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An automotive engine weighing 240 kg is supported on four springs with linear characteristics. Each of the front two springs have a stiffness of 16MN/m while the stiffness of each rear spring is 32MN/m. The engine speed (in rpm), at which resonance is likely to occur, is
A class III mathematics teacher gave the following questions to her students:  \(\begin{equation} \frac{ \begin{array}[b]{r} 256 \\ + 173 \end{array} }{ } \end{equation}\) \(\begin{equation} \frac{ \begin{array}[b]{r} 28 \\ + 32 \end{array} }{ } \end{equation}\) \(\begin{equation} \frac{ \begin{array}[b]{r} 129 \\ + 76 \end{array} }{ } \end{equation}\) Later she asks the students to solve a worksheet that has similar questions. Which of the following statements is appropriate for the given situation?
To an addition problem, \(\begin{equation} \frac{ \begin{array}[b]{r} 56 \\ +38 \end{array} }{ } \end{equation}\)  a class 2 student responded as \(\begin{equation} \frac{ \begin{array}[b]{r} 56\\ +38 \end{array} }{ 84 } \end{equation}\)As a reflective mathematics teacher, what will be your reaction to the child's answer? 
Which of the following is true? A: If the sum of cube of three numbers is thrice the product of the three numbers, then the sum of three numbers will be non-zero. B: For quadratic equation ax2 + bx + c = 0, If b2 < 4ac, then the given equation has only one real root. C: In the equation, x2 – (a + b)x + ab = 0, the roots of this equation will be ‘a’, ‘b’.
If the signs '+' and '×' are interchanged, which of the following equations will be correct? equation: A 90 ÷ 6 + 4 – 20 × 12 = 52 equation: B 24 + 4 × 10 – 4 ÷ 4 = 36 equation: C 34 × 12 ÷ 6 + 10 – 6 = 28 equation: D 42 ÷ 14 + 6 × 4 – 12 = 30
If the equation of parabola is 3y2 = 8x then which of the following statements is/are true: Equation of directrix is: 3x + 2 = 0 Equation of axis is: y = 0 Equation of latus rectum is: 3x - 2 = 0
The given equation becomes correct after interchanging two signs. One of the four alternatives under it specifies the interchange of signs in the equation which when made will make the equation correct. Find the correct alternative? 9 + 5 ÷ 4 × 3 - 6 = 12
Consider the statements given below: A: Sum of roots of a quadratic equation ax2 + bx + c = 0 is (c/a). B: If one root of a quadratic equation is (p + qi), then root must be (q + pi). C: Roots of the equation 3x2 + 4x = 5 are all real. Which of the statement(s) is/are TRUE?
Consider the following remarks pertaining to the irrotational flow: 1. The Laplace equation of stream function \(\frac{{{\delta ^2}{\rm{\Psi }}}}{{\delta {x^2}}} + \frac{{{\delta ^2}{\rm{\Psi }}}}{{\delta {y^2}}} = 0\) must be satisfied for the flow to be potential. 2. The Laplace equation for the velocity potential \(\frac{{{\delta ^2}{\rm{\varphi }}}}{{\delta {x^2}}} + \frac{{{\delta ^2}{\rm{\varphi }}}}{{\delta {y^2}}} = 0\) must be satisfied to fulfil the orate . of mass conservation i.e continuity equation.. Which of the above statements is/are correct?
Given two quadratic equations, I. x2 - 31x + 240 = 0 Equation I has two roots x1, x2. (x1 > x2) II. 3y2 – 7y – 3 = 8y - 3y2 - 9 Equation II has two roots y1, y2. (y2 > y1) Find the equation whose roots are (– 2y1 + x1), - (y2 – x2).