Practice questions
90156 published questions with worked solutions.
- One mole of phenol is treated with dilute HNO₃ at 298 K to give a mixture of products. The mixture is separated by steam...
- The values of pressure equilibrium constant recorded at different temperatures for the following equilibrium reaction have been...
- If the half life of a first order reaction is 6.93 minutes then the time required for completion of 99% of the reaction will be...
- Let f : ℝ → ℝ be defined as f(x)= 2x^2-3x+2 3x^2+x+3 . Then f is:
- Consider the quadratic equation (n²−2n+2)x²−3x+(n²−2n+2)²=0, n∈ℝ. Let α be the minimum value of the product of its roots and β be...
- Let S= z∈ℂ : z²+√6 iz−3=0 . Then _ z S z^8 is equal to:
- The sum of all possible values of θ∈[0,2π], for which the system of equations: x cos3θ−8y−12z=0, x cos2θ+3y+3z=0, x+y+3z=0 has a...
- The sum 1+ 12(1^2+2^2)+ 13(1^2+2^2+3^2)+ upto 10 terms is equal to:
- A building has ground floor and 10 more floors. Nine persons enter a lift at the ground floor. The lift goes up to the 10th...
- Let C be a circle having centre in the first quadrant and touching the x-axis at a distance of 3 units from the origin. If the...
- The eccentricity of an ellipse E with centre at the origin O is √3/2 and its directrices are x=±4√6/3. Let H : x²/a²−y²/b²=1 be a...
- Let x=9 be a directrix of an ellipse E, whose centre is at the origin and eccentricity is 1/3. Let P(α,0), α>0, be a focus of E...
- If ( ^ -1 (x 2))= ( ^ -1 1-x^2 ), x∈(0,1), then the value of x is:
- The shortest distance between the lines x-4 1= y-3 2= z-2 -3 and x+2 2= y-6 4= z-5 -5 is:
- Let a=2 i+3 j+3 k and b=6 i+3 j+3 k. Then the square of the area of the triangle with adjacent sides determined by the vectors (2...
- Let _ x 2 ( (x-2))(rx^2+(p-2)x-2p) (x-2)^2 =5 for some r,p∈ℝ. If the set of all possible values of q, such that the roots of the...
- Let f : ℝ→ℝ be such that f(xy)=f(x)f(y), for all x,y∈ℝ and f(0)≠0. Let g : [1,∞)→ℝ be a differentiable function such that...
- The area of the region (x,y) : x²−8x≤y≤−x is:
- The value of the integral _ -1 ^ 1 ( x^3+|x|+1 x^2+2|x|+1 )dx is equal to:
- Let R= (x,y)∈ℕ×ℕ : log_e(x+y)≤2 . Then the minimum number of elements, required to be added in R to make it a transitive...