Description : Find the equation of the normal to the curve `x = acostheta` and `y = b sintheta` at `theta`
Last Answer : Find the equation of the normal to the curve `x = acostheta` and `y = b sintheta` at `theta`
Description : Solve the following inequations `(i) (sinx-2)(2sinx-1) lt 0` `(ii) (2cosx-1)(cosx) le 0` `(iii) sinx+sqrt(3)cosx ge 1` `(iv) cos^(2)x+sinx le 2` `(v)
Last Answer : Solve the following inequations `(i) (sinx-2)(2sinx-1) lt 0` `(ii) (2cosx-1)(cosx) le 0` `(iii) sinx+sqrt(3) ... ^(2)x+sinx le 2` `(v) tan^(2)x gt 3`
Description : Solve the following inequalities `(i) |log_(3)x|-log_(3)x-3 lt 0` `(ii)(x-1)/(log_(3)(9-3^(x))-3) le 1` `(iii)log_((x-1)/(x-5))(x-2) gt 0` `(iv) log_(
Last Answer : Solve the following inequalities `(i) |log_(3)x|-log_(3)x-3 lt 0` `(ii)(x-1)/(log_(3)(9-3^(x))-3) le 1` ... gt 0` `(iv) log_(x)(x^(3)-x^(2)-2x) lt 3`
Description : Solve the following inequalities `(i) log_(5)(3x-1) lt 1` `(ii) (log_(.5)x)^(2)+log_(.5)x-2 le 0` `(iii) log_(3)(x+1)+log_(3)(x+7) ge 3` `(iv)log_(1//
Last Answer : Solve the following inequalities `(i) log_(5)(3x-1) lt 1` `(ii) (log_(.5)x)^(2)+log_(.5)x-2 le 0` `(iii) ... `(iv)log_(1//2)log_(3)(x^(2)+5)+1 le 0`
Description : Let `0le theta le pi/2` `x=Xcos theta + Ysin theta` `y=Xsin theta - Y cos theta` such that `x^2+4xy+y^2=aX^2+bY^2` where `a,b` are constants such that
Last Answer : Let `0le theta le pi/2` `x=Xcos theta + Ysin theta` `y=Xsin theta - Y cos theta` such that `x^2+4xy+y^2=aX^2+ ... C. `a=3`, `b=-1` D. `theta=(pi)/(3)`
Description : Solve the following in equalities `(i) |x+7| gt 5` `(ii) |x+3| lt 10` `(iii) (x+2) lt |x^(2)+3x+5|``(iv) |(2x-1)/(x-1)| gt 2` `(v) |x-6| le x^(2)-5x+9
Last Answer : Solve the following in equalities `(i) |x+7| gt 5` `(ii) |x+3| lt 10` `(iii) (x+2) lt |x^(2)+3x+5|``(iv) ... -5) lt 0` `(viii) |x-1|+|x-2|+|x-3| le 6`
Description : Let `P={theta:sintheta-costheta=sqrt2cos theta}and Q={theta:sintheta+costheta=sqrt2sintheta}` be two ses. Then,
Last Answer : Let `P={theta:sintheta-costheta=sqrt2cos theta}and Q={theta:sintheta+costheta=sqrt2sintheta}` be two ses. ... QcancelsubeP` C. `PcancelsubeQ` D. `P=Q`
Description : Let `-1/6 < theta < -pi/12` Suppose `alpha_1 and beta_1`, are the roots of the equation `x^2-2xsectheta + 1=0` and `alpha_2 and beta_2` are the
Last Answer : Let `-1/6 < theta < -pi/12` Suppose `alpha_1 and beta_1`, are the roots of the equation `x^2-2xsectheta ... )` B. `2sectheta` C. `-2tantheta` D. `0`
Description : Find the equation of the tangent to the curve `x=theta+sin theta ,y=1+cos theta` at `theta=pi/4`
Last Answer : Find the equation of the tangent to the curve `x=theta+sin theta ,y=1+cos theta` at `theta=pi/4` A. ` ... 1+sqrt2)x+(sqrt2-1) pi` D. None of the above
Description : Evaluate: `int_0^(pi//2)1/((a^2cos^2x+b^2sin^2x)^2)dx`
Last Answer : Evaluate: `int_0^(pi//2)1/((a^2cos^2x+b^2sin^2x)^2)dx` A. `(pi(a^(2) +b^(2)))/(4a^(3)b^(3))` B. ` ... )+b^(2)))/(4a^(2)b^(2))` C. None of the above D.
