To construct a unique rectangle,
Question: To construct a unique rectangle, the minimum number of measurements required is (a) 4 (b) 3 (c) 2 (d) 1 Solution: (c) Since, in a rectangle, opposite sides are equal and parallel, so we need the measurement of only two adjacent sides, i.e. length and breadth. Also, each angle measures 90. Hence, we require only two measurements to construct a unique rectangle....
Read More →To construct a unique parallelogram,
Question: To construct a unique parallelogram, the minimum number of measurements required is (a) 2 (b) 3 (c) 4 (d) 5 Solution: (b) We know that, in a parallelogram, opposite sides are equal and parallel. Also, opposite angles are equal. So, to construct a parallelogram uniquely, we require the measure of any two non-parallel sides and the measure of an angle. Hence, the minimum number of measurements required to draw a unique parallelogram is 3....
Read More →If a diagonal of a quadrilateral bisects
Question: If a diagonal of a quadrilateral bisects both the angles, then it is a (a) kite (b) parallelogram (c) rhombus (d) rectangle Solution: (c) rhombus...
Read More →The number of sides of a regular polygon
Question: The number of sides of a regular polygon whose each interior angle is of 135ois (a) 6 (b) 7 (c) 8 (d) 9 Solution: Now let us assume number of sides of a regular polygon be n. WKT, sum of all exterior angles of all polygons is equal to 360o. Form the question it is given that each exterior angle has a measure of 45o. Then, n = 360o/Exterior angle n = 360o/(180o 135o) n = 360o/45o n = 8...
Read More →A man saves ₹4000 during the first year, ₹5000 during the second year
Question: A man saves ₹4000 during the first year, ₹5000 during the second year and in this way he increases his savings by ₹1000 every year. Find in what time his savings will be ₹85000. Solution: A Man saves some amount of money every year. In the first year, he saves Rs.4000. In the next year, he saves Rs. 5000 . Like this, he increases his savings by Rs. 1000 ever year. Given a total amount of Rs. 85000 is saved in some 'n' years. According to the above information the savings in every year ...
Read More →PQRS is a trapezium in
Question: PQRS is a trapezium in which PQ||SR and P=130, Q=110. Then R is equal to: (a) 70o (b) 50o (c) 65o (d) 55o Solution: (a) 70o We know that, the adjacent angles in a trapezium are supplementary. R + Q = 180o R + 110o= 180o R = 180o 110o R = 70o...
Read More →If the solve the problem
Question: If $y=e^{x}(\sin x+\cos x)$ Prove that $\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+2 y=0$ Solution: Formula: - (i) $\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{y}_{1}$ and $\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}=\mathrm{y}_{2}$ (ii) $\frac{\mathrm{d}\left(\mathrm{e}^{\mathrm{ax}}\right)}{\mathrm{dx}}=\mathrm{ae}^{\mathrm{ax}}$ (iii) $\frac{\mathrm{d}}{\mathrm{dx}} \mathrm{x}^{\mathrm{n}}=\mathrm{n} \mathrm{x}^{\mathrm{n}-1}$ (iv) chain rule $\frac{\mathrm{df}}{\mathrm{dx}}=\frac{...
Read More →A parallelogram PQRS is constructed
Question: A parallelogram PQRS is constructed with sides QR = 6 cm, PQ = 4 cm and \(\angle PQR\) = 90. Then, PQRS is a (a) square (b) rectangle (c) rhombus (d) trapezium Solution: (b) We know that, if in a parallelogram one angle is of 90, then all angles will be of 90 and a parallelogram with all angles equal to 90 is called a rectangle....
Read More →Two adjacent angles of a parallelogram are in the ratio 1 : 5.
Question: Two adjacent angles of a parallelogram are in the ratio 1 : 5. Then, all the angles of the parallelogram are (a) 30, 150, 30, 150 (b) 85, 95, 85, 95 . (c) 45, 135, 45, 135 (d) 30, 180, 30, 180 Solution: (a) Let the adjacent angles of a parallelogram be x and 5x, respectively. Then, x + 5x = 180 [ adjacent angles of a parallelogram are supplementary] = 6x = 180 = x = 30 The adjacent angles are 30 and 150. Hence, the angles are 30, 150, 30, 150...
