List of practice Questions

There is an error of $\pm 0.04$ cm in the measurement of the diameter of a sphere. When the radius is 10 cm, the percentage error in the volume of the sphere is

The function $f(x) = x^3 + ax^2 + bx + c, a^2 \le 3b$ has

The image of the point (3, 2, 1) in the plane $2x - y + 3z = 7$ is

The radius of the sphere $x^2 + y^2 + z^2 = 12x + 4y + 3z$ is

If the distance between the foci of an ellipse is 6 and the length of the minor axis is 8, then the eccentricity is

The perimeter of the triangle with vertices at (1, 0, 0), (0, 1, 0) and (0, 0, 1) is

The pairs of straight lines $x^2-3xy+2y^2=0$ and $x^2-3xy+2y^2+x-2=0$ form a

The equations of the circle which pass through the origin and makes intercepts of lengths 4 and 8 on the x and y-axes respectively are

The locus of centre of a circle which passes through the origin and cuts off a length of 4 unit from the line $x=3$ is

The diameters of a circle are along $2x+y-7=0$ and $x+3y-11=0$. Then, the equation of this circle, which also passes through (5, 7), is

The transformed equation of $x^2+y^2=r^2$ when the axes are rotated through an angle 36° is

The area (in square unit) of the circle which touches the lines $4x+3y=15$ and $4x+3y=5$ is

The point on the line $3x+4y=5$ which is equidistant from $(1, 2)$ and $(3, 4)$ is

The equation of the straight line perpendicular to the straight line $3x+2y=0$ and passing through the point of intersection of the lines $x+3y-1=0$ and $x-2y+4=0$ is

The value of \( \lambda \) with \( |\lambda| < 16 \) such that \( 2x^2 - 10xy + 12y^2 + 5x + \lambda y - 3 = 0 \) represents a pair of straight lines, is

The area (in square unit) of the triangle formed by $x+y+1=0$ and the pair of straight lines $x^2-3xy+2y^2=0$ is

If $y = \log(\log x)$, then $dy/dx$ is:

The number of ways of selecting 3 balls from a bag containing 5 red and 4 blue balls such that at least one is red is:

If $X$ is a binomial variate with the range 0, 1, 2, 3, 4, 5, 6 and $P(X=2)=4P(X=4),$ then the parameter $p$ of $X$ is

P is a point on the segment joining the feet of two vertical poles of heights a and b. The angles of elevation of the tops of the poles from P are $45^{\circ$ each. Then, the square of the distance between the tops of the poles is

The number of ways in which 5 people can be seated around a circular table is:

If $A$ and $B$ are two events such that $P(A) = 0.4, P(B) = 0.8$ and $P(B|A) = 0.6$, then $P(A \cup B)$ is:

If $3 \cos x \neq 2 \sin x$, then the general solution of $\sin^{2x-\cos 2x=2-\sin 2x$ is

In any $\Delta ABC$, $a(b \cos C-c \cos B)$ equals

The locus of z satisfying the inequality \( \left| \frac{z+2i}{2z+i} \right| < 1 \), where \( z = x + iy \), is