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If 12 sin x − 9sin2 x attains its maximum value at x = α, then write the value of sin α.

If 2x+2y=2x+y, then dydx is equal to

If f(x)={|x+2|/tan^-1(x+2),x≠-2;2,x=-2 then discuss the continuity of f(x) at x=-2

IF lim x tends to 0 sin x/x=1, then if we put x=90 then sin90/90 should be 1/90

If tan20∘=p, then tan160∘−tan110∘1+tan160∘tan110∘=

Find the derivative ofthe function given byand hence find.

For all complex numbers z1,z2 satisfying |z1|=12 and |z2−3−4i|=5 respectively, the minimum values of |z1−z2| is

Let P be the plane containing the line L1:y+z=2, x=0 and is parallel to the line L2:x−z=2,y=0. If the distance of the plane P from the origin is d units, then the value of 3d2 is

Find all points of discontinuity of f,where f isdefined by

a wire of18Ω is bent to form a regular hexagon ABCDEFA then find the equivalent resis†an ce between side AB

The sum of solutions of the equation cosx1+sinx=|tan2x|, x∈(−π2,π2)−{π4,−π4} is

An aeroplane flies 400 m north and 300 m east and then 1200 m upwards then net displacement is1900 m 500 m 1300 m 1400 m

Interval of k for which f(x)=sin x−cos x−kx+b is decreasing for all real values of x.

If f be a real valued function defined as f(x)=x2+x21∫−1t⋅f(t) dt+x31∫−1f(t) dt, then the value of f(1) is

If (−7−24i)1/2=x-iy, then x2+y2=

The shortest distance from the origin to a variable point on the sphere (x−2)2+(y−3)2+(z−6)2=1 is

The median of the odd divisors of 360 is

The general solution(s) of the equation cosθ+cos7θ=0 can be (n∈Z)

The value of tan2 ​(sec-13) + cot2 (cosec-14) is _________________.

15. In how many ways can a batsman can score 20 runs in 6 balls. (A) If he can get runs (0,1,2,3,4,5,6) in 1 ball. (B) lf he can get runs (1,2,3,4,5,6) in 1 ball.

If the variance of a random variable X is σ2 and variance of random variable 2X−5 is mσ2+n. then (m+n2)=

What is the lewis bronsted theory?

If A-1=3-11-156-55-22 and B=12-2-1300-21, find AB-1.

If α,β are natural numbers such that 100α−199β=(100)(100)+(99)(101)+(98)(102)+⋯+(1)(199), then the slope of the line passing through (α,β) and origin is:

The number of value(s) of x satisfying the equation x2−2x=1+√1+x, x∈(2,∞) is

If A (-1, 8), B(4, -2) and C(-5, -3) are the vertices of a triangle. Median through(-1, 8) intersect line segment BC at D. Find the co-ordinates of point D.

The area of the triangle having the points A(1,1,1), B(1,2,3), and C(2,3,1) as its vertices is

Find the number of sets of 5-tuples (A1,A2,A3,A4,A5) so that A1 + A2(sinx)+ A3(cosx) + A4(2cosx) + A5(2sinx) = 0 is true for all values of X?A) 0B) 1C) 2D) Infinite

The A.M of 10 observations is 40, If the sum of 6 observations is 280 then the mean of remaining 4 observations is

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): cosec x cot x

tan A +tan(60+A) - tan (60-A) = what1) 3tan3A 2) tan3A3)cot 3A 4) sin3A

Determine order and degree (when defined) of differential equations. y'+5y=0.

Insert six A.M.s between 15 and -13.

∫10e√xdx=

In △ ABC, if 2(bc cos A + ca cos B + ab cos C) =

If ∫√x2+11−x2dx=1√2f(x)−g(x)+C, where C is a constant of integration, then

Let →a=2^i−3^j,→b=2^i+^j−6^k. If →r×→a=→r×→b and →r⋅(3^i+4^j+2^k)=2, then the value of →r⋅(5^i+6^j+3^k)=

Which of the following is the graph of y=|x−2|

Let f(x) be a function represented by graph given below, then the number of point(s), where f(x) is not differentiable in (0,6] is

d block

. (X+DGK:2

The value of limx→∞lnx−[x][x]−{x} is where [.] denotes the greatest integer function and {.} denotes the fractional part.

Find the angles between the planes whose vector equation are r.(2^i+2^j−3^k)=5 and r.(3^i−3^j+5^k)=3

If 3∫1xdx2x2+3[x]2=14(a⋅ln2+bln3+cln5+dln11), then which of the following statement is/are true ?(where [⋅] denotes the greatest integer function)

Let f(x)=f1(x)−2f2(x),where, f1(x)={min{x2, |x|}, |x|≤1 max{x2, |x|}, |x|&gt;1 and, f2(x)={min{x2, |x|}, |x|&gt;1 max{x2, |x|}, |x|≤1 and, g(x)={min{f(t): −3≤t≤x, −3≤x&lt;0}max{f(t): 0≤t≤x, 0≤x≤3}For x∈(−1,0), f(x)+g(x) is

The last two digits of the number 3400 are :

6 Find derivative of sin x - cos x / sin x + cos x by first principle

34.FIND THE EQUATION OF THE TANGENT AND NORMAL AT THE INDICATED POINTS: (i) y=x pow(4)-6x pow(3)+13x pow(2)-10x+5 at(0,5) (iii)y= x pow(3)-3x+2 at the point whose x-coordinate is 3.

If 0.4i + 0.8j + bk is a unit vector . What is the value of b?

The value of tan2 (sec-13) + cot2 (cosec-14) is _________________.

Let f(x)=f1(x)−2f2(x),where, f1(x)={min{x2, |x|}, |x|≤1 max{x2, |x|}, |x|>1 and, f2(x)={min{x2, |x|}, |x|>1 max{x2, |x|}, |x|≤1 and, g(x)={min{f(t): −3≤t≤x, −3≤x<0}max{f(t): 0≤t≤x, 0≤x≤3}For x∈(−1,0), f(x)+g(x) is