Read More →150 workers were engaged to finish a piece of work in a certain number of days.
Question: 150 workers were engaged to finish a piece of work in a certain number of days. Four workers dropped the second day, four more workers dropped the third day, and so on. It takes 8 more days to finish work now. Find the number of days in which the work was completed. Solution: Given: Initially let the work can be completed in n days when 150 workers work on every day. However every day 4 workers are being dropped from the work so that work took 8 more days to be finished. Finally, it ta...
Read More →PQRS is a square.
Question: PQRS is a square. PR and SQ intersect at O. Then POQ is a (a) Right angle (b) Straight angle (c) Reflex angle (d) Complete angle Solution: (a) Right angle The diagonals in the square intersect each other at right angle i.e. 90o Therefore, POQ is a right angle....
Read More →If the solve the problem
Question: If $y=e^{x}(\sin x+\cos x)$ prove that $\frac{d^{2} y}{d x^{2}}-1 \frac{d y}{d x}+2 y=0$ Solution: Formula: (i) $\frac{d y}{d x}=y_{1}$ and $\frac{d^{2} y}{d x^{2}}=y_{2}$ (ii) $\frac{d\left(e^{a x}\right)}{d x}=a e^{a x}$ (iii) $\frac{\mathrm{d}}{\mathrm{dx}} \mathrm{x}^{\mathrm{n}}=\mathrm{nx}^{\mathrm{n}-1}$ (iv) chain rule $\frac{\mathrm{df}}{\mathrm{dx}}=\frac{\mathrm{d}(\text { wou })}{\mathrm{dt}} \cdot \frac{\mathrm{dt}}{\mathrm{dx}}=\frac{\mathrm{dw}}{\mathrm{ds}} \cdot \frac{...
Read More →A man saved ₹660000 in 20 years.
Question: A man saved ₹660000 in 20 years. In each succeeding year after the first year, he saved ₹2000 more than what he saved in the previous year. How much did he save in the first year? Solution: Given: - Amount saved by a man in 20 years is Rs.660000 Let the amount saved by him in the first year be $a$. In every succeeding year, he saves Rs.2000 more than what he saved in the previous year. Increment of saving of the year when compared last year is Rs. 2000 Hint: - The above information loo...
Read More →Which of the following is not true for an exterior
Question: Which of the following is not true for an exterior angle of a regular polygon with n sides? (a) Each exterior angle = 360o/n (b) Exterior angle = 180o interior angle (c) n = 360o/exterior angle (d) Each exterior angle = ((n 2) 180o)/n) Solution: (d) Each exterior angle = ((n 2) 180o)/n) Because each exterior angle is equal to 360o/n...
Read More →Which of the following can never
Question: Which of the following can never be the measure of exterior angle of a regular polygon? (a) 22 (b) 36 (c)45 (d) 30 Solution: (a) Since, we know that, the sum of measures of exterior angles of a polygon is 360, i.e. measure of each exterior angle =360/n ,where n is the number of sides/angles. Thus, measure of each exterior angle will always divide 360 completely. Hence, 22 can never be the measure of exterior angle of a regular polygon....
Read More →A man accepts a position with an initial salary of ₹26000 per month.
Question: A man accepts a position with an initial salary of ₹26000 per month. It is understood that he will receive an automatic increase of ₹250 in the very next month and each month thereafter. Find this (i) salary for the 10th month, (ii) total earnings during the first year Solution: Given: - An initial salary that will be given = ₹26000 There will be an automatic increase of ₹250 per month from the very next month and thereafter. Hint: - In the given information the salaries he receives ar...
Read More →The sum of angles of a concave
Question: The sum of angles of a concave quadrilateral is (a) more than 360o (b) less than 360o (c) equal to 360o (d) twice of 360o Solution: (c) equal to 360o We know that sum of angles of concave and convex quadrilateral is equal to 360o....