Description : The equation `2sin^3theta+(2lambda-3)sin^2theta-(3lambda+2)sintheta-2lambda=0` has exactly three roots in `(0,2pi)` , then `lambda` can be equal to 0
Last Answer : The equation `2sin^3theta+(2lambda-3)sin^2theta-(3lambda+2)sintheta-2lambda=0` has exactly three roots in `(0,2pi)` , ... -1 B. 0 C. `(1)/(2)` D. 1
Description : If `2cosec theta - cos theta cot theta >= k AA theta in (0,pi),` then value of `k` is
Last Answer : If `2cosec theta - cos theta cot theta >= k AA theta in (0,pi),` then value of `k` is
Description : The sum of all values of `theta in (0,pi/2)` satisfying `sin^(2)2theta+cos^(4)2theta=3/4` is
Last Answer : The sum of all values of `theta in (0,pi/2)` satisfying `sin^(2)2theta+cos^(4)2theta=3/4` is A. `pi` B. `(pi)/(2)` C. `(3pi)/(8)` D. `(5pi)/(4)`
Description : Solve the following inequalities (where `[*]` denotes greatest integer function and `{*}` represent fractional part function) `(i) [x+[x]] lt 0` `(ii)
Last Answer : Solve the following inequalities (where `[*]` denotes greatest integer function and `{*}` represent fractional part ... `(iii) {x} lt (1)/(2)`
Description : Solve the following rational in equalities `(i) ((x-1)(x+2))/((x-3)(x+3)) lt 0` `(ii) ((1-x)^(3)(x+2)^(4))/((x+9)^(2)(x-8))ge0` `(iii) ((x^(2)-3x+1)^(
Last Answer : Solve the following rational in equalities `(i) ((x-1)(x+2))/((x-3)(x+3)) lt 0` `(ii) ((1-x)^(3)(x+2)^(4 ... ` `(vi) 1 lt (3x^(2)-7x+8)/(x^(2)+1) le2`
Description : Find the maximum and minimum values of the function `f(x) = x+ sin 2x, (0 lt x lt pi)`.
Last Answer : Find the maximum and minimum values of the function `f(x) = x+ sin 2x, (0 lt x lt pi)`.
Description : An isosceles triangle of vertical angle `2theta` is inscribed in a circle of radius `a` . Show that the area of the triangle is maximum when `theta=pi
Last Answer : An isosceles triangle of vertical angle `2theta` is inscribed in a circle of radius `a` . Show that the area of ... pi/4` C. `pi/6` D. None of these.
Description : The number of values of `theta` in the interval `(-pi/2,pi/2)` such that `theta != npi/5` for `ninN` and `tan theta = cot 5theta` as well as `sin2thet
Last Answer : The number of values of `theta` in the interval `(-pi/2,pi/2)` such that `theta != npi/5` for ... = cot 5theta` as well as `sin2theta = cos 4theta` is
Description : for `0ltthetaltpi/2 ` the solution(s) of ` sum_(m=1)^6c o s e c(theta+((m-1)pi)/4)c o s e c(theta+(mpi)/n)=4sqrt(2)` is (are):
Last Answer : for `0ltthetaltpi/2 ` the solution(s) of ` sum_(m=1)^6c o s e c(theta+((m-1)pi)/4)c o s e c(theta+(mpi)/n ... (pi)/(6)` C. `(pi)/(12)` D. `(5pi)/(12)`
Description : Solve for `x` `(i) 2^(|x+1|)+2^(|x|)=6` and `x in I` `(ii) x^(2)+x+1+|x-3| le |x^(2)+2x-2|` `(iii) |2x-4|-2|x^(2)+x-3|+2|x-1||x+1|=0`
Last Answer : Solve for `x` `(i) 2^(|x+1|)+2^(|x|)=6` and `x in I` `(ii) x^(2)+x+1+|x-3| le |x^(2)+2x-2|` `(iii) |2x-4|-2|x^(2)+x-3|+2|x-1||x+1|=0`
Description : Solve the following inequlities `(i) sqrt(x-1) lt x-3` `(ii) sqrt(x-3) gt sqrt(7-x)` `(iii) sqrt (x^(2)+4x+9) gt x +2` `(iv) 4-x lt sqrt(2x-x^(2))` `(
Last Answer : Solve the following inequlities `(i) sqrt(x-1) lt x-3` `(ii) sqrt(x-3) gt sqrt(7-x)` `(iii) sqrt (x^(2)+4x+ ... (ix) (|x+2|-|x|)/(sqrt(8-x^(3))) ge 0`
Description : No. of solutions of `16^(sin^2x)+16^(cos^2x)=10, 0 le x le 2 pi` is
