List of practice Questions

In an A.P. the difference between the last and the first terms is 632 and the common difference is 4. Then the number of terms in the A.P. is

If the first term of a G.P. is 1 and the sum of 3^rd and 5^th terms is 90, then the positive common ratio of the G.P. is

Let t_n, n = 1,2,3,... be the n^th term of the A.P. 5, 8, 11,.... Then the value of n for which t_n = 305 is

If a₁, a₂, a₃,..., an are in A. P. with a₁ = 3, an, = 39 and a₁+a₂+...+an = 210, then the value of n is equal to

The value of \(\displaystyle\sum_{k=5}^{36}\frac{1}{k^2-k}\) is equal to

The value of \(\sqrt{(- 25)} + 3\sqrt{(- 4)} + 2\sqrt{(- 9)}\) is equal to

If the real part of the complex number \(z=\frac{p+2i}{p-i}\), \(p\isin\R, p\gt0\ is\ \frac{1}{2}\), then the value of p is equal to

The area of the triangle on the complex plane formed by the points z, z+iz and iz is 128. Then the value of |z| is

The imaginary part of \(z=\frac{2+i}{3-i}\) is

If z=2-i√3, then |z⁴| is equal to

Let a=2-3i be a root of the equation z²-4z+k=0 , where k is a real number. If β is the other root, then the value of α² +β² is

If \(\frac{z}{i}=11-13i\), then \(z+\bar z\) is equal to

Let z₁, z₂ and z₃ be three distinct points in the complex plane such that the segment joining z₁ and z₂ is perpendicular to the segment joining z₁ and z₂. If |z₁-z₂|=5 and|z₁-z₃|=12 then|z₂-z₃| is equal to

A relation R on (0, 1, 2) is given by R = {(0,0), (1, 1), (0, 1), (2, 2), (1, 2)). Then the relation R is

The function \(f\ \R\rightarrow\R\) given by f(x)=7-3x is

Let f(x) = [x], x ∈ R, where [x] denotes the greatest integer ≤ x. Then the images of the elements -4.6 and 2.7 are respectively

Let f(x) = x² and \(g(x) = \sqrt{9+x}\). Then the value of \((f^\circ g-g^\circ f)(4)\) is equal to

The constraints of a linear programming problem are x+2y≤10 and 6x+3y≤18. Which of the following points lie in the feasible region?

The general solution of the differential equation 4xy+12x+(2x²+3)y' = 0 is

The integrating factor of the differential equation xy'+2y-7x³=0 is

The general solution of the differential equation y-xy' = x² + y² is

The area of the region bounded by y = 5x, x-axis and x = 4 is (in square units)

The value of \(\displaystyle\int_{\frac{\pi}{8}}^{\frac{3\pi}{8}}\frac{sin^4x}{sin^4x+cos^4x}dx\) is equal to

The value of \(\displaystyle\int_{0}^{2}\frac{x^2}{(x^3+1)^2}dx\) is equal to

The area of the region bounded by the curves y = x² and y = √x is (in square units)