List of practice Questions

The following set of data is given: 72, 72, 74, 80, 82, 82, 86, 88, 92, 92. The mean deviation from the median is

The 10 letters of the word STATISTICS are arranged randomly. The probability that the 10-letter arrangement starts with CAT is

The projection of \(\vec{b}\) on \(\vec{a}\) is 12. If the angle between \(\vec{a}\) and \(\vec{b}\) is \(60^\circ\), then \(|\vec{b}| =\)

Let \(\vec{a} = 2\hat{i} + 2\hat{j} - 5\hat{k}\) and \(\vec{b} = 2\hat{i} + \hat{j} + \alpha\hat{k}\). If \(|\vec{a} + \vec{b}| = \sqrt{29}\). Then the possible values of \(\alpha\) are

If the position vectors of the points P and Q are, respectively, \(5\vec{a} - 6\vec{b}\) and \(\vec{a} + 2\vec{b}\), then the point R with position vector \(2\vec{a}\) divides the line segment joining P and Q internally in the ratio

If the equation of the straight line passing through the point \((a,1,3)\) and parallel to the vector \(\frac{2}{3}\hat{i} + \frac{3}{2}\hat{j} + \hat{k}\) is \(\frac{3x+6}{b} = \frac{2y-2}{3} = \frac{z-3}{1}\), then the value of \(a+b\) is equal to

A point C lies on the perpendicular bisector of the straight-line segment joining the points A(-3,-6) and B(13,-6). If the point C lies in the first quadrant and the distance between the point C and the midpoint of AB is 8 units, then the coordinates of C are

The equation of a circle is \(x^2 + y^2 + 6x - 8y - 24 = 0\). If a chord of the circle subtends an angle of \(60^\circ\) at the centre of the circle, then the length of the chord is

If the eccentricity and the length of latus rectum of an ellipse are, respectively, \(\frac{1}{5}\) and \(\frac{48}{5}\), then the length of the major axis of the ellipse is

The coordinates of the focus of the parabola given by the equation \(4y - x^2 + 4x - 12 = 0\) are

Let \(|\vec{a}| = 6\) and \(|\vec{b}| = 10\). If \(\vec{a}\) and \(\vec{b}\) make angles \(25^\circ\) and \(85^\circ\), respectively, with the x-axis, then the value of \(|\vec{a} + \vec{b}|\) is equal to

If \(5\pi - 6 \cos^{-1}(\sqrt{3}(2x - 1)) = 0\), then the value of \(x\) is equal to

Let O be the origin and let P be a point on the line \(x + \sqrt{3}y = 10\). If OP is perpendicular to the line, then the angle between OP and the y-axis is

Let A(-4,3), B(0,5) and C(-1,2) be three points. The equation of the straight line which passes through C and bisects the straight-line segment AB is

Let A and P be the area and perimeter of a rectangle respectively. The length and breadth of the rectangle are (x + 2) cm and (x - 2) cm. If \(A \leq 140 cm^2\) and \(P \geq 20 cm\), then the range of possible values of x is

The set of all \(x\) satisfying the inequality \(8 + 3x > 4(x - 3) + 2\) is

If \(\text{cosec } t + \cot t = \frac{5}{2}\), then the value of \(\tan t\) is equal to

If \(\sin \theta = \frac{3}{5}\) and \(\cos \theta < 0\), then the value of \(\tan \theta\) is

\(\sin 15^\circ \sin 45^\circ \sin 75^\circ =\)

The value of \(\sin(x + \frac{7\pi}{4}) + \sin(x - \frac{7\pi}{4})\) is equal to

If \(^n P_5 = 360360\), then \(^n C_5 = \)

If the coefficient of \(x^4\) in the binomial expansion of \((4x + a)^7\) is -1120, then the value of \(a\) is equal to

Let \(A\) and \(B\) be two square matrices each of order 3. If \(|AB| = 21\) and \(|A^{-1}| = -7\), then the value of \(|B|\) is equal to

If the homogeneous system of simultaneous equations \(AX=0\) where \(A = \begin{bmatrix} 9 & 2 & k \\ 1 & -1 & -3 \\ k-1 & 1 & 3 \end{bmatrix}\) has a nontrivial solution, then the possible values of \(k\) are

Let \(A = \begin{bmatrix} 3 & 5\\ -2 & -3 \end{bmatrix}\). If \(BA^2 = A\), where \(B\) is a \(2 \times 2\) matrix, then \(B = \)