Practice questions
88551 published questions with worked solutions.
- Let , be the roots of the quadratic equation 12x^2-20x+3 =0, Z. If 1 2 | - | 3 2 , then the sum of all possible values of is :
- Let the domain of the function f(x) = _3 _5(7- _2(x^2-10x+85)) + ^ -1 ( | 3x-7 17-x | ) be ( , ]. Then + is equal to :
- Let [ ] denote the greatest integer function, and let f(x) = 2 x, x^2 . Let S = x (-2,2): the function g(x)=|x|[x^2] is...
- Let S and S' be the foci of the ellipse x^2 25 + y^2 9 =1 and P( , ) be a point on the ellipse in the first quadrant. If...
- Let C_r denote the coefficient of x^r in the binomial expansion of (1+x)^n, n N , 0 r n. If P_n = C_0 - C_1 + 2^2 3 C_2 - 2^3 4...
- Let a vector a = 2 i - j + k , >0, make an obtuse angle with the vector b =- ^2 i +4 2 j +4 2 k and an angle , 6 < < 2 , with the...
- Let [ ] be the greatest integer function. If = _0^ 64 (x^ 1/3 -[x^ 1/3 ] )dx, then 1 _0^ ( ^2 ^6 + ^6 )d is equal to ____ .
- Let ( + ) = - 1 10 and ( - ) = 3 8 , where 0< < 3 and 0< < 4 . If 2 = 3(1-r 5 ) 11 (s+ 5 ) , r,s N, then r+s is equal to ____ .
- Suppose a,b,c are in A.P. and a^2, 2b^2, c^2 are in G.P. If a<b<c and a+b+c=1, then 9(a^2+b^2+c^2) is equal to ____ .
- Let S be the set of the first 11 natural numbers. Then the number of elements in A = B S: n(B) 2 and the product of all elements...
- If , E and t represent the free space permittivity, electric field and time respectively, then the unit of E t will be :
- Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The...
- In parallax method for the determination of focal length of a concave mirror, the object should always be placed :
- In an open organ pipe v_3 and v_6 are 3^ rd and 6^ th harmonic frequencies, respectively. If v_6-v_3 = 2200 Hz then length of the...
- An electric power line having total resistance of 2 , delivers 1 kW of power of 250 V. The percentage efficiency of transmission...
- The wavelength of light, while it is passing through water is 540 nm. The refractive index of water is 4/3. The wavelength of the...
- Given below are two statements : Statement I: A satellite is moving around earth in the orbit very close to the earth surface....
- Given below are two statements : Statement I: An object moves from position r_1 to position r_2 under a conservative force field...
- A laser beam has intensity of 4.0 10^ 14 W/m². The amplitude of magnetic field associated with beam is ____ T. (Take _0=8.85 10^...
- Light is incident on a metallic plate having work function 110 10^ -20 J. If the produced photoelectrons have zero kinetic energy...