The coefficient of `x^3` in the expansion of `(1+2x+3x^2)^(10)` is - (1) less than 200 (2) less than 400 but greater than 200 (3) greater than 400 (4) 420

The value of int_0^1 e^(x^2)dx is (A) less than e (B) greater than 1 (C) less than e but greater than 1 (D) all of these

If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, then for all real values of x, the expression 3b^2x^2+""6b c x""+""2c^2 is (1) greater than -4ab (2) less than 4ab (3) greater than 4a b (4) less than - 4a b

If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, then for all real values of x, the expression 3b^2x^2+""6b c x""+""2c^2 is (1) greater than 4ab (2) less than 4ab (3) greater than 4a b (4) less than 4a b

If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, then for all real values of x, the expression 3b^2x^2+""6b c x""+""2c^2 is (1) greater than 4ab (2) less than 4ab (3) greater than 4a b (4) less than 4a b

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is (1) less than 500 (2) at least 500 but less than 750 (3) at least 750 but less than 1000 (4) at least 1000

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is (1) less than 500 (2) at least 500 but less than 750 (3) at least 750 but less than 1000 (4) at least 1000

The number of distinct terms in the expansion of is (x^(3)+(1)/(x^(3))+1)^(200) is (a) 201 (b) 400 (c) 401 (d) 500

In a single throw of a die, find the probability of getting a number : (i) greater than 2 (ii) less than or equal to 2 (iii) not greater than 2.

The probability of an impossible event is (a)1 (b) 0 (c) less than 0 (d) greater than 1

The values of a for which the equation 2x^(2) -2(2a+1) x+a(a+1) = 0 may have one root less them a and other root greater than a are given by