List of practice Questions

The volume of a right circular cone with radius 6 cm and height 7 cm is:
(use \(\pi = \frac{22}{7}\))
If two cubes each of volume 64 cm\(^3\) are joined end to end together, then the surface area of the resulting cuboid is:
The roots of the quadratic equation \(x^2 - 4x + 4 = 0\) are:
The area of a sector, whose radius is 7 cm with the angle 72° is:
If \(\csc \theta + \cot \theta = k\), then the value of \(\csc \theta\) is:
If two concentric circles of radii 5 cm and 3 cm are drawn, then the length of the chord of the larger circle which touches the smaller circle is:
Area of the triangle formed by the points \((-5, -1)\), \((3, -5)\) and \((5, 2)\) is:
If the areas of two similar triangles are 81 cm\(^2\) and 49 cm\(^2\) respectively. If the altitude of the smaller triangle is 3.5 cm, then the corresponding altitude of the bigger triangle is:
The centroid of the triangle with vertices \((1, -1)\), \((0, 6)\), and \((-3, 0)\) is:
Bond angle in BeCl\(_2\) molecule is
Identify the set of molecules in which the central atom has only one lone pair of electrons in their valence shells:
What is the area, in square units, of the triangle formed by the points \( (3, 2), (3, -6) \) and \( (5, 2) \)?
If -1, -2 are two zeros of a polynomial \(2x^3 + ax^2 + bx - 2\), then the values of \(a\) and \(b\) are
The product of prime factors of 2024 is:
The number of electrons gained by non-metallic element is equal to its
If \(\alpha, \beta\) are the zeros of the polynomial \(P(x) = 3x^2 - x - 4\), then \(\alpha \times \beta =\)
The pair of equations \(x + y = 5\) and \(2x + 2y = k\) has infinitely many solutions if \(k =\)
In \(\triangle ABC\), if \(DE \parallel BC\), \(AE/CE = 3/5\) and \(AB = 5.6\) cm, then \(AD =\):
In △ABC, if DE ∥ BC
The focal length of a concave mirror is 20 cm. At what distance the object is placed to obtain the virtual image?
A girl of height 90 cm is walking away from the base of a lamp post at a speed of 120 cm/sec. If the lamp post is 360 cm above the ground, then the length of her shadow after 4 seconds is:
Coating of Eudragit NE40D on tablets is done to prepare:
In \(\triangle ABC\), if \(DE \parallel BC\), \(AD = x\), \(DB = x - 2\), \(AE = x + 2\), and \(EC = x - 1\), then the value of \(x\) is:
△ABC, if DE ∥ BC, AD = x, DB = x−2,
If the vectors \[ \mathbf{a} = 2i - j + k, \quad \mathbf{b} = i + 2j - 3k, \quad \mathbf{c} = 3i + pj + 5k \] are coplanar, find \( p \).
The coordinates of the point which divides the line segment joining the points \((4, -3)\) and \((8, 5)\) in the ratio 3:1 internally is:

The number of real solutions of the equation \((x^2 - 15x + 55)^{x^2 - 5x + 6} = 1\) is __________.