List of practice Questions

A shopkeeper sold \(\frac23\) of his stock of rice at a profit of \( 5\%\) and the remaining stock at a loss of \(2\%\). If his total profit was \( ₹\)\( 1000\), then the cost price of the whole stock of rice is:

If \(A (2,3), B(2,4) C(4,9)\)and \(D (x,8)\) are the vertices of a parallelogram \(ABCD\), then find the value of \(x.\)

A solid hemisphere of radius \(24 cm\) is melted and identical cones each of base radius\( 8 cm\) and height \( 6 cm \) are formed. How many such cones are formed?

For the problem max Z = ax + by, x≥0, y ≥0, which of the following is NOT a valid constraint to make it a linear programming problem?

The value of tan(cos^-1x) is:

Let\[f(x)=\begin{cases} 2x-1, x<1\\ 1, x=1 \\ x^2,x>1 \end{cases}\]then at x = 1

If |\(\vec{a}\)| = 5, |\(\vec{b}\)| = 2 and |\(\vec{a}\) · \(\vec{b}\) | = 8 then the value of |\(\vec{a} \)×\(\vec{b} \)| is:

The direction ratios of the line perpendicular to the lines \(\frac{x-7}{-6}= \frac{y+17}{4}= \frac{z-6}{2} \space and \space \frac {x+5}{6}=\frac{y+3}{3}=\frac{z-4}{-6}\) are proportional to:

If \(A = \begin{bmatrix} 4&5&2\\ 3&-1&7\end{bmatrix}\), then the sum of the elements of the matrix AA^T is:

Match List I with List II

List I	List II
\(A.\ [1 + (\frac{dy}{dx})^2] = \frac{d^2y}{dx^2}\)	I. order 2, degree 3
\(B. \ (\frac{d^3y}{dx^2})^2 - 3\frac{d^2y}{dx^2} + 2(\frac{dy}{dx})^4 = y^4\)	II. order 2, degree 1
\(C. \ (\frac{dy}{dx})^2 + (\frac{d^2y}{dx^2})^3 = 0\)	III. order 1, degree 2
\(D.\ (\frac{dy}{dx})^2 + 6y^3 = 0\)	IV. order 3, degree 2

Choose the correct answer from the options given below:

If, A = \(\begin{bmatrix}a& d& l\\[0.3em]b& e& m\\[0.3em]c& f& n\\[0.3em] \end{bmatrix}\)and B = \(\begin{bmatrix}l& m& n\\[0.3em]a& b& c\\[0.3em]d& e& f\\[0.3em]  \end{bmatrix}\), then

If A is a non-identity invertible symmetric matrix, then \(A^{-1}\) is:

The function f(x) = \(|x - 1|\) is

The value of \(\int_1^4|x-1|dx \)  is :

Maximum slope of the curve \(y = -2x^3 + 6x^2 + 5x - 20\) is:

he trend line for the sales (in lakhs) is given by \(y_c=84+12(x-2017).\) The estimated sale for theyear \(2024 \) is :

Choose the wrong statement from the following:

Match List - I with List II. If \(A = \begin{vmatrix}3&-2&3 \\2 &1 &-1 \\4 &-3 &2\end{vmatrix}\)

Choose the correct answer from the options given below:

The points of discontinuity of the function \(f\) defined by \(f(x) = \begin{cases} x+2 & x≤1 \\ x-2 &1<x<2\\ 0& x≥2\end{cases}\) are:

The value of C which satisfies Rolle's Theorem for f(x) = sin⁴x + cos⁴x in \([0, \frac{π}{2}]\). Then C is:

The quantity of water that must be added to 36 litres of milk at 2 ½ litres for ₹120 so as to have mixture worth ₹36 for a litre is:

If A is a square matrix of order 3 and |A|=5, then |adj(adjA)| is:

If \(y = log(\frac{x^5}{e^5})\), then \(\frac{d^2y}{dx^2}\) is,

A carpenter earns a profit of ₹50 and ₹80 on one chair and one table respectively. The requirement and availability of wood and labour are tabled as:

The number of chairs and tables in appropriate units to be manufactured for maximum profit are, respectively:

The function f(x) - x³ , x ∈ R has :