Practice questions
88551 published questions with worked solutions.
- Considering the principal values of inverse trigonometric functions, the value of the expression (2 ^ -1 ( 2 13 )-2 ^ -1 ( 3 10 )...
- Given below are two statements : Statement I : The function f:R R defined by f(x)= x 1+|x| is one-one. Statement II : The...
- An ellipse has its center at (1,-2), one focus at (3,-2) and one vertex at (5,-2). Then the length of its latus rectum is :
- Let the ellipse E: x^2 144 + y^2 169 =1 and the hyperbola H: x^2 16 - y^2 ^2 =-1 have the same foci. If e and L respectively...
- Let P_1: y=4x^2 and P_2: y=x^2+27 be two parabolas. If the area of the bounded region enclosed between P_1 and P_2 is six times...
- Let the circle x^2+y^2=4 intersect x-axis at the points A(a,0), a>0 and B(b,0). Let P(2 , 2 ), 0< < 2 and Q(2 ,2 ) be two points...
- Let [.] denote the greatest integer function. Then _ - /2 ^ /2 ( 12(3+[x]) 3+[ x]+[ x] )dx is equal to:
- Let y=y(x) be the solution of the differential equation x dy dx -y=x^2 x, x (0, ). If y ( 2 )= 2 , then 6y ( 6 )-8y ( 4 ) is...
- The sum of all the elements in the range of f(x)= Sgn ( x)+ Sgn ( x)+ Sgn ( x)+ Sgn ( x), x n 2 , n Z, where Sgn (t)= cases 1, &...
- Let A= z C: |z-2| 4 and B= z C: |z-2|+|z+2|=5 . Then the max |z_1-z_2|: z_1 A and z_2 B is
- Let f(x)= dx x^ (2/3) +2x^ (1/2) be such that f(0)=-26+24 _e(2). If f(1)=a+b _e(3), where a,b Z, then a+b is equal to:
- 6 3^ 26 + 10.1 3^ 25 + 10.2 3^ 24 + 10.2^2 3^ 23 + + 10.2^ 24 3 is equal to
- Three persons enter in a lift at the ground floor. The lift will go upto the 10^ th floor. The number of ways, in which the three...
- Let f be a differentiable function satisfying f(x)=1-2x+ _0^x e^ (x-t) f(t)dt, x R and let g(x)= _0^x (f(t)+2)^ 15 (t-4)^6(t+12)^...
- If the distance of the point P(43, , ), <0, from the line r =4 i - k + (2 i +3 k ), R along a line with direction ratios 3,-1,0...
- Let A= bmatrix 3 & -4 1 & -1 bmatrix and B be two matrices such that A^ 100 =100B+I. Then the sum of all the elements of B^ 100...
- A nucleus has mass number and radius R_ . Another nucleus has mass number and radius R_ . If = 8 then R_ /R_ is :
- A plane electromagnetic wave is moving in free space with velocity c = 3 10^8 m/s and its electric field is given as E =54 (kz-...
- The mean free path of a molecule of diameter 5 10^ -10 m at the temperature 41°C and pressure 1.38 10^5 Pa, is given as ____ m....
- In an experiment, a set of reading are obtained –1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm. The expected least count of the instrument...