Last Answer : No. of solutions of `16^(sin^2x)+16^(cos^2x)=10, 0 le x le 2 pi` is
Description : Let `cos(alpha+beta)=(4)/(5)` and let `sin(alpha-beta)=(5)/(13)`, where `0 le alpha`, `beta=(pi)/(4)`. Then`tan2alpha=`
Last Answer : Let `cos(alpha+beta)=(4)/(5)` and let `sin(alpha-beta)=(5)/(13)`, where `0 le alpha`, `beta=(pi)/(4)`. Then ... 19)/(12)` C. `(20)/(7)` D. `(25)/(16)`
Description : `(i) int(2cos x)/(sqrt(1-4cos^(2) x))dx " "(ii) int (x+1)/(sqrt(x^(2)+1))dx`
Last Answer : `(i) int(2cos x)/(sqrt(1-4cos^(2) x))dx " "(ii) int (x+1)/(sqrt(x^(2)+1))dx`
Description : What are both solutions between 0 degrees and 360 degrees of the equation cos theta 911?
Last Answer : They are 35.1 and 324.9 degrees.
Description : Solve : `8a - 7 lt (6a)/(5) + 27, a in Q`
Last Answer : Solve : `8a - 7 lt (6a)/(5) + 27, a in Q`
Description : Solve : `(4t)/(5) - (5)/(3) lt (t)/(4) + (3)/(2), t in Q`
Last Answer : Solve : `(4t)/(5) - (5)/(3) lt (t)/(4) + (3)/(2), t in Q`
Description : Solve for `y : (4y)/(3) -5 lt 10`
Last Answer : Solve for `y : (4y)/(3) -5 lt 10` A. `y lt 27//24` B. `t lt 33//4` C. `y lt 45//4` D. `y lt 59//4`
Description : The roots of the equation `2x^(2) + 3x + c = 0` (where `x lt 0`) could be `"______"`.
Last Answer : The roots of the equation `2x^(2) + 3x + c = 0` (where `x lt 0`) could be `"______"`.
Description : What are both solutions between -180 and 180 degrees of the equation (tan theta -7over10)?
Last Answer : They are theta = -34.99 degrees and 145.09 deg.
Description : Solve : `(14y)/(3) + (3)/(2) le (20y)/(3) - (83)/(4)`, where `y in Z`
Last Answer : Solve : `(14y)/(3) + (3)/(2) le (20y)/(3) - (83)/(4)`, where `y in Z`
Description : Solve for `x, 8x + 4 le 20` in the set of natural numbers
Last Answer : Solve for `x, 8x + 4 le 20` in the set of natural numbers
Description : `int(1)/(sin x cos x + 2cos^(2)x)dx`
Last Answer : `int(1)/(sin x cos x + 2cos^(2)x)dx`
Description : If `5(tan^2x - cos^2x)=2cos 2x + 9`, then the value of cos4x is
Last Answer : If `5(tan^2x - cos^2x)=2cos 2x + 9`, then the value of cos4x is A. `(-3)/(5)` B. `(1)/(3)` C. `(2)/(9)` D. `-(7)/(9)`
Description : If `(m + 2) sintheta + (2m-1) costheta = 2m+1`, then
Last Answer : If `(m + 2) sintheta + (2m-1) costheta = 2m+1`, then A. `tantheta=(3)/(4)` B. `tantheta=(2m)/(m^(2 ... `tantheta=(2m)/(m^(2)-1)` D. `tantheta=(4)/(3)`
Description : If the roots of a quadratic equation `ax^(2) + bx + c` are complex, then `b^(2) lt "____"`
Last Answer : If the roots of a quadratic equation `ax^(2) + bx + c` are complex, then `b^(2) lt "____"`
Description : Arrange the following in correct order of their stability ? `(I) CH-=overset(Theta)C " "(II) CH_(2)=overset(Theta)CH " "(III) CH_(3)-overset(Theta)CH_
Last Answer : Arrange the following in correct order of their stability ? `(I) CH-=overset(Theta)C " "(II) CH_(2)=overset( ... gt III gt I` D. `II gt I gt III`
Description : Reaction I `Ph-overset(O)overset(||)(C)-NH_(2) overset(overset(Theta)(OD),Br_(2))rarrA` Reaction II `Ph-overset(O)overset(||)(C)-ND_(2) overset(overse
Last Answer : Reaction I `Ph-overset(O)overset(||)(C)-NH_(2) overset(overset(Theta)(OD),Br_(2))rarrA` Reaction II `Ph- ... Both `Ph-NH_(2)` D. Both `Ph-ND_(2)`
Description : If sin theta equals 3/4 and theta is in quadrant II what is the value of tan theta?
