Practice questions
88551 published questions with worked solutions.
- Let ω be a complex number such that 2ω + 1 = z where z = -3 . If vmatrix 1 & 1 & 1 1 & - ^2 - 1 & ^2 1 & ^2 & ^7 vmatrix = 3k,...
- If A = bmatrix 2 & -3 -4 & 1 bmatrix , then adj (3A^2 + 12A) is equal to
- If S is the set of distinct values of 'b' for which the following system of linear equations x + y + z = 1 x + ay + z = 1 ax + by...
- A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men....
- The value of ( ^ 21 C_1 - ^ 10 C_1) + ( ^ 21 C_2 - ^ 10 C_2) + ( ^ 21 C_3 - ^ 10 C_3) + ( ^ 21 C_4 - ^ 10 C_4) + + ( ^ 21 C_ 10 -...
- _ x 2 x - x ( - 2x)^3 equals :
- If for x (0, 1 4 ), the derivative of ^ -1 ( 6x x 1 - 9x^3 ) is x g(x), then g(x) equals :
- The normal to the curve y(x – 2)(x – 3) = x + 6 at the point where the curve intersects the y-axis passes through the point :
- Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq....
- Let I_n = ^nx ,dx, (n > 1). If I_4 + I_6 = a ^5x + bx^5 + C, where C is a constant of integration, then the ordered pair (a, b)...
- The integral _ 4 ^ 3 4 dx 1 + x is equal to :
- The area (in sq. units) of the region (x, y) : x ≥ 0, x + y ≤ 3, x^2 4y and y 1 + x is :
- If (2 + x) dy dx + (y + 1) x = 0 and y(0) = 1, then y ( 2 ) is equal to :
- Let k be an integer such that the triangle with vertices (k, –3k), (5, k) and (–k, 2) has area 28 sq. units. Then the orthocentre...
- The radius of a circle, having minimum area, which touches the curve y = 4 - x^2 and the lines, y = |x| is :
- The eccentricity of an ellipse whose centre is at the origin is 1 2 . If one of its directrices is x = – 4, then the equation of...
- A hyperbola passes through the point P( 2 , 3 ) and has foci at (±2, 0). Then the tangent to this hyperbola at P also passes...
- The distance of the point (1, 3, –7) from the plane passing through the point (1, –1, –1), having normal perpendicular to both...
- Let a = 2 i + j - 2 k and b = i + j . Let c be a vector such that | c - a | = 3, |( a b ) c | = 3 and the angle between c and a b...
- A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of...