,x+y and x−y is

If the angle between the asymptotes of hyperbola x2a2−y2b2=1 is π3. Then the eccentricity of conjugate hyperbola is

Findf(x),where f(x) =

18. Let A be the 44 matrix with real entries such that determinant of every 22 submatrix is 0 then (a)adj (A)=0 (b)det (A)=0 (c) A=0 (d)AX=0 has infinite number of solutions

If (1+ax)n=1+8x+24x2+..., then which of the following is/are correct?

Let y(x) be a solution of (1+x2)dydx+2xy−4x2=0 and y(0)=–1. Then y(1) is equal to

The equation of plane passing through the point (1,1,1) and perpendicular to the planes 2x+y−2z=5 and 3x−6y−2z=7 is

Co-ordinates of a point equidistant from the points (0,0,0), (a, 0, 0), (0, b, 0), (0, 0, c) is

∫1x2(x4+1)34 dx is equal to __________

letters always never though

How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?

Value of limx→08x8[1−cosx22−cosx24+cosx22cosx24] is

Let A be a non-singular square matrix of order 3 and B=adj (adj(adj(A−1)))−1 and C=adj(adj(adj(B−1)))−1. Then

The mid-point of the segment of the normal of a curve from any point of the curve to the x-axis lies on the parabola 4y2=x. If the curve passes through the origin, then the value of −4c, where c is the constant of integration, is

If a vector=b vector=a-b vector is true then the angle between a and b is

sin x + sin 3x19.= tan 2xcosx+ cos 3x

x2+5x+6 can be factorised as

12.5+15.8+18.11+....+1(3n−1)(3n+2)=n6n+4

Given f(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩x,0≤x&lt;1212x=121−x12&lt;x&lt;1 and g(x)=(x−12)2,x∈R. Then the area (in sq. units) of the region bounded by the curves y=f(x) and y=g(x) between the lines 2x=1 to 2x=√3 is:

If α + β = 90° and α=β2, then tan α tan β = ________.

23+234 )0.3,4.4

John has a total of $4.30 in dimes (1 dime =$0.10) and quarter (1 quarter =$0.25), and he has 19 coins in total. Which of the following systems of equations can be used to find the number of dimes, d and the number of quarters, q he has?

The number of non-integral values of x satisfying sin[2cos−1{cot(2tan−1x)}]=0 is

Using integration finds the area of the region bounded by the triangle whose vertices are (–1, 0), (1, 3) and (3, 2).

If A is a matrix of order 3x3 and |a| = 2 then the determinant of cofactor matrix of A is

(2).Express the following in the form P/Q where P and Q are integers and Q is not equal to 0 {zero} :- (a) 2.3bar (b) 43.52bar

If sin x f(x) = 1, then f'(x) is equal to

The approximate value of 52.01, where ln5=1.6095, is

The number of distinct real values of λ for which vectors −λ2^i+^j+^k,^i−λ2^j+^k and ^i+^j−λ2^k are coplanar is

Let A be a square matrix of order 3 such that A = 11 and B be the matrix of confactors of elements of A. Then, B2 = ________________.

In a debate competition, each person speaks for 328 minIf 16 people took part in it, then the competition lasted for min.

Question 11The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is:A) 28B) 30C) 35D) 38

If u, vand w are functions of x, then show thatin two ways-first byrepeated application of product rule, second by logarithmicdifferentiation.

∫1x2(x4+1)34 dx is equal to __________

9. log (logx)

5.(1-i)-(-1 + i6)

Find the area of the circle 4 x 2 + 4 y 2 = 9 which is interior to the parabola x 2 = 4 y

Findthe inverse of each of the matrices, if it exists.

The value of ∫(2−tan2x1+tan2x)dx is(where C is constant of integration)

The number of all 3×3 matrices A, with entries from the set {−1,0,1} such that the sum of the diagonal elements of (AAT) is 3, is

If x(n) is right sided discrete time signal and X(z) is z-transform of x(n). If X(z)=zz−0.1, then value of ∞∑n=−∞nx(n) is ______. 0.12

Let E,F and G be three events having probabilities P(E)=18, P(F)=16 and P(G)=14, and let P(E∩F∩G)=110. For any event H, if Hc denotes its complement, then which of the following statements is(are) TRUE?

The range of y=x−12x−7,x≠72 is

A PHYSICAL QUANTITY IS MEASURED AND ITS VALUE ISFOUND TO BE nu WHERE n=numerical value and u = unit THEN1)n IS PROPORTIONAL TO SQUARE OF u2)n IS PROPORTIONAL TO u3)n IS PROPORTIONAL TO SQUARE ROOT OF u4)n IS INVERSELY PROPORTIONAL TO u

Solve the given inequality for real x: 4x + 3 &lt; 5x + 7

If f′′(x)&gt;0 ∀ x∈R , f′(3)=0 and g(x)=f(tan2x−2tanx+4) for 0&lt;x&lt;π2, then g(x) is increasing in :

Let the mean and variance of four numbers 3,7,x and y(x>y) be 5 and 10 respectively. Then the mean of four numbers 3+2x,7+2y,x+y and x−y is

Given f(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩x,0≤x<1212x=121−x12<x<1 and g(x)=(x−12)2,x∈R. Then the area (in sq. units) of the region bounded by the curves y=f(x) and y=g(x) between the lines 2x=1 to 2x=√3 is:

Solve the given inequality for real x: 4x + 3 < 5x + 7

If f′′(x)>0 ∀ x∈R , f′(3)=0 and g(x)=f(tan2x−2tanx+4) for 0<x<π2, then g(x) is increasing in :