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Sum of all terms in in G.P is 5 times the sum of odd terms. The common ratio is

For a real number r let [r] denote the largest integer less than or equal to r. Let agt1 be a real number which is not an integer and let k be the smallest positive integer positive integer such that [a^(k)]gt[a]^(k). Thenwhich of the following statements is always true?

If bara,barb and barc are non coplanar vectors such that barb times barc=barb then

A line y=mx +1 intersects the circle (x-3)^2+(y+2)^2=25 at the points P and Q . If the midpoint of the line segment PQ has x-coordinate -(3)/(5), then which one of the following options is correct ?

If the median of the data 6,7,x-2,x,18 and 21 written in ascending order is 16, then the variance of that data is

In the experiment of tossing a coin n times, if the variable X denotes the number of heads and P(X=4),P(X=5),P(X=6) are in arithmetic progression then find n.

Assuming the validity of the operations on the r.h.s. find dy/dt y = sqrt[[sin x + sqrt{{sin x + sqrt((sin x + ........)}])}]

The value of P for which both the roots of the equation4x^(2)-20Px +(25P^(2)+15P-66)=0 are less than 2, lies in

Evaluate the following determinates |{:(1,omega),(omega,-omega):}| where omega is the cube root of unity

If the lines x-2y+3=0, 3x+ky+7=0 cut the coordinate axes in concylic points, then k=

The tangent at a point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets directrics at Q and Q. A circle is drawn assuming PQ as diameter. Statement-1 This circle passes through the foci of the ellipse because Statement-2 PQ subtends 90^(@) at the corresponding focus.

If A = [(0,1),(1,0) ]then A^(2) is equal to :

If (1+x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + "….." + C_(n)x^(n), then C_(0) - (C_(0) + C_(1)) +(C_(0) + C_(1) + C_(2)) - (C_(0) + C_(1) + C_(2) + C_(3))+"….."(-1)^(n-1) (C_(0) + C_(1) + "……" + C_(n-1)) is (where n is even integer and C_(r) = .^(n)C_(r))

If the remainders obtained when a polynomial f(x) is divided with x, x-1, x+1 respectively are 1, -2, 3 then find the remainder when f(x) is divided with x^(3)-x ?

Find the Principle values of the following : tan^(-1)(-sqrt(3))

Evaluate : (i) Lim_(nrarroo) sum_(r=0)^(nrarr1) (1)/(sqrt(n^(2)-r^(2))) , (ii)Lim_(nrarroo) 3/n[1+sqrt((n)/(n+3))+sqrt((n)/(n+6))+sqrt((n)/(n+9))+"....."+sqrt((n)/(n+3(n-1)))] (iii) lim_(nrarroo) (sum_(r=1)^(2n) (3nr^(2)+2n^(2)r))

A pair of dice is rolled. What is the probability that neither die shows a 2 given that they sum to 7.

How many 4 digit numbers are there, without repetition of digits, If each number is divisible by 5 ?

If (1+x+x^2+____x^100) (1-x+x^2-x^3+___+x^150) =a_0+a_1x+a_2x^2+____ +a_250 x^250 Then the value of a_0+a_2 + a_4+____ + a_250 is equal to ___

If log_(e)5, log_(e)(5^(x) -1) and log_(e)(5^(x)-(11)/(5)) are in A.P then the values of x are

Three numbers are chosen at random without replacement from {1,2,3,….8}. The probability that their minimum is 3, given that their maximum is 6, is

Let W(x,y) =x ^(2) + xy+y ^(2) and x = sin t, y = cos t in t in (0, 2pi) verify the above theorem.

Compute the length of the segment of the straight line rho= a sec (varphi- (pi)/(3)) between varphi= 0 and varphi=(pi)/(2)

If veca=(3hati-hatj)/(sqrt(10)) and vecb=(hati+3hatj+hatk)/(sqrt(11)), then the value of (2veca+vecb)".[(veca xx vecb)xx(veca-3vecb)]

Integrate the following functions (sin^-1x)^2

Refers to question 15.Determine the maximum distance that the man can travel.

int e^(2x) (2sinx + cosx) dx =

If A+B+C=90^(@) then (cos 2A+cos 2B+cos 2C-1)/(sin A sin B sin C)=

If int(dx)/(1+e^(x))=x+f(x)+C , then f(x) is equal to

The mid point of the chord x+2y+3=0 of the hyperbola x^(2)-y^(2)=4 is

At what points in the interval [0, 2pi], does the function sin (2x) attain its maximum value ?

If the angle between the two equal circles with centres (-2,0),(2,3) is 120^@then the radius of the circle is

If bar(a) = overset(^)(i) + overset(^)(j) - overset(^)(k), bar(b) = 2 overset(^)(i) + 3 overset(^)(j) + 2 overset(^)(k), bar(c ) = - overset(^)(i) + overset(^)(j) +3 overset(^)(k) then the volume of tetrahedron is

The tangents drawn from the origin x^(2)+y^(2)-2rx-2hy+h^(2)=0 are per-pendicular if

The real values of 'a' for which the quadratic equation 2x^2 - (a^3 + 8a - 1) x + a^2 - 4a = 0 possess roots of opposite sign is given by:

In the spacethe equationby + cz + d = 0represents a plane perpendicular to the

k-^n C_1 (k-1)+^n C_2 (k-2)-…..+(-1)^n ""^n C_n (k-n)=

Locus of perpendicular from center upon normal to the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1 is

If a,b,c are rational , the roots of equationx^2-2ax+(a^2-b^2+2bc-c^2)=0 are :

Match the following. I. int (1)/(sqrt(4-x^(2)))dx= "" a) (1)/(2) Sinh^(-1))(x)/(2)+c II. int (1)/(sqrt(4+x^(2)))dx= "" b)Cosh^(-1)(x)/(2)+c III. int (1)/(x^(2)-4))dx= "" c) "Sin"^(-1)(x)/(2)+c

|{:(sin35^@,-cos35^@),(sin55^@,cos55^@):}|=.........

A vector vecr is inclined to x-axis at 45^(@) and to y-axis at 60^(@). If |vecr|=8 units find vecr.

The scatterplot above shows the numbers of people diagnosed with melanoma, in ten - thousands, from 1940 to 1970. Based on the data shown in the figure, which of the following values is closest to the range of the number of incidences of melanoma between 1945 and 1950?

Given PV=C (constant). The percentage of increase in V corresponding to an increase 1% in the value of P is

A bag contain 6 white and 4 red balls if 3 balls are drawn at random the probability of getting 1 red ball and 2 white balls is

Find the value of the integral underset(-pi//2)overset(pi//2)int sin^(2) theta . Cos^(7)theta d theta

Evalute the following integrals int (1)/(x) sqrt((x - 1)/(x + 1))dx =

If (1+x+x^2+__x^100) (1-x+x^2-x^3+_+x^150) =a_0+a_1x+a_2x^2+____ +a_250 x^250 Then the value of a_0+a_2 + a_4+____ + a_250 is equal to ___