Last Answer : 0.75
Description : Spurious tuples may occur due to i. Bad normalization ii. Theta joins iii. Updating tables from join a) i& ii b) ii & iii c) i& iii d) ii & iii
Last Answer : a) i& ii b) ii & iii
Description : he quantitative effect of temperature on chemical equilibrium is given by the (A) Van’t-Hoff equation (B) Le-Chatelier's principle (C) Arrhenius equation (D) None of these
Last Answer : (A) Van’t-Hoff equation
Description : "The rate at which a substance reacts is proportional to its active mass and the rate of a chemical reaction is proportional to the product of active masses of the reacting substances". This is the (A) Lewis- ... (B) Statement of Van't Hoff Equation (C) Le-Chatelier's principle (D) None of these
Last Answer : (D) None of these
Description : If the sum of all the solutions of the equation `8 cosx.(cos(pi/6+x)cos(pi/6-x)-1/2)=1` in `[0,pi]` is `k pi` then k is equal to
Last Answer : If the sum of all the solutions of the equation `8 cosx.(cos(pi/6+x)cos(pi/6-x)-1/2)=1` in `[0,pi]` is `k pi` ... (20)/(9)` C. `(2)/(3)` D. `(13)/(9)`
Description : Let `S={xepsilon(-pi,pi):x!=0,+pi/2}`The sum of all distinct solutions of the equation `sqrt3secx+cosecx+2(tan x-cot x)=0` in the set S is equal to
Last Answer : Let `S={xepsilon(-pi,pi):x!=0,+pi/2}`The sum of all distinct solutions of the equation `sqrt3secx+cosecx+2(tan x- ... 2pi)/(9)` C. `0` D. `(5pi)/(9)`
Description : For `x in (0,pi)` the equation `sinx+2sin2x-sin3x=3` has
Last Answer : For `x in (0,pi)` the equation `sinx+2sin2x-sin3x=3` has A. infinitely many solution B. three solutions C. one solution D. no solution
Description : If the arithmetic mean of the roots of the equation `4cos^(3)x-4cos^(2)x-cos(pi+x)-1=0` in the interval `[0,315]` is equal to `kpi`, then the value of
Last Answer : If the arithmetic mean of the roots of the equation `4cos^(3)x-4cos^(2)x-cos(pi+x)-1=0` in the interval `[0,315 ... is A. `10` B. `20` C. `50` D. `80`
Description : if the equation `sin (pi x^2) - sin(pi x^2 + 2 pi x) = 0` is solved for positive roots, then in the increasing sequence of positive root
Last Answer : if the equation `sin (pi x^2) - sin(pi x^2 + 2 pi x) = 0` is solved for positive roots, then in the ... `1` D. third term is `(-1+sqrt(11))/(2)`
Description : Let `theta ,phi in [0,2pi]` be such that `2 cos theta (1-sin phi)=sin^2 theta ((tan)theta/2+(cot)theta/2) cos phi -1, tan(2pi-theta) > 0 and -1 <
Last Answer : Let `theta ,phi in [0,2pi]` be such that `2 cos theta (1-sin phi)=sin^2 theta ((tan)theta/2+(cot)theta/2) ... (3pi)/(2)` D. `(3pi)/(2) lt phi lt 2pi`
Description : One moles of anhydrous `AB` dissolves in water and liberates `21.0 J mol^(-1)` of heat. The valueof `DeltaH^(Theta)` (hydration) of `AB` is `-29.4 J m
Last Answer : One moles of anhydrous `AB` dissolves in water and liberates `21.0 J mol^(-1)` of heat. The valueof `DeltaH^(Theta) ... mol^(-1)` D. `-8.4 J mol^(-1)`
Description : If cos and theta 0.65 what is the value of sin and theta?
Last Answer : You can use the Pythagorean identity to solve this:(sin theta) squared + (cos theta) squared = 1.