Read More →find the problem
Question: Find $\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}$, where $\mathrm{y}=\log \left(\frac{\mathrm{x}^{2}}{\mathrm{e}^{2}}\right)$ Solution: Formula: - (i) $\frac{d y}{d x}=y_{1}$ and $\frac{d^{2} y}{d x^{2}}=y_{2}$ (ii) $\frac{\mathrm{d}\left(\mathrm{e}^{\mathrm{ax}}\right)}{\mathrm{dx}}=\mathrm{ae}^{\mathrm{ax}}$ (iii) $\frac{\mathrm{d}}{\mathrm{dx}} \mathrm{x}^{\mathrm{n}}=\mathrm{n} \mathrm{x}^{\mathrm{n}-1}$ Given: - $y=\log \left(\frac{x^{2}}{e^{2}}\right)$ Differentiating w.r....
Read More →Which of the following can be four interior
Question: Which of the following can be four interior angles of a quadrilateral? (a) 140o, 40o, 20o, 160o (b) 270o, 150o, 30o, 20o (c) 40o, 70o, 90o, 60o (d) 110o, 40o, 30o, 180o Solution: (a) 140o, 40o, 20o, 160o We know that sum of interior angles of quadrilaterals is 360o. So, 140o+ 40o+ 20o+ 160o= 360o In option (d) has angle sum equal to 360o, but one angle is 180oif it is considered then the quadrilateral becomes a triangle....
Read More →If the adjacent angles of a parallelogram
Question: If the adjacent angles of a parallelogram are equal, then the parallelogram is a (a) rectangle (b) trapezium (c) rhombus (d) any of the three Solution: (a) rectangle...
Read More →Arun buys a scooter for ₹44000. He pays ₹8000 in cash and agrees to pay
Question: Arun buys a scooter for ₹44000. He pays ₹8000 in cash and agrees to pay the balance in annual instalments of ₹4000 each plus 10% interest on the unpaid amount. How much did he pay for it? Solution: Given: The amount that is to be paid to buy a scooter = 44000 The amount that he paid by cash = ₹8000 Remaining balance = ₹36000 Annual instalment = ₹4000 + interest@10% on the unpaid amount Thus, our instalments are 7600, 7200, 6800. Total number of instalments $=\frac{\text { The remaining...
Read More →Length of one of the diagonals
Question: Length of one of the diagonals of a rectangle whose sides are 10 cm and 24 cm is (a) 25 cm (b) 20 cm (c) 26 cm (d) 3.5 cm Solution: (c) 26 cm PQRS is a rectangle, Where SR = 24 cm, QR = 10 cm Now, consider the triangle QRS From the rule of Pythagoras theorem, QS2= SR2+ QR2 QS2= 242+ 102 QS2= 576 + 100 QS2= 676 QS = 676 QS = 26 cm...
Read More →If the solve the problem
Question: If $y=\cot x$ show that $\frac{d^{2} y}{d x^{2}}+2 y \frac{d y}{d x}=0$ Solution: Formula: - (i) $\frac{d y}{d x}=y_{1}$ and $\frac{d^{2} y}{d x^{2}}=y_{2}$ (ii) $\frac{\mathrm{d}(\cot x)}{d x}=-\operatorname{cosec}^{2} x$ (iii) $\frac{\mathrm{d}}{\mathrm{dx}} \mathrm{x}^{\mathrm{n}}=\mathrm{nx}^{\mathrm{n}-1}$ (iv) chain rule $\frac{\mathrm{df}}{\mathrm{dx}}=\frac{\mathrm{d}(\text { wou })}{\mathrm{dt}} \cdot \frac{\mathrm{dt}}{\mathrm{dx}}=\frac{\mathrm{dw}}{\mathrm{ds}} \cdot \frac{...
Read More →The sum of adjacent angles
Question: The sum of adjacent angles of a parallelogram is (a) 180 (b) 120 (c) 360 (d) 90 Solution: (a) By property of the parallelogram, we know that, the sum of adjacent angles of a parallelogram is 180....
Read More →If PQRS is a parallelogram,
Question: If PQRS is a parallelogram, then P R is equal to (a) 60o (b) 90o (c) 80o (d) 0o Solution: (d) 0o We know that opposite angles P and R are equal in parallelogram. So, P R = 0o...
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